CN109580388B - Method for measuring shear yield surface and volume yield surface of rock and soil material - Google Patents

Method for measuring shear yield surface and volume yield surface of rock and soil material Download PDF

Info

Publication number
CN109580388B
CN109580388B CN201910055005.7A CN201910055005A CN109580388B CN 109580388 B CN109580388 B CN 109580388B CN 201910055005 A CN201910055005 A CN 201910055005A CN 109580388 B CN109580388 B CN 109580388B
Authority
CN
China
Prior art keywords
stress
shear
yield
formula
volume
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910055005.7A
Other languages
Chinese (zh)
Other versions
CN109580388A (en
Inventor
马少坤
李涛
刘莹
覃璐
韦爱文
阮耀民
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guangxi University
Original Assignee
Guangxi University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Guangxi University filed Critical Guangxi University
Priority to CN201910055005.7A priority Critical patent/CN109580388B/en
Publication of CN109580388A publication Critical patent/CN109580388A/en
Application granted granted Critical
Publication of CN109580388B publication Critical patent/CN109580388B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/24—Investigating strength properties of solid materials by application of mechanical stress by applying steady shearing forces
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014—Type of force applied
    • G01N2203/0025—Shearing

Landscapes

  • Physics & Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)

Abstract

一种岩土材料剪切屈服面与体积屈服面的测定方法，涉及计量固体变形技术领域。为了判断岩土材料的受力屈服，采用二次多项式拟合剪切屈服面，采用椭圆和双曲线拟合体积屈服面。通过恒定平均应力三轴试验及常规三轴压缩试验对二次多项式剪切屈服条件进行参数回归；通过不排水的恒定平均应力三轴试验及常规三轴压缩试验对椭圆和双曲线体积屈服条件进行参数回归。根据剪切屈服条件、体积屈服条件及相关参数绘制屈服面的回归曲线。根据剪切屈服条件和体积屈服条件的在工程中的具体响应值，评价岩土材料是否发生剪切屈服或体积屈服。本方法能够在工程上判断岩土材料在受力后是否存在屈服，以便采取相应措施，防止材料产生破坏，造成跨塌事故。

Figure 201910055005

A method for measuring shear yield surface and volume yield surface of geotechnical materials relates to the technical field of measuring solid deformation. In order to judge the stress yield of geotechnical materials, the shear yield surface is fitted by quadratic polynomial, and the volume yield surface is fitted by ellipse and hyperbola. Parametric regression of quadratic polynomial shear yield conditions by constant mean stress triaxial test and conventional triaxial compression test; elliptical and hyperbolic volume yield conditions by undrained constant mean stress triaxial test and conventional triaxial compression test Parametric regression. Draw the regression curve of the yield surface according to the shear yield condition, volume yield condition and related parameters. According to the specific response values of the shear yield condition and the volume yield condition in the project, evaluate whether the geotechnical material has shear yield or volume yield. This method can judge whether the geotechnical material has yielded after being stressed in engineering, so that corresponding measures can be taken to prevent the material from being damaged and causing a span collapse accident.

