CN109580388A - A kind of measuring method in rock-soil material shear yielding face and volume yield surface - Google Patents
A kind of measuring method in rock-soil material shear yielding face and volume yield surface Download PDFInfo
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- 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
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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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。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.
Description
Technical field
The invention belongs to the fields of metering of solids deformation, especially a kind of rock-soil material shear yielding face and volume yield surface
Measuring method.
Background technique
The stress deformation for predicting rock-soil material first has to the constitutive model for establishing rock-soil material.Establish rock-soil material
Constitutive model, first have to measurement rock-soil material shear yielding face and volume yield surface.
Currently, a large amount of geotechnical engineering test results, which show that the shear yielding face of rock-soil material has, is not passed through meridian plane original
The trend of point and the characteristic for increasing non-linear expansion with mean stress in π plane；Volume yield surface cuts contracting part and meridian
The characteristic that there is the intersection in face its slope to change with mean stress increase；The friendship for cutting swollen part with meridian plane of volume yield surface
Line has the not characteristic for straight line.
From Nanjing sand (Nanjing Zhu Jianqun, Kong Lingwei, Zhong Fangjie sand strength characteristic and static liquefaction phenomenon analysis [J] rock
Soil mechanics, 2008,29 (6): 1461-1465.), (Ding Hao, Huang Bo, Chen Yunmin wait to be saturated for the sample that do not drain of Fujian standard sand
Research [J] geotechnical engineering journal of back-pressure setting and shearing strength, 2012,34 (7): 1313- in sand triaxial test
1319.), ([D] is studied in influence of the stress path to saturated sand mechanical characteristic to Xuzhou Lin Jiaba sand factory sand under the emerging high pressure of road
China Mining University, 2014.), (Kong Gangqiang, Liu Lu, Liu Hanlong wait the transparent native deformation characteristic three of glass sand to the transparent soil of glass sand
Shaft experiment study [J] geotechnical engineering journal, 2013, (6): 1140-1146.), (Ma Ling, Qi Jilin, Yu Fan wait to Frozen Sand
In Frozen Sand triaxial test Particle Breakage study [J] geotechnical engineering journal, 2015,37 (3): 544-550.), Jiangsu sea sand
(Li Shue, Jin Mingdong, Chen Zhiming wait sea sand soil Study on Triaxial Tests [J] low temperature Building technology, 2013,35 (7): 18- to soil
19.) observe that the shear yielding face in π plane increases showing for non-linear expansion of slowing down with mean stress in triaxial test
As；And from the draining sample of Fujian standard sand, (Guo Ying, Han Jie shear fine sand CU close in saturation at quadrat method and stress path
Characteristic influences [J] geotechnical engineering journal, 2016,38 (s2): 79-84.) (Luo Aizhong, Shao Shengjun, Wang Taotao .XAGT-1 type are true
Triaxial cell is structurally consummate and saturated sand true triaxial test [J] science and technology and engineering, 2014,14 (19): 283-
288.), Feng Pusha (Qin Liman based on energy dissipation Soil Constitutive Relation study [D] Dalian University of Technology, 2006.), certain
(Wei Song, Zhu Jungao, Wang Junjie wait the steady state strength unconsolidated-undrained triaxial test of sand to study [J] rock to earth dam sand
Stone mechanics and engineering journal, 2005,24 (22): 4151-4157.), (Wei Houzhen, Yan Rongtao, Chen Pan wait different to certain silty sand
Hemihydrate content carbonated hydrate sand Study on Triaxial Tests [J] rock-soil mechanics, 2011,32 (S2): 198-203.)
It is observed in triaxial test the phenomenon that the shear yielding face in π plane increases non-linear acceleration expansion with mean stress.From upper
All tests stated are, it is also observed that shear yielding face has the tendency that being not passed through meridian plane origin.
From Fujian standard sand, (Ding Hao, Huang Bo, Chen Yunmin wait back-pressure setting and shearing strength in saturated sand triaxial test
Research [J] geotechnical engineering journal, 2012,34 (7): 1313-1319.), Xuzhou Lin Jiaba sand factory sand is (under the emerging high pressure of road
[D] China Mining University is studied in influence of the stress path to saturated sand mechanical characteristic, 2014.) it is observed in triaxial test
Cut the contracting part and the intersection of