Figure 201910055005

Description

Method for measuring shear yield surface and volume yield surface of rock and soil material
Technical Field
The invention belongs to the field of solid deformation measurement, and particularly relates to a method for measuring a shear yield surface and a volume yield surface of a rock-soil material.
Background
To predict the stressed deformation of the geotechnical material, a constitutive model of the geotechnical material is firstly established. To establish a constitutive model of the geotechnical material, a shear yield surface and a volume yield surface of the geotechnical material are measured firstly.
At present, a large number of geotechnical engineering test results show that the shear yield surface of the geotechnical material has the tendency of not passing through the meridian plane origin and the characteristic of nonlinear expansion along with the increase of average stress on a pi plane; the intersection line of the shearing part of the volume yielding surface and the meridian plane has the characteristic that the slope of the intersection line changes along with the increase of the average stress; the intersection line of the shear expansion part of the volume yielding surface and the meridian plane has the characteristic of being not a straight line.
From Nanjing sand (Zhujian, Chongwei, Stangjie, Nanjing sand strength characteristics and static liquefaction phenomenon analysis [ J ]. geotechnics, 2008,29(6):1461-, 2015,37(3): 544-; and from the influence of drainage samples (Guo Ying, Konji. sampling method and stress path on the shearing characteristics of saturated medium-density fine sand CU [ J ] geotechnical engineering report, 2016,38(s2):79-84.) (loeve loyal, Shaosheng, King peach. XAGT-1 type true triaxial pressure chamber structure perfection and saturated sandy soil true triaxial test [ J ] scientific technology and engineering, 2014,14(19): 283) 288.), Fenggu sand (Qin Maran. research on the natural relationship of soil based on energy dissipation [ D ]. university of great continental engineering, 2006.), certain dam body sandy soil (Weisong, Zhujun Gao, Wangjie, etc.. steady state strength consolidation non-drainage test research [ J ] rock mechanics and engineering report, 2005,24 (4157): Wei, Wei Yao, Piao sand (Zhao Gao, Miao sand) containing different hydrates, 2011,32(S2):198-203.) were observed in the triaxial test, the phenomenon of non-linear accelerated expansion of the shear yield plane on the pi plane with the increase of the average stress. It was also observed from all the tests described above that there was a tendency for the shear yielding surface to not pass through the meridian plane origin.
The phenomenon that the intersection line of the shearing and shrinking part of the volume yielding surface and the meridian plane has the slope which is reduced along with the increase of the average stress is observed from a triaxial test of a saturated sandy soil triaxial test, wherein the triaxial test of the saturated sandy soil (Ninghao, Huangbo, Chenyunming, and the like, the research of back pressure setting and shear strength [ J ]. geotechnical engineering report, 2012,34(7):1313 + 1319 ]), and the research of the influence of a stress path under high pressure on the mechanical property of the saturated sandy soil [ D ]. university of China mining 2014 ] of the Xuzhou Irahu dam sand factory sand; the phenomenon that the slope increases along with the increase of the average stress is observed in a triaxial test of steady-state strength consolidation non-drainage triaxial test research of sand soil (Weisong, Zhujungao, Wangjunjie, and the like) of a dam body of a certain dam (Weisong, Zhujungao, Wangjunjie, and the like) [ J ] rock mechanics and engineering report, 2005,24(22):4151 plus 4157 ])), Nanjing sand (Zhujia group, Konjawei, Hougejie, Nanjing sand strength characteristics and static liquefaction phenomenon analysis [ J ] geotechnics, 2008,29(6):1461 plus 1465 ]); the phenomenon that the slope is reduced firstly and then increased along with the increase of the average stress is observed from a constant average stress triaxial test of Fujian standard sand (Guo Ying, Konji. sampling method and stress path influence [ J ] geotechnical engineering report, 2016,38(s2):79-84.) on the shearing characteristics of saturated medium-density fine sand CU; the phenomenon that the slope is increased firstly and then reduced along with the increase of the average stress is observed from a triaxial test of Nanjing sand (Zhujian, Chongwei, Belgium, Nanjing sand strength characteristics and static liquefaction phenomenon analysis [ J ]. geotechnical, 2008,29(6): 1461-1465.). From the research on the back pressure setting and the shear strength in the Fujian standard sand (Dinghao, Huangbo, Chenyunming, etc.; geotechnical engineering report, 2012,34(7): 1313-.
Theories describing the nonlinear expansion of the yield surface of a material in the pi-plane with the increase of the average stress are Hooke-Brown conditions (Hoek E., Carranza-Torres C., Corkum B., Hoek-Brown failure criterion-2002 edition [ C ]// Procedents of the Fifth North American Rock mechanical System symposium.Torto, 2002:18-22.), Desertical models (Desai C.S., Gallagher R.H., Mechanics of Engineering Materials [ M ] London Williams, 1984.), Laudi type Single yield surface models (Kim M.K., Lade P.V. Single yielding property model for the yield surface of a material in the pi-plane (Gekk. P.V. simple property model: chemical Engineering J.) (chemical Engineering J.S.) (chemical Engineering J.: 1, chemical Engineering J.307, chemical Engineering J.S.) (chemical Engineering J.) (chemical Engineering J.307, chemical Engineering J.S.) (chemical Engineering. S.: 13. S.: chemical Engineering. 12. S. (chemical Engineering. 12. 3. K.) (chemical Engineering. 12. 6. chemical Engineering. K.) (chemical Engineering. S.) (chemical Engineering. 12. S.) (chemical Engineering. S.) (chemical Engineering. A Lade double yielding surface model (Lade P.V. Elasto-plastic stress-strain for Cohesion soil with cured yield surface [ J ]. International Journal of Solids & Structures,1977,13(11): 1019-. The post-processing model is widely applied, the shear yield condition of the post-processing model describes that the shear yield surface expands nonlinearly along with the increase of average stress, the expansion speed attenuates along with the increase of the average stress, but the shear yield surface of the geotechnical material on the pi plane expands nonlinearly along with the increase of the average stress. Meanwhile, the shear yield condition describes that the shear yield surface passes through the origin of the meridian plane, and the regression effect of the shear yield surface is poor for the geotechnical materials with higher cohesive force. In addition, the volume yield condition of the 'post-processing' model describes that the intersection line of the shear-expansion part of the volume yield surface and the meridian plane is a straight line, so that the regression effect of the volume yield surface of the rock-soil material is poor.
The Chinese patent application 201611094782.5 discloses a method for measuring the yield surface of a metal material, which adopts a pretension-torsion deformation loading path to measure the evolution law of the subsequent yield surface. The method is not applicable to rock and soil materials. The shear yield surface of geotechnical materials expands with increasing average stress, which metallic materials do not normally have, nor is this document concerned. Geotechnical materials not only yield in shear but also in volume, which is not generally the case for metallic materials, nor is this document concerned.
The Chinese patent application 201710312003.2 discloses a method for measuring a yield surface by cross-shaped tensile pre-deformation loading, which adopts a loading path of one direction of pre-tensile deformation and then the other direction of re-tensile deformation to measure the yield surface. The method is not applicable to rock and soil materials. The shear yield surface of geotechnical materials expands with increasing average stress, which metallic materials do not normally have, nor is this document concerned. Geotechnical materials not only yield in shear but also in volume, which is not generally the case for metallic materials, nor is this document concerned.
The Chinese patent application 201710611974.7 discloses an analysis method for predicting yield surface of periodic lattice material, which considers the coupling effect of internal structure axial force and bending moment when the material is actually stressed, firstly obtains the yield condition of the periodic lattice material representative voxel by theoretical derivation, and then uses finite element analysis software to realize large-batch comprehensive calculation by programming. The method is not applicable to rock and soil materials. The shear yield surface of geotechnical materials expands with increasing average stress, and this property is not considered in this document. Geotechnical materials not only yield in shear but also in volume, which is not taken into account.
Disclosure of Invention
The invention aims to provide a method for measuring a shear yield surface and a volume yield surface of a rock-soil material, wherein the shear yield surface and the volume yield surface can be used for judging whether the rock-soil material has shear yield or volume yield after being stressed in engineering so as to take corresponding measures to prevent the material from being damaged and causing a collapse accident.
The invention achieves the purpose of measuring the shear yield surface and the volume yield surface of the rock-soil material through a constant average stress triaxial test, which requires a triaxial tester to control the average stress to be a constant value in the test. The mean stress is a well-known concept and refers to the mean of the three principal stresses of a material. The specific value of the average stress controlled by the triaxial tester in the test is equal to the specific value of the average stress of the geotechnical material in the actual engineering, and the average stress of the whole test process is a constant value, which belongs to the prior art.
The invention achieves the above purpose by the following technical scheme: a method for measuring the shear yield surface and the volume yield surface of rock-soil material comprises a step of measuring the shear yield surface, a step of measuring the shear shrinkage part of the volume yield surface and a step of measuring the shear expansion part of the volume yield surface, when a triaxial tester can control the average stress to be constant,
the measuring steps of the shear yield surface are as follows:
interpretation of the symbols in the following steps: f. ofsFor shear yield function, when fsShear yielding occurs when f is greater than or equal to 0s<No shear yield occurs at 0; xisIs relative bias stress and is defined by formula (2); hsIs a shear hardening parameter; p is the mean stress; ksThe shear isotropic hardening coefficient at the actual average stress is defined by formula (3); s is the bias stress tensor; alpha is alphasAlpha when considering follow-up hardening for the bias back stress tensorsAs a variable, alpha when the follow-up hardening is not taken into accountsIs 0;
Figure GDA0002776964450000031
shear isotropic hardening coefficient when considering isotropic hardening with reference to average stress
Figure GDA0002776964450000032
As a variable, when isotropic hardening is not considered
Figure GDA0002776964450000033
Is a set constant; b issA quadratic polynomial defined by formula (4); cA、CB、CCPerforming regression determination for shear yield condition parameters through at least 3 different constant average stress triaxial tests; q is generalized shear stress;
Figure GDA0002776964450000034
generalized shear strain; sigma1Is a large principal stress; sigma3Is a small principal stress; epsilon1Is a large principal strain; epsilon3Is a small principal strain.
(1) The shear yield function is in the form of formula (1), formula (2), formula (3) and formula (4), and according to geotechnical test code SL237-1999, the constant mean stress triaxial test is adopted to respectively perform corresponding monotone loading tests on the material through at least 3 different constant mean stresses. The conditions of monotonic loading are the same as the loading conditions of the actual engineering, including loading rate, temperature, consolidation and drainage conditions.
Figure GDA0002776964450000041
ξs＝s-αs(Hs) (2)
Figure GDA0002776964450000042
Bs＝CAp2+CBp+CC (4)
(2) According to geotechnical test code SL237-1999, data are collected for each mean stress condition of a constant mean stress triaxial test and converted into principal stress sigma1、σ3And principal strain ε1、ε3The data of (1).
(3) σ is expressed according to the formulae (5) and (6)1、σ3、ε1And ε3Q-converted to each mean stress condition
Figure GDA0002776964450000043
A relationship curve.
q＝|σ1-σ3| (5)
Figure GDA0002776964450000044
(4) Selecting one of the average stresses as a reference average stress within the average stress range of the engineering application, and correspondingly q < - >, of the reference average stress
Figure GDA0002776964450000045
The relation curve is the reference mean responseQ in force —)
Figure GDA0002776964450000046
A relationship curve.
(5) Selecting one of them in the strain range of engineering application
Figure GDA0002776964450000047
As a reference shear hardening parameter.
(6) Substituting q corresponding to the reference shear hardening parameter of each average stress into K in formula (7)s(ii) a Substituting q corresponding to the reference shear hardening parameter of the reference average stress into formula (7)
Figure GDA0002776964450000048
P at each mean stress is substituted by formula (7). And forming a linear equation system, wherein the number of linear equations is equal to that of the constant average stress triaxial tests.
Figure GDA0002776964450000049
(7) Solving the linear equation set by solving the contradictory equation set to obtain the shearing yield condition parameter CA、CB、CC。
(8) Will shear yield condition parameter CA、CB、CCAnd (4) substituting the formula (1), the formula (3) and the formula (4) to obtain the shear yield function of the rock-soil material.
(9) Substituting q corresponding to each shear hardening parameter level at the reference average stress into K in the formula (7)sA first step of; c is to beA、CB、CCThe value of (3) is substituted for the formula (7). With p as the horizontal axis variable, KsAnd (4) plotting the formula (7) on the meridian plane for the longitudinal axis variable to obtain a regression curve of the shear yield surface of the rock-soil material.
Measuring the shear part of the volume yield surface:
interpretation of the symbols in the following steps: f. ofv1Is an elliptical volume yield function when fv1Volume yield occurs at > 0, when fv1<No hair at 0Yielding by volume; p is the mean stress; hvIs a volume hardening parameter; q is generalized shear stress; y isv1The volume yield stress at the actual principal stress difference is defined by formula (9); Δ p is the increment of the mean stress when Δ p>Loading in the forward direction at 0, when Δ p<Reverse loading is performed when the load is 0;
Figure GDA00027769644500000410
the bulk yield stress at which the primary stress difference is 0, defined by formula (10); b isv1A quadratic polynomial defined by formula (11); alpha is alphavIs the ball back stress tensor;
Figure GDA00027769644500000411
the volume isotropic hardening coefficient when the main stress difference is 0; cG、CH、CIThe parameters are elliptic volume yield condition parameters, and are determined by the regression of the actually measured volume yield surface of at least 3 different hardening parameter levels; sigma1Is a large principal stress; sigma3Is a small principal stress; p' is the effective mean stress; u is the pore water pressure.
(1) The elliptical volume yield function is in the form of equation (8), equation (9), equation (10) and equation (11), and the material is subjected to a corresponding monotonic loading test with at least 3 different constant volume strains, respectively, using a non-draining triaxial test according to geotechnical test code SL 237-1999. The conditions of the monotonic loading are the same as the loading conditions of the actual engineering, including loading rate and temperature.
Figure GDA0002776964450000051
Figure GDA0002776964450000052
Figure GDA0002776964450000053
Figure GDA0002776964450000054
Wherein: alpha when considering follow-up hardeningvIs a variable, and is a function of,
Figure GDA0002776964450000055
alpha when the follow-up hardening is not consideredvTo be 0, only Δ p is calculated in the formulae (8) and (10)>0, etc.
(2) According to geotechnical test code SL237-1999, data of each volume strain condition of the triaxial test are collected and converted into principal stress sigma1、σ3Main strain epsilon1、ε3And pore water pressure u.
(3) σ is expressed according to the formulae (5), (12) and (13)1、σ3And u is converted into a q-p' relation curve of each volume strain condition on the meridian plane, and the curve is the intersection line of the volume yield plane and the meridian plane of each confining pressure condition.
q＝|σ1-σ3| (5)
p＝(σ1+2σ3)/3 (12)
p′＝p-u (13)
(4) The shear portion of the volume yielding surface on the q-p 'curve for each volume strain condition is selected to have a characteristic point representative in shape that is not on the p' coordinate axis.
(5) Substituting the abscissa of a point on the q-p' curve at a primary stress difference of 0 into that in equation (14)
Figure GDA0002776964450000056
Substituting the abscissa of a characteristic point selected by the shear part of the volume yielding surface on the q-p' relation curve except for the difference of the main stress of 0 into Y in the formula (14)v1(ii) a The ordinate of a characteristic point selected by the shear part of the volume yielding surface on the q-p' relation curve except the main stress difference is substituted by an equation (14). Forming a system of linear equations, the number of linear equations and the difference in hardnessThe measured volume yield faces at the normalized parameter level are equal in number.
Figure GDA0002776964450000057
(6) Solving the linear equation set by solving the contradictory equation set to obtain the elliptic volume yield condition parameter CG、CH、CI。
(7) Subjecting the ellipse volume to yield condition parameter CG、CH、CIAnd (4) substituting the formula (8), the formula (9), the formula (10) and the formula (11) to obtain the elliptical volume yield condition of the rock-soil material.
(8) By substituting p in formula (14) on the volume yield plane at a primary stress difference of 0
Figure GDA0002776964450000058
C is to beG、CH、CIThe value of (3) is substituted for the formula (14). With q as the vertical axis variable, Yv1And (3) plotting the formula (14) on the meridian plane by using the variable of the horizontal axis to obtain a regression curve of the shear part of the volume yield surface of the rock-soil material.
Measuring the volume yield surface shear swelling part:
interpretation of the symbols in the following steps: f. ofv2Is a hyperbolic volumetric yield function when fv2Volume yield occurs at > 0, when fv2<No volume yield at 0; p is the mean stress; hvIs a volume hardening parameter; q is generalized shear stress; y isv2The volume yield stress at the actual principal stress difference is defined by equation (16); Δ p is the increment of the mean stress when Δ p>Loading in the forward direction at 0, when Δ p<Reverse loading is performed when the load is 0;
Figure GDA0002776964450000061
the bulk yield stress at which the primary stress difference is 0, defined by formula (10); b isv2A quadratic polynomial defined for formula (17); alpha is alphavIs the ball back stress tensor;
Figure GDA0002776964450000062
the volume isotropic hardening coefficient when the main stress difference is 0; cD、CE、CF.Determining hyperbolic volume yield condition parameters through actually measured volume yield surface regression of at least 3 different hardening parameter levels; sigma1Is a large principal stress; sigma3Is a small principal stress; p' is the effective mean stress; u is the pore water pressure.
(1) The hyperbolic volumetric yield function is in the form of formula (15), formula (16), formula (10) and formula (17), and according to geotechnical test code SL237-1999, the material is subjected to corresponding monotonic loading tests through at least 3 different constant volumetric strains respectively, using a non-draining triaxial test. The conditions of the monotonic loading are the same as the loading conditions of the actual engineering, including loading rate and temperature.
Figure GDA0002776964450000063
Figure GDA0002776964450000064
Figure GDA0002776964450000065
Figure GDA0002776964450000066
Wherein: alpha when considering follow-up hardeningvIs a variable, and is a function of,
Figure GDA0002776964450000067
alpha when the follow-up hardening is not consideredvTo be 0, only Δ p is calculated in the equations (15) and (10)>0, etc.
(2) According to geotechnical test code SL237-1999, data of each volume strain condition of the triaxial test are collected and converted into principal stress sigma1、σ3Main strain epsilon1、ε3And pore water pressure u.
(3) σ is expressed according to the formulae (5), (12) and (13)1、σ3And u is converted into a q-p' relation curve of each volume strain condition on the meridian plane, and the curve is the intersection line of the volume yield plane and the meridian plane of each confining pressure condition.
q＝|σ1-σ3| (5)
p＝(σ1+2σ3)/3 (12)
p′＝p-u (13)
(4) The volume yield surface shear expansion on the q-p 'curve for each volume strain condition is selected to be a characteristic point representative in shape, which is not on the p' coordinate axis.
(5) Substituting the abscissa of a point on the q-p' curve at a primary stress difference of 0 into that in equation (18)
Figure GDA0002776964450000068
Substituting the abscissa of a characteristic point selected by the shear-swelling part of the volume yielding surface on the q-p' relation curve except for the difference of the main stress of 0 into Y in the formula (18)v2(ii) a Substituting the ordinate of a characteristic point selected by the shear expansion part of the volume yielding surface on the q-p' relation curve except the main stress difference of 0 into an expression (18). And forming a linear equation system, wherein the number of the linear equations is equal to the number of the measured volume yield surfaces of different hardening parameter levels.
Figure GDA0002776964450000069
(6) Solving the linear equation set by solving the contradictory equation set to obtain the hyperbolic volume yield condition parameter CD、CE、CF。
(7) Hyperbolic volume yield condition parameter CD、CE、CFAnd (5) substituting the equations (15), (16), (10) and (17) to obtain hyperbolic volume yield conditions of the rock and soil material.
(8) By substituting p in formula (18) on the volume yield plane at a primary stress difference of 0
Figure GDA0002776964450000071
C is to beD、CE、CFThe value of (3) is substituted for the formula (18). With q as the vertical axis variable, Yv2And (3) drawing the formula (18) on the meridian plane by using the variable of the horizontal axis to obtain a regression curve of the shear-swelling part of the volume yield surface of the rock-soil material.
When the triaxial tester can not control the average stress to be constant, the shear yield surface is measured by adopting an equivalent constant average stress triaxial test method,
the method for measuring the shear yield surface by the equivalent constant average stress triaxial test method comprises the following steps:
interpretation of the symbols in the following steps: f. ofsFor shear yield function, when fsShear yielding occurs when f is greater than or equal to 0s<No shear yield occurs at 0; xisIs relative bias stress and is defined by formula (2); hsIs a shear hardening parameter; p is the mean stress; ksThe shear isotropic hardening coefficient at the actual average stress is defined by formula (3); s is the bias stress tensor; alpha is alphasAlpha when considering follow-up hardening for the bias back stress tensorsAs a variable, alpha when the follow-up hardening is not taken into accountsIs 0;
Figure GDA0002776964450000072
shear isotropic hardening coefficient when considering isotropic hardening with reference to average stress
Figure GDA0002776964450000073
As a variable, when isotropic hardening is not considered
Figure GDA0002776964450000074
Is a set constant; b issA quadratic polynomial defined by formula (4); cA、CB、CCPerforming regression determination for shear yield condition parameters through at least 3 different constant average stress triaxial tests; q is generalized shear stress;
Figure GDA0002776964450000075
generalized shear strain; sigma1Is a large principal stress; sigma3Is a small principal stress; epsilon1Is a large principal strain; epsilon3Is a small principal strain.
(1) The shear yield function is in the form of formula (1), formula (2), formula (3) and formula (4), and according to geotechnical test code SL237-1999, the conventional triaxial compression test is adopted to respectively perform corresponding monotone loading tests on the material through at least 3 different constant confining pressures. The conditions of monotonic loading are the same as the loading conditions of the actual engineering, including loading rate, temperature, consolidation and drainage conditions.
Figure GDA0002776964450000076
ξs＝s-αs(Hs) (2)
Figure GDA0002776964450000077
Bs＝CAp2+CBp+CC (4)
(2) According to geotechnical test code SL237-1999, data of each confining pressure condition of the conventional triaxial compression test is collected and converted into main stress sigma1、σ3And principal strain ε1、ε3The data of (1).
(3) σ is expressed according to the formulae (5) and (6)1、σ3、ε1And ε3Q-converted into each confining pressure condition
Figure GDA0002776964450000078
A relationship curve.
q＝|σ1-σ3| (5)
Figure GDA0002776964450000079
(4) σ is expressed according to the formula (5) and the formula (12)1And σ3Converted into a q-p relationship which is monotonically loaded in the meridian plane.
p＝(σ1+2σ3)/3 (12)
(5) And interpolating and extrapolating the shear hardening parameter equipotential points of the q-p relation curve on the meridian plane to form a shear hardening parameter equipotential line.
(6) And respectively setting the stress path line of the triaxial test with equivalent constant average stress within the average stress range of each stress path of the conventional triaxial compression test, wherein the line is parallel to the meridian plane ordinate axis.
(7) The shear hardening parameter equipotential line is intersected with the set equivalent constant average stress triaxial test stress path line, and the intersection point of the two lines is the equivalent constant average stress triaxial test stress path characteristic point.
(8) And in the average stress range of engineering application, selecting the average stress of one equivalent constant average stress triaxial test stress path line as the reference average stress.
(9) Selecting one of the shear hardening parameters equipotential lines within the strain range of the engineering application
Figure GDA0002776964450000081
As a reference shear hardening parameter.
(10) In the range of the characteristic point of the stress path of the triaxial test with equivalent constant average stress, q corresponding to the reference shear hardening parameter of each average stress is substituted into K in the formula (7)s(ii) a Substituting q corresponding to the reference shear hardening parameter of the reference average stress into formula (7)
Figure GDA0002776964450000082
P at each mean stress is substituted by formula (7). And forming a linear equation system, wherein the number of linear equations is equal to the number of the equivalent constant average stress triaxial tests.
Figure GDA0002776964450000083
(11) Solving the linear equation set by solving the contradictory equation set to obtain the shearing yield condition parameter CA、CB、CC。
(12) Will shear yield condition parameter CA、CB、CCAnd (4) substituting the formula (1), the formula (3) and the formula (4) to obtain the shear yield function of the rock-soil material.
(13) Q corresponding to each shear hardening parameter level at the time of reference average stress is substituted in formula (7)
Figure GDA0002776964450000084
C is to beA、CB、CCThe value of (3) is substituted for the formula (7). With p as the horizontal axis variable, KsAnd (4) plotting the formula (7) on the meridian plane for the longitudinal axis variable to obtain a regression curve of the shear yield surface of the rock-soil material.
The application of the parameters measured by the method for measuring the shear yield surface and the volume yield surface of the rock and soil material in evaluating the shear yield surface of the rock and soil material comprises the following application steps:
(1) to follow the hardening law, the off-back stress tensor α is used in the algorithmsIs shown as
αs.n+1＝αs.n+Δαs.n+1 (19)
Figure GDA0002776964450000085
Wherein: subscriptnRefers to the last increment; subscriptn+1Is referred to as the present increment; the symbol Δ means that the variable is in increments; t is time;
Figure GDA0002776964450000086
from a particular follow-up hardening law,
(2) in order to connect the equi-hardening law, the equi-hardening coefficient in confining pressure is referenced in the algorithm
Figure GDA0002776964450000087
Is shown as
Figure GDA0002776964450000088
Figure GDA0002776964450000089
Wherein:
Figure GDA00027769644500000810
from a particular isotropic hardening law,
(3) checking and calculating shear yield condition
Figure GDA00027769644500000811
When f iss.n+1The increment generates shear yield when the increment is more than or equal to 0; when f iss.n+1<At 0 this increment no shear yield occurs.
The application of the parameters measured by the method for measuring the shear yield surface and the volume yield surface of the rock-soil material in evaluating the volume yield surface of the rock-soil material comprises the following application steps:
(1) to follow the hardening law, the off-back stress tensor α is used in the algorithmvIs shown as
αv.n+1＝αv.n+Δαv.n+1 (24)
Figure GDA0002776964450000091
Wherein: subscriptnRefers to the last increment; subscriptn+1Is referred to as the present increment; the symbol Δ means that the variable is in increments; t is time;
Figure GDA0002776964450000092
from a particular follow-up hardening law,
(2) in order to connect the equi-hardening law, the equi-hardening coefficient of the algorithm when the main stress difference is used as a reference
Figure GDA0002776964450000093
Is shown as
Figure GDA0002776964450000094
Figure GDA0002776964450000095
Wherein:
Figure GDA0002776964450000096
from a particular isotropic hardening law,
(3) checking elliptic volume yield condition and hyperbolic volume yield condition
Figure GDA0002776964450000097
Figure GDA0002776964450000098
Figure GDA0002776964450000099
Figure GDA00027769644500000910
Figure GDA00027769644500000911
When f isv1.n+1F is not less than 0v2.n+1When the increment is more than or equal to 0, the volume yield is generated; in other cases, the increment does not generate volume yield。
The technical principle of the invention is as follows:
i, shear yield condition
The test results show that the shear yield surface of the rock-soil material has the tendency of not passing through the meridian plane origin and the characteristic of nonlinear expansion along with the increase of the average stress on the pi plane. The test results also show that the shapes of the shear hardening curves of the rock-soil materials in different constant average stress triaxial tests are similar, namely the subsequent shear yield stresses of two different average stresses always keep a constant proportional relation. Based on the above facts, the shear yield surface of the rock-soil material can be described by using the following quadratic polynomial shear yield condition.
Figure GDA00027769644500000912
Wherein: f. ofsIs a shear yield function; xisIs relative bias stress and is defined by formula (2); hsIs a shear hardening parameter; p is the mean stress; ksThe shear isotropic hardening coefficient at the actual average stress, i.e., the generalized shear stress (q) at the actual average stress yield, is defined by equation (3).
ξs＝s-αs(Hs) (2)
Wherein: s is the bias stress tensor; alpha is alphasAlpha when considering follow-up hardening for the bias back stress tensorsAs a variable, alpha when the follow-up hardening is not taken into accountsIs 0.
Figure GDA0002776964450000101
Wherein:
Figure GDA0002776964450000102
shear isotropic hardening coefficient at the reference mean stress, i.e., generalized shear stress (q) at the yield of the reference mean stress, when isotropic hardening is considered
Figure GDA0002776964450000103
As a variable, when isotropic hardening is not considered
Figure GDA0002776964450000104
Is a set constant; b issIs a coefficient relating to the average stress, and is defined by equation (4).
Bs＝CAp2+CBp+CC (4)
Wherein: cA、CB、CCFor the shear yield condition parameters, regression was performed by at least 3 different constant mean stress triaxial tests.
The formula (1), the formula (2), the formula (3) and the formula (4) are second-order polynomial shear yield conditions of the rock and soil material. Wherein the meaning of formula (3) and formula (4) is that the subsequent shear yield stress at the actual average stress can be predicted when the subsequent shear yield stress at the base average stress and the actual average stress are known.
Elliptic volume yield condition
The elliptical volume yield condition of the "post-construction" model proposed by Zhengglung et al (1989) is mainly used to describe the shear effect of soil, as
Figure GDA0002776964450000105
Wherein: q is generalized shear stress;
Figure GDA0002776964450000106
is plastic volume strain
Figure GDA0002776964450000107
As a function of (c). The general form in which equation (32) can be written as a yield function is
Figure GDA0002776964450000108
Wherein: f. ofv1Is oval in volumeAnd (4) performing a function. The ratio of the major axis to the minor axis of the elliptical yield condition can be expressed as
Figure GDA0002776964450000109
The test results show that the intersection line of the shearing part of the volume yield plane of the geotechnical material and the meridian plane has the phenomenon that the slope of the intersection line changes along with the increase of the average stress. If an elliptical yield condition is employed, this phenomenon can be described as Bv1Changing with increasing average stress. Based on the above facts, B can be described by the formula (11)v1As a function of the average stress.
Figure GDA00027769644500001010
Wherein:
Figure GDA00027769644500001011
is the bulk yield stress at a primary stress difference of 0, i.e., p yielding at a primary stress difference of 0, i.e., the major axis of the elliptical yield condition
Figure GDA00027769644500001012
Is defined by formula (10); hvIs a volume hardening parameter; cG、CH、CIIs an ellipse volume yield condition parameter, is a constant, and is determined by the measured ellipse volume yield surface regression of at least 3 different hardening parameter levels.
Figure GDA00027769644500001013
Wherein: alpha is alphavIs the ball back stress tensor; alpha when considering follow-up hardeningvAs a variable, alpha when the follow-up hardening is not taken into accountvIs 0;
Figure GDA00027769644500001014
the volume isotropic hardening coefficient when the main stress difference is 0. When considering follow-upWhen the curing agent is cured,
Figure GDA00027769644500001015
when the follow-up hardening is not considered, equation (10) calculates Δ p only>0, and αvIs 0. As in formula (5)
Figure GDA00027769644500001016
By using
Figure GDA00027769644500001017
Is shown by combining formula (34) to obtain
Figure GDA00027769644500001018
Wherein: y isv1The volume yield stress is the actual main stress difference and is specially used for the elliptical volume yield condition, as shown in formula (9); Δ p is the increment of the mean stress, Δ p>0 is positive loading, Δ p<And when 0, the loading is reversed. When the follow-up hardening is not considered, equation (8) calculates Δ p only>0, etc.
Figure GDA0002776964450000111
The formula (11), the formula (10), the formula (8) and the formula (9) are improved elliptical volume yield conditions of the geotechnical material. The significance of the improvement made by the formulas (11) and (9) is that the subsequent bulk yield stress at the actual difference in primary stress can be predicted when the subsequent bulk yield stress at the difference in primary stress of 0 and the generalized shear stress at the difference in actual primary stress are known.
Hyperbolic volume yield condition
The test results show that the intersection line of the shear expansion part of the volume yield surface of the rock-soil material and the meridian plane is not a straight line, and the shape of the rock-soil material is more similar to a hyperbola. Based on the above observations, the following hyperbola can be used to describe the shear-expansion portion of the volume yield surface of the geotechnical material.
Figure GDA0002776964450000112
Wherein:
Figure GDA0002776964450000113
is a hyperbolic solid semi-axis,
Figure GDA0002776964450000114
Is a dashed semi-axis of a hyperbola. The hyperbolic volumetric yield condition may be expressed as
Figure GDA0002776964450000115
Wherein: f. ofv2Is a hyperbolic volumetric yield function when fv2Volume yield occurs at > 0, when fv2<No volume yield at 0; y isv2The volume yield stress is the actual main stress difference and is specially used for hyperbolic volume yield conditions, and the hyperbolic volume yield conditions are represented by a formula (36);
Figure GDA0002776964450000116
the ratio of the real half axis to the imaginary half axis of the hyperbolic yield condition can be expressed as
Figure GDA0002776964450000117
Wherein: b isv2Is the inverse of the slope of the hyperbolic asymptote.
The test results show that the slope of the extreme state line of the volume yield surface of the geotechnical material has the sign of changing along with the increase of the average stress. That is to say Bv2Is a function of the mean stress. Based on the above observation, B can be described by the formula (17)v2As a function of the average stress.
Figure GDA0002776964450000118
Wherein: cD、CE、CFThe hyperbolic volume yield condition parameters are constants and are determined by actually measured hyperbolic volume yield surface regression of at least 3 different hardening parameter levels. If adopted
Figure GDA0002776964450000119
As a hyperbolic focal length, then
Figure GDA00027769644500001110
The combined vertical type (36), the formula (37) and the formula (38) are obtained
Figure GDA00027769644500001111
The equations (15), (17) and (16) are hyperbolic volume yield conditions of the rock-soil material. Wherein the significance of formula (17) and formula (16) is that the subsequent bulk yield stress at the actual difference in primary stress can be predicted when the subsequent bulk yield stress at the difference in primary stress of 0 and the generalized shear stress at the difference in actual primary stress are known.
The invention has the beneficial effects that:
(1) since the shear yield function is a quadratic polynomial of the mean stress, i.e. equation (4) bs＝CAp2+CBp+CCThe shear yield condition regression curve can not only expand along with the nonlinear deceleration of the average stress, but also expand along with the nonlinear acceleration of the average stress;
(2) the shear yield surface can not pass through the origin of the meridian plane, so that the soil regression effect on the soil with higher cohesive force is good;
(3) the improved elliptical volume yield condition can describe the phenomenon that the intersection line of the shearing part of the volume yield surface of the geotechnical material and the meridian plane has the slope which changes along with the change of the average stress;
(4) the hyperbolic volume yield condition can describe the phenomenon that the intersection line of the shear-expansion part of the volume yield surface of the rock-soil material and the meridian plane is not a straight line;
(5) the acquisition mode of the parameters is simple, and only a conventional triaxial compression test is needed.
(6) Through the equivalent constant average stress triaxial test, the shear yield condition can be measured when the triaxial tester can not control the average stress to be constant.
(7) And in the vicinity of the reference average stress and the reference shear hardening parameter, the error of the shear yield stress is less than 5 percent, which indicates that the regression effect of the shear yield surface is good.
(8) And when the main stress difference is low, the error of the elliptical volume yield stress is less than 5%, which shows that the regression effect of the elliptical volume yield surface is good.
(9) When the main stress difference is high, the error of the hyperbolic volume yield stress is less than 5 percent, which shows that the regression effect of the hyperbolic volume yield surface is good.
The beneficial effects are proved by a triaxial test of constant average stress of Fujian standard sand, a conventional triaxial compression test of Fujian standard sand and a conventional triaxial compression test of Nanjing sand.
Drawings
FIG. 1 is a generalized shear stress-generalized shear strain relation test curve of Fujian standard sand constant average stress triaxial test.
FIG. 2 is the yield surface after shear for the Fujian Standard Sand constant mean stress triaxial test.
FIG. 3 is the volume subsequent yield surface of the Fujian Standard Sand constant mean stress triaxial test.
FIG. 4 is a generalized shear stress-generalized shear strain relation test curve of a Fujian standard sand conventional triaxial compression test.
FIG. 5 is a schematic diagram of an equivalent constant mean stress triaxial test generated stress path.
FIG. 6 is the shear-successor yield surface of the Fujian standard sand conventional triaxial compression test.
FIG. 7 is the volume subsequent yield surface of Fujian standard sand for a conventional triaxial compression test.
Fig. 8 is a generalized shear stress-generalized shear strain relation test curve of a conventional triaxial compression test of Nanjing sand.
Figure 9 is the shear after yield surface of Nanjing sand for a conventional triaxial compression test.
Fig. 10 is the volume subsequent yield surface of the nanjing sand conventional triaxial compression test.
Detailed Description
The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and examples.
Example 1
The present embodiment is an application example of the method for measuring a shear yield surface and a volume yield surface of a rock-soil material, wherein a triaxial tester can control an average stress to be a constant value, and Fujian standard sand is used as a test material, and the method comprises a shear yield surface measuring step, a volume yield surface shear shrinkage portion measuring step and a volume yield surface shear swelling portion measuring step.
The measuring steps of the shear yield surface are as follows:
interpretation of the symbols in the following steps: f. ofsFor shear yield function, when fsShear yielding occurs when f is greater than or equal to 0s<No shear yield occurs at 0; xisIs relative bias stress and is defined by formula (2); hsIs a shear hardening parameter; p is the mean stress; ksThe shear isotropic hardening coefficient at the actual average stress is defined by formula (3); s is the bias stress tensor; alpha is alphasAlpha when considering follow-up hardening for the bias back stress tensorsAs a variable, alpha when the follow-up hardening is not taken into accountsIs 0;
Figure GDA0002776964450000131
shear isotropic hardening coefficient when considering isotropic hardening with reference to average stress
Figure GDA0002776964450000132
As a variable, when isotropic hardening is not considered
Figure GDA0002776964450000133
Is a set constant; b issA quadratic polynomial defined by formula (4); cA、CB、CCFor shear yield condition parameters, generalPerforming regression determination through at least 3 different constant average stress triaxial tests; q is generalized shear stress;
Figure GDA0002776964450000134
generalized shear strain; sigma1Is a large principal stress; sigma3Is a small principal stress; epsilon1Is a large principal strain; epsilon3Is a small principal strain.
(1) The shear yield function is in the form of formula (1), formula (2), formula (3) and formula (4), and according to geotechnical test code SL237-1999, the constant mean stress triaxial test is adopted to respectively perform corresponding monotone loading tests on the material through at least 3 different constant mean stresses. The conditions of monotonic loading are the same as the loading conditions of the actual engineering, including loading rate, temperature, consolidation and drainage conditions.
Figure GDA0002776964450000135
ξs＝s-αs(Hs) (2)
Figure GDA0002776964450000136
Bs＝CAp2+CBp+CC (4)
In this example, the Fujian standard sand sample was subjected to 3 monotonic loading tests under the conditions of 3 different constant average stresses. The soil sample had a relative density of 0.5. The test specimen was cylindrical and had a diameter of 39.1mm and a height of 80 mm. The 3 constant mean stresses were 0.1MPa, 0.2MPa and 0.3MPa, respectively. The condition of monotonous loading is the same as the loading condition of the actual engineering, such as the loading rate is 6kPa/min, the room temperature, the equidirectional consolidation and the drainage.
(2) According to geotechnical test code SL237-1999, data are collected for each mean stress condition of a constant mean stress triaxial test and converted into principal stress sigma1、σ3And principal strain ε1、ε3The data of (1).
(3) σ is expressed according to the formulae (5) and (6)1、σ3、ε1And ε3Q-converted to each mean stress condition
Figure GDA0002776964450000137
A relationship curve.
q＝|σ1-σ3| (5)
Figure GDA0002776964450000138
Q-of Fujian standard sand constant average stress triaxial test
Figure GDA0002776964450000139
The relationship test curve is shown in FIG. 1.
(4) Selecting one of the average stresses as a reference average stress within the average stress range of the engineering application, and correspondingly q < - >, of the reference average stress
Figure GDA00027769644500001310
The relation is q-at the reference mean stress
Figure GDA00027769644500001311
A relationship curve.
(5) Selecting one of them in the strain range of engineering application
Figure GDA00027769644500001312
As a reference shear hardening parameter.
Selecting
Figure GDA0002776964450000141
As a reference shear hardening parameter.
(6) Substituting q corresponding to the reference shear hardening parameter of each average stress into K in formula (7)s(ii) a Substituting q corresponding to the reference shear hardening parameter of the reference average stress into formula (7)
Figure GDA0002776964450000142
P at each mean stress is substituted by formula (7). And forming a linear equation system, wherein the number of linear equations is equal to that of the constant average stress triaxial tests.
Figure GDA0002776964450000143
Generalized shear stress (q) obtained from the fixed drainage constant mean stress triaxial test sampling of Fujian standard sand is shown in Table 1.
TABLE 1 generalized shear stress/MPa for Fujian Standard Sand
Figure GDA0002776964450000144
The system of linear equations is
Figure GDA0002776964450000145
(7) Solving the linear equation set by solving the contradictory equation set to obtain the shearing yield condition parameter CA、CB、CC。
The shearing yield condition parameters of Fujian standard sand are as follows: cA＝0.1793、CB＝4.7938、CC＝0.0341。
(8) Will shear yield condition parameter CA、CB、CCAnd (4) substituting the formula (1), the formula (3) and the formula (4) to obtain the shear yield function of the rock-soil material. The shear yield function of Fujian standard sand is:
Figure GDA0002776964450000146
(9) q corresponding to each shear hardening parameter level at the time of reference average stress is substituted in formula (7)
Figure GDA0002776964450000147
C is to beA、CB、CCThe value of (3) is substituted for the formula (7). With p as a function of the abscissaAmount, KsAnd (4) plotting the formula (7) on the meridian plane for the longitudinal axis variable to obtain a regression curve of the shear yield surface of the rock-soil material. Obtaining the subsequent shear yield surface corresponding to each shear hardening parameter level obtained by regression, and referring to figure 2; the scatter point of the yield surface after shear for each shear hardening parameter level obtained from the test is shown in fig. 2. As can be seen from fig. 2, the shear yield plane expands with mean stress non-linearly with acceleration and does not pass through the origin of the meridional plane. At a confining pressure of about 0.2MPa
Figure GDA0002776964450000148
When the shear yield surface is close to the shear yield surface, the regression effect is good, and the error is less than 5%.
The application of the parameters measured by the method for measuring the shear yield surface and the volume yield surface of the rock and soil material in evaluating the shear yield surface of the rock and soil material comprises the following application steps:
(1) to follow the hardening law, the off-back stress tensor α is used in the algorithmsIs shown as
αs.n+1＝αs.n+Δαs.n+1 (19)
Figure GDA0002776964450000149
Wherein: subscriptnRefers to the last increment; subscriptn+1Is referred to as the present increment; the symbol Δ means that the variable is in increments; t is time;
Figure GDA00027769644500001410
from a specific follow-up hardening law. If the last increment is transmitteds.n＝[0.1,0.2,0.15,0.01,0.01,0.01]MPa; this increment
Figure GDA00027769644500001411
Δ t ═ 0.1 s; then the book is increased
Figure GDA00027769644500001412
(2) To connect the isotropic hardening law, an algorithmCoefficient of isotropic hardening at medium reference confining pressure
Figure GDA0002776964450000151
Is shown as
Figure GDA0002776964450000152
Figure GDA0002776964450000153
Wherein:
Figure GDA0002776964450000154
from a specific isotropic hardening law. If the last increment is transmitted
Figure GDA0002776964450000155
This increment
Figure GDA0002776964450000156
Δ t ═ 0.1 s; then the book is increased
Figure GDA0002776964450000157
(3) Checking and calculating shear yield condition
Figure GDA0002776964450000158
When f iss.n+1The increment generates shear yield when the increment is more than or equal to 0; when f iss.n+1<At 0 this increment no shear yield occurs.
If the amount of this increase ssn+1＝[1,1,1,0,0,0]MPa, p ═ 0.3 MPa; the shear yield conditions of the incremental Fujian standard sand are as follows:
Figure GDA0002776964450000159
this increment yields in shear.
Measuring the shear part of the volume yield surface:
interpretation of the symbols in the following steps: f. ofv1Is an elliptical volume yield function when fv1Volume yield occurs at > 0, when fv1<No volume yield at 0; p is the mean stress; hvIs a volume hardening parameter; q is generalized shear stress; y isv1The volume yield stress at the actual principal stress difference is defined by formula (9); Δ p is the increment of the mean stress when Δ p>Loading in the forward direction at 0, when Δ p<Reverse loading is performed when the load is 0;
Figure GDA00027769644500001510
the bulk yield stress at which the primary stress difference is 0, defined by formula (10); b isv1A quadratic polynomial defined by formula (11); alpha is alphavIs the ball back stress tensor;
Figure GDA00027769644500001511
the volume isotropic hardening coefficient when the main stress difference is 0; cG、CH、CIThe parameters are elliptic volume yield condition parameters, and are determined by the regression of the actually measured volume yield surface of at least 3 different hardening parameter levels; sigma1Is a large principal stress; sigma3Is a small principal stress; p' is the effective mean stress; u is the pore water pressure.
(1) The elliptical volume yield function is in the form of equation (8), equation (9), equation (10) and equation (11), and the material is subjected to a corresponding monotonic loading test with at least 3 different constant volume strains, respectively, using a non-draining triaxial test according to geotechnical test code SL 237-1999. The conditions of the monotonic loading are the same as the loading conditions of the actual engineering, including loading rate and temperature.
Figure GDA00027769644500001512
Figure GDA00027769644500001513
Figure GDA00027769644500001514
Figure GDA00027769644500001515
Wherein: alpha when considering follow-up hardeningvIs a variable, and is a function of,
Figure GDA00027769644500001516
alpha when the follow-up hardening is not consideredvTo be 0, only Δ p is calculated in the formulae (8) and (10)>0, etc. In this example, the fujian standard sand sample was subjected to 3 monotone loading tests under 3 conditions of different constant volume strains. The soil sample had a relative density of 0.5. The test specimen was cylindrical and had a diameter of 39.1mm and a height of 80 mm. The 3 constant ambient pressures are respectively 0.2MPa, 0.3MPa and 0.4 MPa. The condition of monotonic loading is the same as the loading condition of the actual engineering, such as the loading rate is 6kPa/min and the room temperature.
(2) According to geotechnical test code SL237-1999, data of each volume strain condition of the triaxial test are collected and converted into principal stress sigma1、σ3Main strain epsilon1、ε3And pore water pressure u.
(3) σ is expressed according to the formulae (5), (12) and (13)1、σ3And u is converted into a q-p' relation curve of each volume strain condition on the meridian plane, and the curve is the intersection line of the volume yield plane and the meridian plane of each confining pressure condition.
q＝|σ1-σ3| (5)
p＝(σ1+2σ3)/3 (12)
p′＝p-u (13)
The q-p' relation test curve of the Fujian standard sand non-drainage constant average stress triaxial test is shown in figure 3.
(4) The shear portion of the volume yielding surface on the q-p 'curve for each volume strain condition is selected to have a characteristic point representative in shape that is not on the p' coordinate axis. The Fujian standard sand volume yield surface characteristic point data are shown in Table 2.
TABLE 2 Fujian Standard Sand volume yield surface characteristic point data/MPa
Figure GDA0002776964450000161
(5) Substituting the abscissa of a point on the q-p' curve at a primary stress difference of 0 into that in equation (14)
Figure GDA0002776964450000162
Substituting the abscissa of a characteristic point selected by the shear part of the volume yielding surface on the q-p' relation curve except for the difference of the main stress of 0 into Y in the formula (14)v1(ii) a The ordinate of a characteristic point selected by the shear part of the volume yielding surface on the q-p' relation curve except the main stress difference is substituted by an equation (14). And forming a linear equation system, wherein the number of the linear equations is equal to the number of the measured volume yield surfaces of different hardening parameter levels.
Figure GDA0002776964450000163
The system of linear equations is
Figure GDA0002776964450000164
(6) Solving the linear equation set by solving the contradictory equation set to obtain the elliptic volume yield condition parameter CG、CH、CI. The parameters of the elliptical volume yield condition of Fujian standard sand are as follows: cG＝-26.9447、CH＝15.2498、CI＝-1.6947。
(7) Subjecting the ellipse volume to yield condition parameter CG、CH、CIAnd (4) substituting the formula (8), the formula (9), the formula (10) and the formula (11) to obtain the elliptical volume yield condition of the rock-soil material. The elliptical volume yield condition of Fujian standard sand is as follows:
Figure GDA0002776964450000165
(8) by substituting p in formula (14) on the volume yield plane at a primary stress difference of 0
Figure GDA0002776964450000166
C is to beG、CH、CIThe value of (3) is substituted for the formula (14). With q as the vertical axis variable, Yv1And (3) plotting the formula (14) on the meridian plane by using the variable of the horizontal axis to obtain a regression curve of the shear part of the volume yield surface of the rock-soil material. The volume successor yield surface corresponding to each average stress obtained by regression is shown in fig. 3; the volume-following yield surface for each mean stress from the test is shown in figure 3. As can be seen from FIG. 3, the regression effect of the shear part of the volume yielding surface is good at low main stress difference, and the error is less than 5%.
Measuring the volume yield surface shear swelling part:
interpretation of the symbols in the following steps: f. ofv2Is a hyperbolic volumetric yield function when fv2Volume yield occurs at > 0, when fv2<No volume yield at 0; p is the mean stress; hvIs a volume hardening parameter; q is generalized shear stress; y isv2The volume yield stress at the actual principal stress difference is defined by equation (16); Δ p is the increment of the mean stress when Δ p>Loading in the forward direction at 0, when Δ p<Reverse loading is performed when the load is 0;
Figure GDA0002776964450000171
the bulk yield stress at which the primary stress difference is 0, defined by formula (10); b isv2A quadratic polynomial defined for formula (17); alpha is alphavIs the ball back stress tensor;
Figure GDA0002776964450000172
the volume isotropic hardening coefficient when the main stress difference is 0; cD、CE、CFHyperbolic volume yield condition parameters determined by actual measurement volume yield surface regression of at least 3 different hardening parameter levels; sigma1Is a large principal stress; sigma3Is smallA principal stress; p' is the effective mean stress; u is the pore water pressure.
(1) The hyperbolic volumetric yield function is in the form of formula (15), formula (16), formula (10) and formula (17), and according to geotechnical test code SL237-1999, the material is subjected to corresponding monotonic loading tests through at least 3 different constant volumetric strains respectively, using a non-draining triaxial test. The conditions of the monotonic loading are the same as the loading conditions of the actual engineering, including loading rate and temperature.
Figure GDA0002776964450000173
Figure GDA0002776964450000174
Figure GDA0002776964450000175
Figure GDA0002776964450000176
Wherein: alpha when considering follow-up hardeningvIs a variable, and is a function of,
Figure GDA0002776964450000177
alpha when the follow-up hardening is not consideredvTo be 0, only Δ p is calculated in the equations (15) and (10)>0, etc. In this example, the fujian standard sand sample was subjected to 3 monotone loading tests under 3 conditions of different constant volume strains. The soil sample had a relative density of 0.5. The test specimen was cylindrical and had a diameter of 39.1mm and a height of 80 mm. The 3 constant ambient pressures are respectively 0.2MPa, 0.3MPa and 0.4 MPa. The condition of monotonic loading is the same as the loading condition of the actual engineering, such as the loading rate is 6kPa/min and the room temperature.
(2) According to geotechnical test code SL237-1999, data of each volume strain condition of the triaxial test are collected and converted into principal stress sigma1、σ3Main strain epsilon1、ε3And pore water pressure u.
(3) σ is expressed according to the formulae (5), (12) and (13)1、σ3And u is converted into a q-p' relation curve of each volume strain condition on the meridian plane, and the curve is the intersection line of the volume yield plane and the meridian plane of each confining pressure condition.
q＝|σ1-σ3| (5)
p＝(σ1+2σ3)/3 (12)
p′＝p-u (13)
The q-p' relation test curve of the Fujian standard sand non-drainage constant average stress triaxial test is shown in figure 3.
(4) The volume yield surface shear expansion on the q-p 'curve for each volume strain condition is selected to be a characteristic point representative in shape, which is not on the p' coordinate axis. The Fujian standard sand volume yield surface characteristic point data are shown in Table 2.
(5) Substituting the abscissa of a point on the q-p' curve at a primary stress difference of 0 into that in equation (18)
Figure GDA0002776964450000181
Substituting the abscissa of a characteristic point selected by the shear-swelling part of the volume yielding surface on the q-p' relation curve except for the difference of the main stress of 0 into Y in the formula (18)v2(ii) a Substituting the ordinate of a characteristic point selected by the shear expansion part of the volume yielding surface on the q-p' relation curve except the main stress difference of 0 into an expression (18). And forming a linear equation system, wherein the number of the linear equations is equal to the number of the measured volume yield surfaces of different hardening parameter levels.
Figure GDA0002776964450000182
The system of linear equations is
Figure GDA0002776964450000183
(6) Solving the linear equation set by solving the contradictory equation set to obtain the hyperbolic volume yield condition parameter CD、CE、CF。
Hyperbolic volume yield condition parameters of Fujian standard sand are as follows: cD＝-0.2777、CE＝0.1220、CF＝0.6395。
(7) Hyperbolic volume yield condition parameter CD、CE、CFAnd (5) substituting the equations (15), (16), (10) and (17) to obtain hyperbolic volume yield conditions of the rock and soil material. Hyperbolic volume yield conditions of Fujian standard sand are as follows:
Figure GDA0002776964450000184
Figure GDA0002776964450000185
Figure GDA0002776964450000186
Figure GDA0002776964450000187
(8) by substituting p in formula (18) on the volume yield plane at a primary stress difference of 0
Figure GDA0002776964450000188
C is to beD、CE、CFThe value of (3) is substituted for the formula (18). With q as the vertical axis variable, Yv2And (3) drawing the formula (18) on the meridian plane by using the variable of the horizontal axis to obtain a regression curve of the shear-swelling part of the volume yield surface of the rock-soil material. The volume successor yield surface corresponding to each average stress obtained by regression is shown in fig. 3; the volume-following yield surface for each mean stress from the test is shown in figure 3. As can be seen from FIG. 3, the volume yield surface shear at high principal stress differenceThe regression effect of the expansion part is good, and the error is less than 5%.
The application of the parameters measured by the method for measuring the shear yield surface and the volume yield surface of the rock-soil material in evaluating the volume yield surface of the rock-soil material comprises the following application steps:
(1) to follow the hardening law, the off-back stress tensor α is used in the algorithmvIs shown as
αv.n+1＝αv.n+Δαv.n+1 (24)
Figure GDA0002776964450000189
Wherein: subscriptnRefers to the last increment; subscriptn+1Is referred to as the present increment; the symbol Δ means that the variable is in increments; t is time;
Figure GDA00027769644500001810
from a specific follow-up hardening law. If the last increment is transmittedv.n0.1 MPa; this increment
Figure GDA00027769644500001811
Δ t ═ 0.1 s; then the book is increased
Figure GDA00027769644500001812
(2) In order to connect the equi-hardening law, the equi-hardening coefficient of the algorithm when the main stress difference is used as a reference
Figure GDA00027769644500001813
Is shown as
Figure GDA0002776964450000191
Figure GDA0002776964450000192
Wherein:
Figure GDA0002776964450000193
from a specific isotropic hardening law. If the last increment is transmitted
Figure GDA0002776964450000194
This increment
Figure GDA0002776964450000195
Δ t ═ 0.1 s; then the book is increased
Figure GDA0002776964450000196
(3) Checking elliptic volume yield condition and hyperbolic volume yield condition
Figure GDA0002776964450000197
Figure GDA0002776964450000198
Figure GDA0002776964450000199
Figure GDA00027769644500001910
Figure GDA00027769644500001911
When f isv1.n+1F is not less than 0v2.n+1When the increment is more than or equal to 0, the volume yield is generated; in other cases, the present increment does not yield volumetrically.
If the amount of this increment pn+1＝1MPa，q＝0.0015MPa，Δp>0; the volume yield condition of the incremental Fujian standard sand is as follows:
Figure GDA00027769644500001912
Figure GDA00027769644500001913
Figure GDA00027769644500001914
Figure GDA00027769644500001915
fv2.n+1＝|pn+1|-Yv2.n+1＝|1|-(-20.1998)＝21.1998MPa>no volume yield occurs at 0 this increment.
Example 2
The present embodiment is another application example of the method for measuring a shear yield surface and a volume yield surface of a rock-soil material, according to the present invention, a triaxial tester cannot control an average stress to be a constant value, and the method adopts fujian standard sand as a test material, and includes a shear yield surface measuring step, a volume yield surface shear shrinkage portion measuring step, and a volume yield surface shear swelling portion measuring step.
The method for measuring the shear yield surface by the equivalent constant average stress triaxial test method comprises the following steps:
interpretation of the symbols in the following steps: f. ofsFor shear yield function, when fsShear yielding occurs when f is greater than or equal to 0s<No shear yield occurs at 0; xisIs relative bias stress and is defined by formula (2); hsIs a shear hardening parameter; p is the mean stress; ksThe shear isotropic hardening coefficient at the actual average stress is defined by formula (3); s is the bias stress tensor; alpha is alphasAlpha when considering follow-up hardening for the bias back stress tensorsAs a variable, alpha when the follow-up hardening is not taken into accountsIs 0;
Figure GDA0002776964450000201
shear isotropic hardening coefficient when considering isotropic hardening with reference to average stress
Figure GDA0002776964450000202
As a variable, when isotropic hardening is not considered
Figure GDA0002776964450000203
Is a set constant; b issA quadratic polynomial defined by formula (4); cA、CB、CCPerforming regression determination for shear yield condition parameters through at least 3 different constant average stress triaxial tests; q is generalized shear stress;
Figure GDA0002776964450000204
generalized shear strain; sigma1Is a large principal stress; sigma3Is a small principal stress; epsilon1Is a large principal strain; epsilon3Is a small principal strain.
(1) The shear yield function is in the form of formula (1), formula (2), formula (3) and formula (4), and according to geotechnical test code SL237-1999, the conventional triaxial compression test is adopted to respectively perform corresponding monotone loading tests on the material through at least 3 different constant confining pressures. The conditions of monotonic loading are the same as the loading conditions of the actual engineering, including loading rate, temperature, consolidation and drainage conditions.
Figure GDA0002776964450000205
ξs＝s-αs(Hs) (2)
Figure GDA0002776964450000206
Bs＝CAp2+CBp+CC (4)
In this example, 4 monotone loading tests were performed on Fujian standard sand samples under 4 different conditions of constant confining pressure. The soil sample had a relative density of 0.6. The test specimen was cylindrical and had a diameter of 39.1mm and a height of 80 mm. The 4 constant ambient pressures are respectively 0.05MPa, 0.1MPa, 0.15MPa and 0.2 MPa. The condition of monotonic loading is the same as the loading condition of the actual engineering, such as the loading rate is 0.08mm/min, the room temperature, the equidirectional consolidation and the drainage.
(2) According to geotechnical test code SL237-1999, data of each confining pressure condition of the conventional triaxial compression test is collected and converted into main stress sigma1、σ3And principal strain ε1、ε3The data of (1).
(3) σ is expressed according to the formulae (5) and (6)1、σ3、ε1And ε3Q-converted into each confining pressure condition
Figure GDA0002776964450000207
A relationship curve.
q＝|σ1-σ3| (5)
Figure GDA0002776964450000208
Q-of Fujian standard sand routine triaxial compression test
Figure GDA0002776964450000209
The relationship test curve is shown in FIG. 4.
(4) σ is expressed according to the formula (5) and the formula (12)1And σ3Converted into a q-p relationship which is monotonically loaded in the meridian plane.
p＝(σ1+2σ3)/3 (12)
(5) And interpolating and extrapolating the shear hardening parameter equipotential points of the q-p relation curve on the meridian plane to form a shear hardening parameter equipotential line.
(6) And respectively setting the stress path line of the triaxial test with equivalent constant average stress within the average stress range of each stress path of the conventional triaxial compression test, wherein the line is parallel to the meridian plane ordinate axis.
(7) The shear hardening parameter equipotential line is intersected with the set equivalent constant average stress triaxial test stress path line, and the intersection point of the two lines is the equivalent constant average stress triaxial test stress path characteristic point. A schematic diagram of the stress path generated by the equivalent constant mean stress triaxial test is shown in fig. 5.
Generalized shear stress (q) obtained from conventional triaxial compression test sampling of drainage of fujian standard sand is shown in table 3.
TABLE 3 actual measurement of generalized shear stress (q)/MPa for Fujian Standard Sand routine triaxial compression test
Figure GDA0002776964450000211
Generalized shear stress (q) of the equivalent constant mean stress triaxial test of the generated Fujian standard sand is shown in Table 4.
TABLE 4 generalized shear stress (q)/MPa for equivalent constant mean stress triaxial test of Fujian standard sand
Figure GDA0002776964450000212
(8) And in the average stress range of engineering application, selecting the average stress of one equivalent constant average stress triaxial test stress path line as the reference average stress. 0.2343MPa was chosen as the baseline mean stress.
(9) Selecting one of the shear hardening parameters equipotential lines within the strain range of the engineering application
Figure GDA0002776964450000213
As a reference shear hardening parameter. Selecting
Figure GDA0002776964450000214
As a reference shear hardening parameter.
(10) In the range of the characteristic point of the stress path of the triaxial test with equivalent constant average stress, q corresponding to the reference shear hardening parameter of each average stress is substituted into K in the formula (7)s(ii) a Substituting q corresponding to the reference shear hardening parameter of the reference average stress into formula (7)
Figure GDA0002776964450000215
P at each mean stress is substituted by formula (7). And forming a linear equation system, wherein the number of linear equations is equal to the number of the equivalent constant average stress triaxial tests.
Figure GDA0002776964450000216
The system of linear equations is
Figure GDA0002776964450000217
(11) Solving the linear equation set by solving the contradictory equation set to obtain the shearing yield condition parameter CA、CB、CC。
The shearing yield condition parameters of Fujian standard sand are as follows: cA＝0.2889、CB＝4.3259、CC＝-0.0341。
(12) Will shear yield condition parameter CA、CB、CCAnd (4) substituting the formula (1), the formula (3) and the formula (4) to obtain the shear yield function of the rock-soil material. The shear yield function of Fujian standard sand is:
Figure GDA0002776964450000218
(13) q corresponding to each shear hardening parameter level at the time of reference average stress is substituted in formula (7)
Figure GDA0002776964450000219
C is to beA、CB、CCThe value of (3) is substituted for the formula (7). With p as the horizontal axis variable, KsAnd (4) plotting the formula (7) on the meridian plane for the longitudinal axis variable to obtain a regression curve of the shear yield surface of the rock-soil material. Obtaining the subsequent shear yield surface corresponding to each shear hardening parameter level obtained by regression, and referring to fig. 6; subsequent yield surface after shearing corresponding to each shear hardening parameter level obtained from testSee fig. 6. As can be seen from fig. 6, the shear yield plane expands with mean stress non-linearly with acceleration and does not pass through the origin of the meridional plane. At about 0.2343MPa of mean stress
Figure GDA0002776964450000221
And when the stress is close to the stress, the regression effect of the yield surface is good in shearing, and the error is less than 5%.
The application of the parameters measured by the method for measuring the shear yield surface and the volume yield surface of the rock and soil material in evaluating the shear yield surface of the rock and soil material comprises the following application steps:
(1) to follow the hardening law, the off-back stress tensor α is used in the algorithmsIs shown as
αs.n+1＝αs.n+Δαs.n+1 (19)
Figure GDA0002776964450000222
Wherein: subscriptnRefers to the last increment; subscriptn+1Is referred to as the present increment; the symbol Δ means that the variable is in increments; t is time;
Figure GDA0002776964450000223
from a specific follow-up hardening law. If the last increment is transmitteds.n＝[0.1,0.2,0.15,0.01,0.01,0.01]MPa; this increment
Figure GDA0002776964450000224
Δ t ═ 0.1 s; then the book is increased
Figure GDA0002776964450000225
(2) In order to connect the equi-hardening law, the equi-hardening coefficient in confining pressure is referenced in the algorithm
Figure GDA0002776964450000226
Is shown as
Figure GDA0002776964450000227
Figure GDA0002776964450000228
Wherein:
Figure GDA0002776964450000229
from a specific isotropic hardening law. If the last increment is transmitted
Figure GDA00027769644500002210
This increment
Figure GDA00027769644500002211
Δ t ═ 0.1 s; then the book is increased
Figure GDA00027769644500002212
(3) Checking and calculating shear yield condition
Figure GDA00027769644500002213
When f iss.n+1The increment generates shear yield when the increment is more than or equal to 0; when f iss.n+1<At 0 this increment no shear yield occurs.
If the amount of this increase ssn+1＝[1,1,1,0,0,0]MPa, p ═ 0.3 MPa; the shear yield conditions of the incremental Fujian standard sand are as follows:
Figure GDA00027769644500002214
this increment yields in shear.
Measuring the shear part of the volume yield surface:
interpretation of the symbols in the following steps: f. ofv1Is an elliptical volume yield function when fv1Volume yield occurs at > 0, when fv1<No volume yield at 0; p is the mean stress; hvIs a volume hardening parameter; q is generalized shear stress; y isv1The volume yield stress at the actual principal stress difference is defined by formula (9); Δ p is the increment of the mean stress when Δ p>Loading in the forward direction at 0, when Δ p<Reverse loading is performed when the load is 0;
Figure GDA00027769644500002215
the bulk yield stress at which the primary stress difference is 0, defined by formula (10); b isv1A quadratic polynomial defined by formula (11); alpha is alphavIs the ball back stress tensor;
Figure GDA00027769644500002216
the volume isotropic hardening coefficient when the main stress difference is 0; cG、CH、CIThe parameters are elliptic volume yield condition parameters, and are determined by the regression of the actually measured volume yield surface of at least 3 different hardening parameter levels; sigma1Is a large principal stress; sigma3Is a small principal stress; p' is the effective mean stress; u is the pore water pressure.
(1) The elliptical volume yield function is in the form of equation (8), equation (9), equation (10) and equation (11), and the material is subjected to a corresponding monotonic loading test with at least 3 different constant volume strains, respectively, using a non-draining triaxial test according to geotechnical test code SL 237-1999. The conditions of the monotonic loading are the same as the loading conditions of the actual engineering, including loading rate and temperature.
Figure GDA0002776964450000231
Figure GDA0002776964450000232
Figure GDA0002776964450000233
Figure GDA0002776964450000234
Wherein: alpha when considering follow-up hardeningvIs a variable, and is a function of,
Figure GDA0002776964450000235
alpha when the follow-up hardening is not consideredvTo be 0, only Δ p is calculated in the formulae (8) and (10)>0, etc. In this example, the fujian standard sand sample was subjected to 3 monotone loading tests under 3 conditions of different constant volume strains. The soil sample had a relative density of 0.7. The test specimen was cylindrical and had a diameter of 39.1mm and a height of 80 mm. The 3 constant ambient pressures are respectively 0.05MPa, 0.1MPa and 0.15 MPa. The condition of monotonic loading is the same as the loading condition of the actual engineering, such as the loading rate is 5kPa/min and the room temperature.
(2) According to geotechnical test code SL237-1999, data of each volume strain condition of the triaxial test are collected and converted into principal stress sigma1、σ3Main strain epsilon1、ε3And pore water pressure u.
(3) σ is expressed according to the formulae (5), (12) and (13)1、σ3And u is converted into a q-p' relation curve of each volume strain condition on the meridian plane, and the curve is the intersection line of the volume yield plane and the meridian plane of each confining pressure condition.
q＝|σ1-σ3| (5)
p＝(σ1+2σ3)/3 (12)
p′＝p-u (13)
The q-p' relation test curve of the Fujian standard sand non-drainage constant confining pressure triaxial test is shown in figure 7.
(4) The shear portion of the volume yielding surface on the q-p 'curve for each volume strain condition is selected to have a characteristic point representative in shape that is not on the p' coordinate axis. The Fujian standard sand volume yield surface characteristic point data are shown in Table 5.
TABLE 5 Fujian Standard Sand volume yield surface characteristic points data/MPa
Figure GDA0002776964450000236
(5) Substituting the abscissa of a point on the q-p' curve at a primary stress difference of 0 into that in equation (14)
Figure GDA0002776964450000237
Substituting the abscissa of a characteristic point selected by the shear part of the volume yielding surface on the q-p' relation curve except for the difference of the main stress of 0 into Y in the formula (14)v1(ii) a The ordinate of a characteristic point selected by the shear part of the volume yielding surface on the q-p' relation curve except the main stress difference is substituted by an equation (14). And forming a linear equation system, wherein the number of the linear equations is equal to the number of the measured volume yield surfaces of different hardening parameter levels.
Figure GDA0002776964450000238
The system of linear equations is
Figure GDA0002776964450000241
(6) Solving the linear equation set by solving the contradictory equation set to obtain the elliptic volume yield condition parameter CG、CH、CI。
The parameters of the elliptical volume yield condition of Fujian standard sand are as follows: cG＝-8.0176、CH＝2.6323、CI＝0.6412。
(7) Subjecting the ellipse volume to yield condition parameter CG、CH、CIAnd (4) substituting the formula (8), the formula (9), the formula (10) and the formula (11) to obtain the elliptical volume yield condition of the rock-soil material. The elliptical volume yield condition of Fujian standard sand is as follows:
Figure GDA0002776964450000242
(8) by substituting p in formula (14) on the volume yield plane at a primary stress difference of 0
Figure GDA0002776964450000243
C is to beG、CH、CIThe value of (3) is substituted for the formula (14). With q as the vertical axis variable, Yv1And (3) plotting the formula (14) on the meridian plane by using the variable of the horizontal axis to obtain a regression curve of the shear part of the volume yield surface of the rock-soil material. The volume corresponding to each confining pressure obtained by regression is followed by a yield surface, which is shown in figure 7; the volume corresponding to each confining pressure obtained from the test is followed by the yield surface, see fig. 7. As can be seen from FIG. 7, the regression effect of the shear part of the volume yielding surface is good at low main stress difference, and the error is less than 5%.
Measuring the volume yield surface shear swelling part:
interpretation of the symbols in the following steps: f. ofv2Is a hyperbolic volumetric yield function when fv2Volume yield occurs at > 0, when fv2<No volume yield at 0; p is the mean stress; hvIs a volume hardening parameter; q is generalized shear stress; y isv2The volume yield stress at the actual principal stress difference is defined by equation (16); Δ p is the increment of the mean stress when Δ p>Loading in the forward direction at 0, when Δ p<Reverse loading is performed when the load is 0;
Figure GDA0002776964450000244
the bulk yield stress at which the primary stress difference is 0, defined by formula (10); b isv2A quadratic polynomial defined for formula (17); alpha is alphavIs the ball back stress tensor;
Figure GDA0002776964450000245
the volume isotropic hardening coefficient when the main stress difference is 0; cD、CE、CFHyperbolic volume yield condition parameters determined by actual measurement volume yield surface regression of at least 3 different hardening parameter levels; sigma1Is a large principal stress; sigma3Is a small principal stress; p' is the effective mean stress; u is the pore water pressure.
(1) The hyperbolic volumetric yield function is in the form of formula (15), formula (16), formula (10) and formula (17), and according to geotechnical test code SL237-1999, the material is subjected to corresponding monotonic loading tests through at least 3 different constant volumetric strains respectively, using a non-draining triaxial test. The conditions of the monotonic loading are the same as the loading conditions of the actual engineering, including loading rate and temperature.
Figure GDA0002776964450000246
Figure GDA0002776964450000247
Figure GDA0002776964450000248
Figure GDA0002776964450000249
Wherein: alpha when considering follow-up hardeningvIs a variable, and is a function of,
Figure GDA00027769644500002410
alpha when the follow-up hardening is not consideredvTo be 0, only Δ p is calculated in the equations (15) and (10)>0, etc. In this example, the fujian standard sand sample was subjected to 3 monotone loading tests under 3 conditions of different constant volume strains. The soil sample had a relative density of 0.7. The test specimen was cylindrical and had a diameter of 39.1mm and a height of 80 mm. The 3 constant ambient pressures are respectively 0.05MPa, 0.1MPa and 0.15 MPa. The condition of monotonic loading is the same as the loading condition of the actual engineering, such as the loading rate is 5kPa/min and the room temperature.
(2) According to geotechnical test code SL237-1999, data of each volume strain condition of the triaxial test are collected and converted into principal stress sigma1、σ3Main strain epsilon1、ε3And pore water pressure u.
(3) σ is expressed according to the formulae (5), (12) and (13)1、σ3And u is converted to a q-p' relationship curve for each volume strain condition in the meridian plane,the curve is the intersection line of the volume yielding surface and the meridian plane under each confining pressure condition.
q＝|σ1-σ3| (5)
p＝(σ1+2σ3)/3 (12)
p′＝p-u (13)
The q-p' relation test curve of the Fujian standard sand non-drainage constant confining pressure triaxial test is shown in figure 7.
(4) The volume yield surface shear expansion on the q-p 'curve for each volume strain condition is selected to be a characteristic point representative in shape, which is not on the p' coordinate axis. The Fujian standard sand volume yield surface characteristic point data are shown in Table 5.
(5) Substituting the abscissa of a point on the q-p' curve at a primary stress difference of 0 into that in equation (18)
Figure GDA0002776964450000251
Substituting the abscissa of a characteristic point selected by the shear-swelling part of the volume yielding surface on the q-p' relation curve except for the difference of the main stress of 0 into Y in the formula (18)v2(ii) a Substituting the ordinate of a characteristic point selected by the shear expansion part of the volume yielding surface on the q-p' relation curve except the main stress difference of 0 into an expression (18). And forming a linear equation system, wherein the number of the linear equations is equal to the number of the measured volume yield surfaces of different hardening parameter levels.
Figure GDA0002776964450000252
The system of linear equations is
Figure GDA0002776964450000253
(6) Solving the linear equation set by solving the contradictory equation set to obtain the hyperbolic volume yield condition parameter CD、CE、CF。
Hyperbolic volume of Fujian standard sand is bentThe parameters of the clothes condition are as follows: cD＝-5.2951、CE＝1.1163、CF＝0.6343。
(7) Hyperbolic volume yield condition parameter CD、CE、CFAnd (5) substituting the equations (15), (16), (10) and (17) to obtain hyperbolic volume yield conditions of the rock and soil material. Hyperbolic volume yield conditions of Fujian standard sand are as follows:
Figure GDA0002776964450000254
Figure GDA0002776964450000255
Figure GDA0002776964450000256
Figure GDA0002776964450000257
(8) by substituting p in formula (18) on the volume yield plane at a primary stress difference of 0
Figure GDA0002776964450000261
C is to beD、CE、CFThe value of (3) is substituted for the formula (18). With q as the vertical axis variable, Yv2And (3) drawing the formula (18) on the meridian plane by using the variable of the horizontal axis to obtain a regression curve of the shear-swelling part of the volume yield surface of the rock-soil material. The volume corresponding to each confining pressure obtained by regression is followed by a yield surface, which is shown in figure 7; the volume corresponding to each confining pressure obtained from the test is followed by the yield surface, see fig. 7. As can be seen from FIG. 7, the regression effect of the shear-swelling part of the volume yielding surface is good at high main stress difference, and the error is less than 5%.
The application of the parameters measured by the method for measuring the shear yield surface and the volume yield surface of the rock-soil material in evaluating the volume yield surface of the rock-soil material comprises the following application steps:
(1) is composed ofThe joint follow-up hardening law is adopted, and the back bias stress tensor alpha is adopted in the algorithmvIs shown as
αv.n+1＝αv.n+Δαv.n+1 (24)
Figure GDA0002776964450000262
Wherein: subscriptnRefers to the last increment; subscriptn+1Is referred to as the present increment; the symbol Δ means that the variable is in increments; t is time;
Figure GDA0002776964450000263
from a specific follow-up hardening law. If the last increment is transmittedv.n0.1 MPa; this increment
Figure GDA0002776964450000264
Δ t ═ 0.1 s; then the book is increased
Figure GDA0002776964450000265
(2) In order to connect the equi-hardening law, the equi-hardening coefficient of the algorithm when the main stress difference is used as a reference
Figure GDA0002776964450000266
Is shown as
Figure GDA0002776964450000267
Figure GDA0002776964450000268
Wherein:
Figure GDA0002776964450000269
from a specific isotropic hardening law. If the last increment is transmitted
Figure GDA00027769644500002610
This increment
Figure GDA00027769644500002611
Δ t ═ 0.1 s; then the book is increased
Figure GDA00027769644500002612
(3) Checking elliptic volume yield condition and hyperbolic volume yield condition
Figure GDA00027769644500002613
Figure GDA00027769644500002614
Figure GDA00027769644500002615
Figure GDA00027769644500002616
Figure GDA00027769644500002617
When f isv1.n+1F is not less than 0v2.n+1When the increment is more than or equal to 0, the volume yield is generated; in other cases, the present increment does not yield volumetrically.
If the amount of this increment pn+1＝1MPa，q＝0.0015MPa，Δp<0; the volume yield condition of the incremental Fujian standard sand is as follows:
Figure GDA0002776964450000271
Figure GDA0002776964450000272
Figure GDA0002776964450000273
Figure GDA0002776964450000274
fv2.n+1＝Yv2.n+1-|pn+1|＝9.5145×10-4-|1|＝-0.9990MPa<no volume yield occurs at 0 this increment.
Example 3
The embodiment is another application example of the method for measuring the shear yield surface and the volume yield surface of the rock-soil material, at the moment, a triaxial tester cannot control the average stress to be a constant value, and Nanjing sand is used as a test material, and the method comprises a step of measuring the shear yield surface, a step of measuring the shear shrinkage part of the volume yield surface and a step of measuring the shear swelling part of the volume yield surface.
The method for measuring the shear yield surface by the equivalent constant average stress triaxial test method comprises the following steps:
interpretation of the symbols in the following steps: f. ofsFor shear yield function, when fsShear yielding occurs when f is greater than or equal to 0s<No shear yield occurs at 0; xisIs relative bias stress and is defined by formula (2); hsIs a shear hardening parameter; p is the mean stress; ksThe shear isotropic hardening coefficient at the actual average stress is defined by formula (3); s is the bias stress tensor; alpha is alphasAlpha when considering follow-up hardening for the bias back stress tensorsAs a variable, alpha when the follow-up hardening is not taken into accountsIs 0;
Figure GDA0002776964450000275
shear isotropic hardening coefficient when considering isotropic hardening with reference to average stress
Figure GDA0002776964450000276
As a variable, when isotropic hardening is not consideredTime of flight
Figure GDA0002776964450000277
Is a set constant; b issA quadratic polynomial defined by formula (4); cA、CB、CCPerforming regression determination for shear yield condition parameters through at least 3 different constant average stress triaxial tests; q is generalized shear stress;
Figure GDA0002776964450000278
generalized shear strain; sigma1Is a large principal stress; sigma3Is a small principal stress; epsilon1Is a large principal strain; epsilon3Is a small principal strain.
(1) The shear yield function is in the form of formula (1), formula (2), formula (3) and formula (4), and according to geotechnical test code SL237-1999, the conventional triaxial compression test is adopted to respectively perform corresponding monotone loading tests on the material through at least 3 different constant confining pressures. The conditions of monotonic loading are the same as the loading conditions of the actual engineering, including loading rate, temperature, consolidation and drainage conditions.
Figure GDA0002776964450000279
ξs＝s-αs(Hs) (2)
Figure GDA00027769644500002710
Bs＝CAp2+CBp+CC (4)
In the present example, 3 monotone loading tests were performed on the Nanjing sand sample under 3 conditions of different constant ambient pressures. The soil sample relative density was 0.48. The test specimen was cylindrical and had a diameter of 39.1mm and a height of 80 mm. The 3 constant ambient pressures are respectively 0.05MPa, 0.1MPa and 0.2 MPa. The condition of monotonic loading is the same as the loading condition of the actual engineering, such as the loading rate is 0.073mm/min, the room temperature, the equidirectional consolidation and no water drainage.
(2) According to geotechnical test code SL237-1999, data of each confining pressure condition of the conventional triaxial compression test is collected and converted into main stress sigma1、σ3And principal strain ε1、ε3The data of (1).
(3) σ is expressed according to the formulae (5) and (6)1、σ3、ε1And ε3Q-converted into each confining pressure condition
Figure GDA0002776964450000281
A relationship curve.
q＝|σ1-σ3| (5)
Figure GDA0002776964450000282
Q-of conventional triaxial compression test of Nanjing sand
Figure GDA0002776964450000283
The relationship test curve is shown in FIG. 8.
(4) σ is expressed according to the formula (5) and the formula (12)1And σ3Converted into a q-p relationship which is monotonically loaded in the meridian plane.
p＝(σ1+2σ3)/3 (12)
(5) And interpolating and extrapolating the shear hardening parameter equipotential points of the q-p relation curve on the meridian plane to form a shear hardening parameter equipotential line.
(6) And respectively setting the stress path line of the triaxial test with equivalent constant average stress within the average stress range of each stress path of the conventional triaxial compression test, wherein the line is parallel to the meridian plane ordinate axis.
(7) The shear hardening parameter equipotential line is intersected with the set equivalent constant average stress triaxial test stress path line, and the intersection point of the two lines is the equivalent constant average stress triaxial test stress path characteristic point. A schematic diagram of the stress path generated by the equivalent constant mean stress triaxial test is shown in fig. 5.
Generalized shear stress (q) obtained from a non-draining conventional triaxial compression test sample of Nanjing sand is shown in Table 6.
TABLE 6 actual measurement of generalized shear stress (q)/MPa for Nanjing sand conventional triaxial compression test
Figure GDA0002776964450000284
Generalized shear stress (q) of the resulting Nanjing sand in the triaxial equivalent constant average stress test is shown in Table 7.
TABLE 7 generalized shear stress (q)/MPa for Nanjing sand triaxial equivalent constant average stress test
Figure GDA0002776964450000285
(8) And in the average stress range of engineering application, selecting the average stress of one equivalent constant average stress triaxial test stress path line as the reference average stress. 0.1687MPa was chosen as the baseline mean stress.
(9) Selecting one of the shear hardening parameters equipotential lines within the strain range of the engineering application
Figure GDA0002776964450000286
As a reference shear hardening parameter. Selecting
Figure GDA0002776964450000287
As a reference shear hardening parameter.
(10) In the range of the characteristic point of the stress path of the triaxial test with equivalent constant average stress, q corresponding to the reference shear hardening parameter of each average stress is substituted into K in the formula (7)s(ii) a Substituting q corresponding to the reference shear hardening parameter of the reference average stress into formula (7)
Figure GDA0002776964450000288
P at each mean stress is substituted by formula (7). Forming a system of linear equations, the number of linear equations and the equivalent constant averageThe number of stress triaxial tests is equal.
Figure GDA0002776964450000289
The system of linear equations is
Figure GDA0002776964450000291
(11) Solving the linear equation set by solving the contradictory equation set to obtain the shearing yield condition parameter CA、CB、CC。
The shearing yield condition parameters of Nanjing sand are as follows: cA＝-3.6027、CB＝6.2193、CC＝0.0533。
(12) Will shear yield condition parameter CA、CB、CCAnd (4) substituting the formula (1), the formula (3) and the formula (4) to obtain the shear yield function of the rock-soil material. The shear yield function of Nanjing sand was:
Figure GDA0002776964450000292
(13) q corresponding to each shear hardening parameter level at the time of reference average stress is substituted in formula (7)
Figure GDA0002776964450000293
C is to beA、CB、CCThe value of (3) is substituted for the formula (7). With p as the horizontal axis variable, KsAnd (4) plotting the formula (7) on the meridian plane for the longitudinal axis variable to obtain a regression curve of the shear yield surface of the rock-soil material. Obtaining the subsequent shear yield surface corresponding to each shear hardening parameter level obtained by regression, and referring to fig. 9; the scatter point of the yield surface after shear for each shear hardening parameter level obtained from the test is shown in fig. 9. As can be seen from fig. 9, the shear yield plane expands with a non-linear deceleration of the mean stress and does not pass through the origin of the meridional plane. At about 0.1687MPa of mean stress
Figure GDA0002776964450000294
Regression effect of shear yield surface nearGood fruit, error less than 5%.
The application of the parameters measured by the method for measuring the shear yield surface and the volume yield surface of the rock and soil material in evaluating the shear yield surface of the rock and soil material comprises the following application steps:
(1) to follow the hardening law, the off-back stress tensor α is used in the algorithmsIs shown as
αs.n+1＝αs.n+Δαs.n+1 (19)
Figure GDA0002776964450000295
Wherein: subscriptnRefers to the last increment; subscriptn+1Is referred to as the present increment; the symbol Δ means that the variable is in increments; t is time;
Figure GDA0002776964450000296
from a specific follow-up hardening law. If the last increment is transmitteds.n＝[0.1,0.2,0.15,0.01,0.01,0.01]MPa; this increment
Figure GDA0002776964450000297
Δ t ═ 0.1 s; then the book is increased
Figure GDA0002776964450000298
(2) In order to connect the equi-hardening law, the equi-hardening coefficient in confining pressure is referenced in the algorithm
Figure GDA0002776964450000299
Is shown as
Figure GDA00027769644500002910
Figure GDA00027769644500002911
Wherein:
Figure GDA00027769644500002912
from a specific isotropic hardening law. If the last increment is transmitted
Figure GDA00027769644500002913
This increment
Figure GDA00027769644500002914
Δ t ═ 0.1 s; then the book is increased
Figure GDA00027769644500002915
(3) Checking and calculating shear yield condition
Figure GDA00027769644500002916
When f iss.n+1The increment generates shear yield when the increment is more than or equal to 0; when f iss.n+1<At 0 this increment no shear yield occurs.
If the amount of this increase ssn+1＝[1,1,1,0,0,0]MPa, p ═ 0.3 MPa; the shear yield conditions of the incremental Fujian standard sand are as follows:
Figure GDA00027769644500002917
this increment yields in shear.
Measuring the shear part of the volume yield surface:
interpretation of the symbols in the following steps: f. ofv1Is an elliptical volume yield function when fv1Volume yield occurs at > 0, when fv1<No volume yield at 0; p is the mean stress; hvIs a volume hardening parameter; q is generalized shear stress; y isv1The volume yield stress at the actual principal stress difference is defined by formula (9); Δ p is the increment of the mean stress when Δ p>Loading in the forward direction at 0, when Δ p<Reverse loading is performed when the load is 0;
Figure GDA0002776964450000301
volume yield stress at a principal stress difference of 0Defined by formula (10); b isv1A quadratic polynomial defined by formula (11); alpha is alphavIs the ball back stress tensor;
Figure GDA0002776964450000302
the volume isotropic hardening coefficient when the main stress difference is 0; cG、CH、CIThe parameters are elliptic volume yield condition parameters, and are determined by the regression of the actually measured volume yield surface of at least 3 different hardening parameter levels; sigma1Is a large principal stress; sigma3Is a small principal stress; p' is the effective mean stress; u is the pore water pressure.
(1) The elliptical volume yield function is in the form of equation (8), equation (9), equation (10) and equation (11), and the material is subjected to a corresponding monotonic loading test with at least 3 different constant volume strains, respectively, using a non-draining triaxial test according to geotechnical test code SL 237-1999. The conditions of the monotonic loading are the same as the loading conditions of the actual engineering, including loading rate and temperature.
Figure GDA0002776964450000303
Figure GDA0002776964450000304
Figure GDA0002776964450000305
Figure GDA0002776964450000306
Wherein: alpha when considering follow-up hardeningvIs a variable, and is a function of,
Figure GDA0002776964450000307
alpha when the follow-up hardening is not consideredvTo be 0, only Δ p is calculated in the formulae (8) and (10)>0, etc. This example is implemented by 3 different constants respectivelyAnd 3 monotonous loading tests are carried out on the Nanjing sand sample under the condition of constant volume strain. The soil sample relative density was 0.48. The test specimen was cylindrical and had a diameter of 39.1mm and a height of 80 mm. The 3 constant ambient pressures are respectively 0.05MPa, 0.1MPa and 0.2 MPa. The condition of monotonic loading is the same as the loading condition of the actual engineering, such as the loading rate of 0.073mm/min and the room temperature.
(2) According to geotechnical test code SL237-1999, data of each volume strain condition of the triaxial test are collected and converted into principal stress sigma1、σ3Main strain epsilon1、ε3And pore water pressure u.
(3) σ is expressed according to the formulae (5), (12) and (13)1、σ3And u is converted into a q-p' relation curve of each volume strain condition on the meridian plane, and the curve is the intersection line of the volume yield plane and the meridian plane of each confining pressure condition.
q＝|σ1-σ3| (5)
p＝(σ1+2σ3)/3 (12)
p′＝p-u (13)
The q-p' relation test curve of the Nanjing sand non-drainage constant confining pressure triaxial test is shown in figure 10.
(4) The shear portion of the volume yielding surface on the q-p 'curve for each volume strain condition is selected to have a characteristic point representative in shape that is not on the p' coordinate axis. The data of the characteristic points of the volume yield surface of Nanjing sand are shown in Table 8.
TABLE 8 Nanjing Sand volume yield surface characteristic point data/MPa
Figure GDA0002776964450000311
(5) Substituting the abscissa of a point on the q-p' curve at a primary stress difference of 0 into that in equation (14)
Figure GDA0002776964450000312
Will remove principal stressThe abscissa of a characteristic point selected by the shear part of the volume yielding surface on the q-p' relation curve with the difference of 0 is substituted for Y in the equation (14)v1(ii) a The ordinate of a characteristic point selected by the shear part of the volume yielding surface on the q-p' relation curve except the main stress difference is substituted by an equation (14). And forming a linear equation system, wherein the number of the linear equations is equal to the number of the measured volume yield surfaces of different hardening parameter levels.
Figure GDA0002776964450000313
The system of linear equations is
Figure GDA0002776964450000314
(6) Solving the linear equation set by solving the contradictory equation set to obtain the elliptic volume yield condition parameter CG、CH、CI。
The parameters of the elliptic volume yield condition of the Nanjing sand are as follows: cG＝87.7545、CH＝-21.1092、CI＝1.2392。
(7) Subjecting the ellipse volume to yield condition parameter CG、CH、CIAnd (4) substituting the formula (8), the formula (9), the formula (10) and the formula (11) to obtain the elliptical volume yield condition of the rock-soil material. The elliptical volume yield condition of Fujian standard sand is as follows:
Figure GDA0002776964450000315
(8) by substituting p in formula (14) on the volume yield plane at a primary stress difference of 0
Figure GDA0002776964450000316
C is to beG、CH、CIThe value of (3) is substituted for the formula (14). With q as the vertical axis variable, Yv1And (3) plotting the formula (14) on the meridian plane by using the variable of the horizontal axis to obtain a regression curve of the shear part of the volume yield surface of the rock-soil material. After the volume corresponding to each confining pressure is obtained by regressionThe yield surface, see fig. 10; the volume corresponding to each confining pressure obtained from the test is followed by the yield surface, see fig. 10. As can be seen from fig. 10, the regression effect of the shear part of the volume yielding surface is good at low main stress difference, and the error is less than 5%.
Measuring the volume yield surface shear swelling part:
interpretation of the symbols in the following steps: f. ofv2Is a hyperbolic volumetric yield function when fv2Volume yield occurs at > 0, when fv2<No volume yield at 0; p is the mean stress; hvIs a volume hardening parameter; q is generalized shear stress; y isv2The volume yield stress at the actual principal stress difference is defined by equation (16); Δ p is the increment of the mean stress when Δ p>Loading in the forward direction at 0, when Δ p<Reverse loading is performed when the load is 0;
Figure GDA0002776964450000317
the bulk yield stress at which the primary stress difference is 0, defined by formula (10); b isv2A quadratic polynomial defined for formula (17); alpha is alphavIs the ball back stress tensor;
Figure GDA0002776964450000318
the volume isotropic hardening coefficient when the main stress difference is 0; cD、CE、CFHyperbolic volume yield condition parameters determined by actual measurement volume yield surface regression of at least 3 different hardening parameter levels; sigma1Is a large principal stress; sigma3Is a small principal stress; p' is the effective mean stress; u is the pore water pressure.
(1) The hyperbolic volumetric yield function is in the form of formula (15), formula (16), formula (10) and formula (17), and according to geotechnical test code SL237-1999, the material is subjected to corresponding monotonic loading tests through at least 3 different constant volumetric strains respectively, using a non-draining triaxial test. The conditions of the monotonic loading are the same as the loading conditions of the actual engineering, including loading rate and temperature.
Figure GDA0002776964450000321
Figure GDA0002776964450000322
Figure GDA0002776964450000323
Figure GDA0002776964450000324
Wherein: alpha when considering follow-up hardeningvIs a variable, and is a function of,
Figure GDA0002776964450000325
alpha when the follow-up hardening is not consideredvTo be 0, only Δ p is calculated in the equations (15) and (10)>0, etc. In the present example, 3 monotone loading tests were performed on the Nanjing sand sample under 3 conditions of different constant volume strains. The soil sample relative density was 0.48. The test specimen was cylindrical and had a diameter of 39.1mm and a height of 80 mm. The 3 constant ambient pressures are respectively 0.05MPa, 0.1MPa and 0.2 MPa. The condition of monotonic loading is the same as the loading condition of the actual engineering, such as the loading rate of 0.073mm/min and the room temperature.
(2) According to geotechnical test code SL237-1999, data of each volume strain condition of the triaxial test are collected and converted into principal stress sigma1、σ3Main strain epsilon1、ε3And pore water pressure u.
(3) σ is expressed according to the formulae (5), (12) and (13)1、σ3And u is converted into a q-p' relation curve of each volume strain condition on the meridian plane, and the curve is the intersection line of the volume yield plane and the meridian plane of each confining pressure condition.
q＝|σ1-σ3| (5)
p＝(σ1+2σ3)/3 (12)
p′＝p-u (13)
The q-p' relation test curve of the Nanjing sand non-drainage constant confining pressure triaxial test is shown in figure 10.
(4) The volume yield surface shear expansion on the q-p 'curve for each volume strain condition is selected to be a characteristic point representative in shape, which is not on the p' coordinate axis. The data of the characteristic points of the volume yield surface of Nanjing sand are shown in Table 8.
(5) Substituting the abscissa of a point on the q-p' curve at a primary stress difference of 0 into that in equation (18)
Figure GDA0002776964450000326
Substituting the abscissa of a characteristic point selected by the shear-swelling part of the volume yielding surface on the q-p' relation curve except for the difference of the main stress of 0 into Y in the formula (18)v2(ii) a Substituting the ordinate of a characteristic point selected by the shear expansion part of the volume yielding surface on the q-p' relation curve except the main stress difference of 0 into an expression (18). And forming a linear equation system, wherein the number of the linear equations is equal to the number of the measured volume yield surfaces of different hardening parameter levels.
Figure GDA0002776964450000327
The system of linear equations is
Figure GDA0002776964450000331
(6) Solving the linear equation set by solving the contradictory equation set to obtain the hyperbolic volume yield condition parameter CD、CE、CF。
Hyperbolic volume yield condition parameters of Nanjing sand are as follows: cD＝-12.8960、CE＝2.6531、CF＝0.6198。
(7) Hyperbolic volume yield condition parameter CD、CE、CFAnd (5) substituting the equations (15), (16), (10) and (17) to obtain hyperbolic volume yield conditions of the rock and soil material. Hyperbolic volume yield conditions of Nanjing sand are as follows:
Figure GDA0002776964450000332
Figure GDA0002776964450000333
Figure GDA0002776964450000334
Figure GDA0002776964450000335
(8) substituting p on the volume yield surface at the time of the main stress difference of 0 into Y in the formula (18)v *(ii) a C is to beD、CE、CFThe value of (3) is substituted for the formula (18). With q as the vertical axis variable, Yv2And (3) drawing the formula (18) on the meridian plane by using the variable of the horizontal axis to obtain a regression curve of the shear-swelling part of the volume yield surface of the rock-soil material. The volume corresponding to each confining pressure obtained by regression is followed by a yield surface, which is shown in figure 10; the volume corresponding to each confining pressure obtained from the test is followed by the yield surface, see fig. 10. As can be seen from fig. 10, the regression effect of the shear-swelling portion of the volume yielding surface is good at high main stress difference, and the error is less than 5%.
The application of the parameters measured by the method for measuring the shear yield surface and the volume yield surface of the rock-soil material in evaluating the volume yield surface of the rock-soil material comprises the following application steps:
(1) to follow the hardening law, the off-back stress tensor α is used in the algorithmvIs shown as
αv.n+1＝αv.n+Δαv.n+1 (24)
Figure GDA0002776964450000336
Wherein: subscriptnRefers to the last increment; subscriptn+1Is referred to as the present increment; the symbol Δ means that the variable is in increments; t is time;
Figure GDA0002776964450000337
from a specific follow-up hardening law. If the last increment is transmittedv.n0.1 MPa; this increment
Figure GDA0002776964450000338
Δ t ═ 0.1 s; then the book is increased
Figure GDA0002776964450000339
(2) In order to connect the equi-hardening law, the equi-hardening coefficient of the algorithm when the main stress difference is used as a reference
Figure GDA00027769644500003310
Is shown as
Figure GDA00027769644500003311
Figure GDA00027769644500003312
Wherein:
Figure GDA00027769644500003313
from a specific isotropic hardening law. If the last increment is transmitted
Figure GDA00027769644500003314
This increment
Figure GDA00027769644500003315
Δ t ═ 0.1 s; then the book is increased
Figure GDA00027769644500003316
(3) Checking elliptic volume yield condition and hyperbolic volume yield condition
Figure GDA0002776964450000341
Figure GDA0002776964450000342
Figure GDA0002776964450000343
Figure GDA0002776964450000344
Figure GDA0002776964450000345
When f isv1.n+1F is not less than 0v2.n+1When the increment is more than or equal to 0, the volume yield is generated; in other cases, the present increment does not yield volumetrically. If the amount of this increment pn+1＝1MPa，q＝0.0015MPa，Δp>0; the volume yield condition of the incremental Nanjing sand is as follows:
Figure GDA0002776964450000346
Figure GDA0002776964450000347
Figure GDA0002776964450000348
Figure GDA0002776964450000349
fv2.n+1＝|pn+1|-Yv2.n+1＝|1|-(-21.6579)＝22.6579MPa>0 Ben plusThe volume yield occurs.

Claims (4)

1. A method for measuring the shear yield surface and the volume yield surface of rock-soil material is characterized by comprising a shear yield surface measuring step and a volume yield surface measuring step, when a triaxial tester can control the average stress to be constant in the test,
the measuring steps of the shear yield surface are as follows:
interpretation of the symbols in the following steps: f. ofsFor shear yield function, when fsShear yielding occurs when f is greater than or equal to 0s<No shear yield occurs at 0; xisIs relative bias stress and is defined by formula (2); hsIs a shear hardening parameter; p is the mean stress; ksThe shear isotropic hardening coefficient at the actual average stress is defined by formula (3); s is the bias stress tensor; alpha is alphasAlpha when considering follow-up hardening for the bias back stress tensorsAs a variable, alpha when the follow-up hardening is not taken into accountsIs 0;
Figure FDA0002776964440000011
shear isotropic hardening coefficient when considering isotropic hardening with reference to average stress
Figure FDA0002776964440000012
As a variable, when isotropic hardening is not considered
Figure FDA0002776964440000013
Is a set constant; b issA quadratic polynomial defined by formula (4); cA、CB、CCPerforming regression determination for shear yield condition parameters through at least 3 different constant average stress triaxial tests; q is generalized shear stress;
Figure FDA0002776964440000014
generalized shear strain; sigma1Is a large principal stress; sigma3Is a small principal stress; epsilon1Is a large principal strain; epsilon3In order to have a small principal strain,
(1) the shear yield function is in the form of formula (1), formula (2), formula (3) and formula (4), according to geotechnical test regulation SL237-1999, a constant mean stress triaxial test is adopted, corresponding monotonous loading tests are respectively carried out on the material through at least 3 different constant mean stresses, the monotonous loading conditions are the same as the loading conditions of the actual engineering, including loading rate, temperature, consolidation and drainage conditions,
Figure FDA0002776964440000015
ξs＝s-αs(Hs) (2)
Figure FDA0002776964440000016
Bs＝CAp2+CBp+CC (4)
(2) according to geotechnical test code SL237-1999, data are collected for each mean stress condition of a constant mean stress triaxial test and converted into principal stress sigma1、σ3And principal strain ε1、ε3The data of (a) to (b) to (c),
(3) σ is expressed according to the formulae (5) and (6)1、σ3、ε1And ε3Q-converted to each mean stress condition
Figure FDA0002776964440000017
The relationship between the two curves is shown in the graph,
q＝|σ1-σ3| (5)
Figure FDA0002776964440000018
(4) selecting one of the average stresses as a reference average stress within the average stress range of the engineering application, and correspondingly q < - >, of the reference average stress
Figure FDA0002776964440000019
The relation is q-at the reference mean stress
Figure FDA00027769644400000110
The relationship between the two curves is shown in the graph,
(5) selecting one of them in the strain range of engineering application
Figure FDA00027769644400000111
As a reference shear-hardening parameter,
(6) substituting q corresponding to the reference shear hardening parameter of each average stress into K in formula (7)s(ii) a Substituting q corresponding to the reference shear hardening parameter of the reference average stress into formula (7)
Figure FDA00027769644400000112
Substituting p in each average stress into formula (7) to form a linear equation set, wherein the number of the linear equations is equal to the number of the constant average stress triaxial tests,
Figure FDA00027769644400000113
(7) solving the linear equation set by solving the contradictory equation set to obtain the shearing yield condition parameter CA、CB、CC，
(8) Will shear yield condition parameter CA、CB、CCSubstituting the formula (1), the formula (3) and the formula (4) to obtain the shear yield function of the rock-soil material,
(9) q corresponding to each shear hardening parameter level at the time of reference average stress is substituted in formula (7)
Figure FDA0002776964440000021
C is to beA、CB、CCThe value of (3) is substituted for the formula (7), with p as the horizontal axis variable, KsIs a meridian plane with the longitudinal axis variable of formula (7)Drawing to obtain a regression curve of the shear yield surface of the rock-soil material,
measuring the shear part of the volume yield surface:
interpretation of the symbols in the following steps: f. ofv1Is an elliptical volume yield function when fv1Volume yield occurs at > 0, when fv1<No volume yield at 0; p is the mean stress; hvIs a volume hardening parameter; q is generalized shear stress; y isv1The volume yield stress at the actual principal stress difference is defined by formula (9); Δ p is the increment of the mean stress when Δ p>Loading in the forward direction at 0, when Δ p<Reverse loading is performed when the load is 0;
Figure FDA0002776964440000022
the bulk yield stress at which the primary stress difference is 0, defined by formula (10); b isv1A quadratic polynomial defined by formula (11); alpha is alphavIs the ball back stress tensor;
Figure FDA0002776964440000023
the volume isotropic hardening coefficient when the main stress difference is 0; cG、CH、CIThe parameters are elliptic volume yield condition parameters, and are determined by the regression of the actually measured volume yield surface of at least 3 different hardening parameter levels; sigma1Is a large principal stress; sigma3Is a small principal stress; p' is the effective mean stress; u is the pore water pressure and the pore water pressure,
(1) the elliptical volume yield function is in the form of formula (8), formula (9), formula (10) and formula (11), according to geotechnical test regulation SL237-1999, adopting a non-drainage triaxial test, respectively carrying out corresponding monotonous loading tests on the material through at least 3 different constant volume strains, wherein the monotonous loading conditions are the same as the loading conditions of the actual engineering, including loading rate and temperature,
Figure FDA0002776964440000024
Figure FDA0002776964440000025
Figure FDA0002776964440000026
Figure FDA0002776964440000027
wherein: alpha when considering follow-up hardeningvIs a variable, and is a function of,
Figure FDA0002776964440000028
alpha when the follow-up hardening is not consideredvTo be 0, only Δ p is calculated in the formulae (8) and (10)>In the case of the time point 0, the time point,
(2) according to geotechnical test code SL237-1999, data of each volume strain condition of the triaxial test are collected and converted into principal stress sigma1、σ3Main strain epsilon1、ε3And the pore water pressure u, and,
(3) σ is expressed according to the formulae (5), (12) and (13)1、σ3And u is converted into a q-p' relation curve of each volume strain condition on the meridian plane, the curve is the intersection line of the volume yield plane and the meridian plane of each confining pressure condition,
q＝|σ1-σ3| (5)
p＝(σ1+2σ3)/3 (12)
p′＝p-u (13)
(4) the shear portion of the volume yielding surface on the q-p 'relationship curve for each volume strain condition is selected to have a characteristic point representative in shape, which is not on the p' coordinate axis,
(5) substituting the abscissa of a point on the q-p' curve at a primary stress difference of 0 into that in equation (14)
Figure FDA0002776964440000029
Substituting the abscissa of a characteristic point selected by the shear part of the volume yielding surface on the q-p' relation curve except for the difference of the main stress of 0 into Y in the formula (14)v1(ii) a Substituting the ordinate of a characteristic point selected by the shear part of the volume yielding surface on the q-p' relation curve except the main stress difference of 0 into an equation (14) to form a linear equation set, wherein the number of the linear equations is equal to the number of the measured volume yielding surfaces of different hardening parameter levels,
Figure FDA0002776964440000031
(6) solving the linear equation set by solving the contradictory equation set to obtain the elliptic volume yield condition parameter CG、CH、CI，
(7) Subjecting the ellipse volume to yield condition parameter CG、CH、CISubstituting the formula (8), the formula (9), the formula (10) and the formula (11) to obtain the elliptical volume yield condition of the rock and soil material,
(8) by substituting p in formula (14) on the volume yield plane at a primary stress difference of 0
Figure FDA0002776964440000032
C is to beG、CH、CIIs substituted for formula (14) with q as the vertical axis variable, Yv1Plotting the variables of the horizontal axis on the meridian plane by the formula (14) to obtain a regression curve of the shear part of the volume yield surface of the rock-soil material,
measuring the volume yield surface shear swelling part:
interpretation of the symbols in the following steps: f. ofv2Is a hyperbolic volumetric yield function when fv2Volume yield occurs at > 0, when fv2<No volume yield at 0; p is the mean stress; hvIs a volume hardening parameter; q is generalized shear stress; y isv2The volume yield stress at the actual principal stress difference is defined by equation (16); Δ p is the increment of the mean stress when Δ p>Loading in the forward direction at 0, when Δ p<Reverse loading is performed when the load is 0;
Figure FDA0002776964440000033
the bulk yield stress at which the primary stress difference is 0, defined by formula (10); b isv2A quadratic polynomial defined for formula (17); alpha is alphavIs the ball back stress tensor;
Figure FDA0002776964440000034
the volume isotropic hardening coefficient when the main stress difference is 0; cD、CE、CF.Determining hyperbolic volume yield condition parameters through actually measured volume yield surface regression of at least 3 different hardening parameter levels; sigma1Is a large principal stress; sigma3Is a small principal stress; p' is the effective mean stress; u is the pore water pressure and the pore water pressure,
(1) hyperbolic volume yield functions are in the forms of formula (15), formula (16), formula (10) and formula (17), according to geotechnical test regulation SL237-1999, a non-drainage triaxial test is adopted, corresponding monotonous loading tests are respectively carried out on the material through at least 3 different constant volume strains, the monotonous loading conditions are the same as the loading conditions of actual engineering, including loading rate and temperature,
Figure FDA0002776964440000035
Figure FDA0002776964440000036
Figure FDA0002776964440000037
Figure FDA0002776964440000038
wherein: alpha when considering follow-up hardeningvIs a variable, and is a function of,
Figure FDA0002776964440000039
alpha when the follow-up hardening is not consideredvTo be 0, only Δ p is calculated in the equations (15) and (10)>In the case of the time point 0, the time point,
(2) according to geotechnical test code SL237-1999, data of each volume strain condition of the triaxial test are collected and converted into principal stress sigma1、σ3Main strain epsilon1、ε3And the pore water pressure u, and,
(3) σ is expressed according to the formulae (5), (12) and (13)1、σ3And u is converted into a q-p' relation curve of each volume strain condition on the meridian plane, the curve is the intersection line of the volume yield plane and the meridian plane of each confining pressure condition,
q＝|σ1-σ3| (5)
p＝(σ1+2σ3)/3 (12)
p′＝p-u (13)
(4) selecting a characteristic point representative in shape for the shear-expansion portion of the volume yielding surface on the q-p 'relation curve of each volume strain condition, the characteristic point being not on the p' coordinate axis,
(5) substituting the abscissa of a point on the q-p' curve at a primary stress difference of 0 into that in equation (18)
Figure FDA0002776964440000041
Substituting the abscissa of a characteristic point selected by the shear-swelling part of the volume yielding surface on the q-p' relation curve except for the difference of the main stress of 0 into Y in the formula (18)v2(ii) a Substituting the ordinate of a characteristic point selected by the shear-expansion part of the volume yielding surface on the q-p' relation curve except for the main stress difference of 0 into an equation (18) to form a linear equation set, wherein the number of the linear equations is equal to the number of the actually measured volume yielding surfaces with different hardening parameter levels,
Figure FDA0002776964440000042
(6) solving the linear equation set by solving the contradictory equation set to obtain the hyperbolic volume yield condition parameter CD、CE、CF，
(7) Hyperbolic volume yield condition parameter CD、CE、CFSubstituting the equations (15), (16), (10) and (17) to obtain hyperbolic volume yield condition of the rock-soil material,
(8) by substituting p in formula (18) on the volume yield plane at a primary stress difference of 0
Figure FDA0002776964440000043
C is to beD、CE、CFIs substituted for the value of (18) with q as the vertical axis variable, Yv2And (3) drawing the formula (18) on the meridian plane by using the variable of the horizontal axis to obtain a regression curve of the shear-swelling part of the volume yield surface of the rock-soil material.
2. The method for measuring shear yield surface and volume yield surface of geotechnical material according to claim 1, wherein when the average stress is not controlled to be constant during the triaxial tester's test, the shear yield surface is measured by using the equivalent constant average stress triaxial test method,
the method for measuring the shear yield surface by the equivalent constant average stress triaxial test method comprises the following steps:
interpretation of the symbols in the following steps: f. ofsFor shear yield function, when fsShear yielding occurs when f is greater than or equal to 0s<No shear yield occurs at 0; xisIs relative bias stress and is defined by formula (2); hsIs a shear hardening parameter; p is the mean stress; ksThe shear isotropic hardening coefficient at the actual average stress is defined by formula (3); s is the bias stress tensor; alpha is alphasAlpha when considering follow-up hardening for the bias back stress tensorsAs a variable, alpha when the follow-up hardening is not taken into accountsIs 0;
Figure FDA0002776964440000044
shear isotropic hardening coefficient for reference mean stressWhen the curing is considered to be isotropic
Figure FDA0002776964440000045
As a variable, when isotropic hardening is not considered
Figure FDA0002776964440000046
Is a set constant; b issA quadratic polynomial defined by formula (4); cA、CB、CCPerforming regression determination for shear yield condition parameters through at least 3 different constant average stress triaxial tests; q is generalized shear stress;
Figure FDA0002776964440000047
generalized shear strain; sigma1Is a large principal stress; sigma3Is a small principal stress; epsilon1Is a large principal strain; epsilon3In order to have a small principal strain,
(1) the shear yield function is in the form of formula (1), formula (2), formula (3) and formula (4), according to geotechnical test regulation SL237-1999, the conventional triaxial compression test is adopted, the material is respectively subjected to corresponding monotonous loading tests through at least 3 different constant confining pressures, the monotonous loading condition is the same as the loading condition of the actual engineering, including loading rate, temperature, consolidation and drainage condition,
Figure FDA0002776964440000048
ξs＝s-αs(Hs) (2)
Figure FDA0002776964440000051
Bs＝CAp2+CBp+CC (4)
(2) according to geotechnical test code SL237-1999, data of each confining pressure condition of the conventional triaxial compression test is collected and converted into main stress sigma1、σ3And principal strain ε1、ε3The data of (a) to (b) to (c),
(3) σ is expressed according to the formulae (5) and (6)1、σ3、ε1And ε3Q-converted into each confining pressure condition
Figure FDA0002776964440000052
The relationship between the two curves is shown in the graph,
q＝|σ1-σ3| (5)
Figure FDA0002776964440000053
(4) σ is expressed according to the formula (5) and the formula (12)1And σ3Converted into a q-p relation curve which is loaded monotonously on the meridian plane,
p＝(σ1+2σ3)/3 (12)
(5) interpolating and extrapolating the shear hardening parameter equipotential points of the q-p relation curve on the meridian plane to form a shear hardening parameter equipotential line,
(6) respectively setting stress path lines of the triaxial test with equivalent constant average stress within the average stress range of each stress path of the conventional triaxial compression test, wherein the lines are parallel to the meridian plane ordinate axis,
(7) the shear hardening parameter equipotential line is crossed with the set equivalent constant average stress triaxial test stress path line, the intersection point of the two lines is the equivalent constant average stress triaxial test stress path characteristic point,
(8) in the average stress range of engineering application, the average stress of one equivalent constant average stress triaxial test stress path line is selected as the reference average stress,
(9) selecting one of the shear hardening parameters equipotential lines within the strain range of the engineering application
Figure FDA0002776964440000054
As a reference shear-hardening parameter,
(10) in the equivalenceIn the range of the stress path characteristic point of the constant average stress triaxial test, q corresponding to the reference shear hardening parameter of each average stress is substituted into K in the formula (7)s(ii) a Substituting q corresponding to the reference shear hardening parameter of the reference average stress into formula (7)
Figure FDA0002776964440000055
Substituting p in each average stress into formula (7) to form a linear equation set, wherein the number of the linear equations is equal to the number of the equivalent constant average stress triaxial tests,
Figure FDA0002776964440000056
(11) solving the linear equation set by solving the contradictory equation set to obtain the shearing yield condition parameter CA、CB、CC，
(12) Will shear yield condition parameter CA、CB、CCSubstituting the formula (1), the formula (3) and the formula (4) to obtain the shear yield function of the rock-soil material,
(13) q corresponding to each shear hardening parameter level at the time of reference average stress is substituted in formula (7)
Figure FDA0002776964440000057
C is to beA、CB、CCThe value of (3) is substituted for the formula (7), with p as the horizontal axis variable, KsAnd (4) plotting the formula (7) on the meridian plane for the longitudinal axis variable to obtain a regression curve of the shear yield surface of the rock-soil material.
3. The application of the parameters measured by the method for measuring the shear yield surface and the volume yield surface of the geotechnical material according to claim 1 in evaluating the shear yield surface of the geotechnical material is characterized by comprising the following steps:
(1) to follow the hardening law, the off-back stress tensor α is used in the algorithmsIs shown as
αs.n+1＝αs.n+Δαs.n+1 (19)
Figure FDA0002776964440000061
Wherein: subscriptnRefers to the last increment; subscriptn+1Is referred to as the present increment; the symbol Δ means that the variable is in increments; t is time;
Figure FDA0002776964440000062
from a particular follow-up hardening law,
(2) in order to connect the equi-hardening law, the equi-hardening coefficient in confining pressure is referenced in the algorithm
Figure FDA0002776964440000063
Is shown as
Figure FDA0002776964440000064
Figure FDA0002776964440000065
Wherein:
Figure FDA0002776964440000066
from a particular isotropic hardening law,
(3) checking and calculating shear yield condition
Figure FDA0002776964440000067
When f iss.n+1The increment generates shear yield when the increment is more than or equal to 0; when f iss.n+1<At 0 this increment no shear yield occurs.
4. The use of the parameters measured by the method for measuring shear yield surface and volume yield surface of geotechnical materials according to claim 1 in evaluating the volume yield surface of geotechnical materials, which is characterized in that, the application steps are,
(1) to follow the hardening law, the off-back stress tensor α is used in the algorithmvIs shown as
αv.n+1＝αv.n+Δαv.n+1 (24)
Figure FDA0002776964440000068
Wherein: subscriptnRefers to the last increment; subscriptn+1Is referred to as the present increment; the symbol Δ means that the variable is in increments; t is time;
Figure FDA0002776964440000069
from a particular follow-up hardening law,
(2) in order to connect the equi-hardening law, the equi-hardening coefficient of the algorithm when the main stress difference is used as a reference
Figure FDA00027769644400000610
Is shown as
Figure FDA00027769644400000611
Figure FDA00027769644400000612
Wherein:
Figure FDA00027769644400000613
from a particular isotropic hardening law,
(3) checking elliptic volume yield condition and hyperbolic volume yield condition
Figure FDA00027769644400000614
Figure FDA00027769644400000615
Figure FDA00027769644400000616
Figure FDA00027769644400000617
Figure FDA0002776964440000071
When f isv1.n+1F is not less than 0v2.n+1When the increment is more than or equal to 0, the volume yield is generated; in other cases, the present increment does not yield volumetrically.
CN201910055005.7A 2019-01-21 2019-01-21 Method for measuring shear yield surface and volume yield surface of rock and soil material Active CN109580388B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910055005.7A CN109580388B (en) 2019-01-21 2019-01-21 Method for measuring shear yield surface and volume yield surface of rock and soil material

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910055005.7A CN109580388B (en) 2019-01-21 2019-01-21 Method for measuring shear yield surface and volume yield surface of rock and soil material

Publications (2)

Publication Number Publication Date
CN109580388A CN109580388A (en) 2019-04-05
CN109580388B true CN109580388B (en) 2021-01-29

Family

ID=65917308

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910055005.7A Active CN109580388B (en) 2019-01-21 2019-01-21 Method for measuring shear yield surface and volume yield surface of rock and soil material

Country Status (1)

Country Link
CN (1) CN109580388B (en)

Families Citing this family (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110096809B (en) * 2019-04-30 2023-03-14 中煤科工集团重庆研究院有限公司 Modeling method for material unstable roadway rock burst based on double-yield contour model
CN110702513B (en) * 2019-10-15 2021-06-18 吉林大学 A test method for measuring hardening curve of metal bar with large strain range
CN111077027B (en) * 2019-12-13 2022-04-29 天津大学 Method for determining shear strength of calcareous sand under high stress
CN111783282B (en) * 2020-06-12 2022-10-21 广西大学 A Simulation Method for Accumulated Vibration Deformation of Materials Based on Nonlinear Variation of Compression Stiffness and Abrupt Shrinkage Characteristics
CN111783332B (en) * 2020-06-12 2022-10-21 广西大学 Finite element simulation method for vibration accumulation deformation of compression non-linear change and shear sudden change characteristic material
CN112432849B (en) * 2020-10-13 2021-09-07 北京交通大学 A method for predicting wood shear strength based on wood compressive strength
CN112858042B (en) * 2020-12-31 2022-10-18 浙江工业大学 A monotonic shear behavior detection method for clean sand and silt based on monotonic triaxial

Family Cites Families (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6205366B1 (en) * 1999-09-14 2001-03-20 Ford Global Technologies, Inc. Method of applying the radial return method to the anisotropic hardening rule of plasticity to sheet metal forming processes
JP5866892B2 (en) * 2011-09-06 2016-02-24 Ｊｆｅスチール株式会社 Stress-strain relationship evaluation method and springback amount prediction method
CN105181435B (en) * 2015-10-15 2016-04-06 中国石油大学(华东) A Construction Method of Elastoplastic Constitutive Model of Rock Material
CN105259035B (en) * 2015-10-26 2016-05-11 中国石油大学(华东) A Construction Method of Aging-Elastoplastic Constitutive Model of Rock Material
CN108280244A (en) * 2017-01-06 2018-07-13 黄瑞源 A kind of exact algorithm of material constitutive relation without iteration
CN107894367A (en) * 2017-10-30 2018-04-10 国家电网公司 A kind of transmission line of electricity collapsible loess constitutive modeling method
CN107860655A (en) * 2017-10-30 2018-03-30 国家电网公司 A kind of overhead transmission line collapsible loess foundation ess-strain simulates method
CN108520158B (en) * 2018-04-26 2019-04-23 山东大学 A cyclic hyperbolic elastic-plastic soil constitutive model and its application method
CN108760463B (en) * 2018-06-13 2020-06-26 广西大学 Model test method for triaxial compression test of soil

Also Published As

Publication number Publication date
CN109580388A (en) 2019-04-05

Similar Documents

Publication Publication Date Title
CN109580388B (en) Method for measuring shear yield surface and volume yield surface of rock and soil material
US10712252B2 (en) Reservoir depletion/injection simulation under true triaxial stress conditions
CN105181435B (en) A Construction Method of Elastoplastic Constitutive Model of Rock Material
Vaid et al. A critical assessment of membrane penetration in the triaxial test
Schapery Deformation and fracture characterization of inelastic composite materials using potentials
O'SULLIVAN et al. Discrete element analysis of the response of granular materials during cyclic loading
Yang et al. Cavity expansion in unsaturated soils exhibiting hydraulic hysteresis considering three drainage conditions
Xu et al. A large triaxial investigation of the stress-path-dependent behavior of compacted rockfill
CN110926944B (en) A method for constructing a constitutive model of rock damage under cyclic loading
Goodman et al. Finite element analysis for discontinuous rocks
CN104794365A (en) Computation method for predicting ultimate bearing capacity of anchor rod based on mathematical model
Prévost Undrained shear tests on clays
CN111783282B (en) A Simulation Method for Accumulated Vibration Deformation of Materials Based on Nonlinear Variation of Compression Stiffness and Abrupt Shrinkage Characteristics
Yan et al. Dynamic Properties of Plain Concrete in Triaxial Stress State.
Scherer Dynamic pressurization method for measuring permeability and modulus: I. Theory
Zhou et al. A new wetting deformation simulation method based on changes in mechanical properties
Atkinson et al. The effect of local drainage in shear zones on the undrained strength of overconsolidated clay
Schmidt et al. Experimental and theoretical investigation of the high‐pressure behavior of concrete
Jia et al. Laboratory investigations of inert gas flow behaviors in compact sandstone
Sivathayalan Fabric, initial state and stress path effects on liquefaction susceptibility of sands
CN111783332B (en) Finite element simulation method for vibration accumulation deformation of compression non-linear change and shear sudden change characteristic material
Jones et al. Interpretation of tangential and radial pressure cells in and on sprayed concrete tunnel linings
Wang et al. Development and application of a large-scale static and dynamic true triaxial apparatus for gravel
Liu et al. A new test method and system for the circumferential deformation of cylindrical standard specimens in geotechnical mechanics and its application
Chen et al. Influence of intermediate principal stress on the strength and deformation behavior of artificial frozen sand

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant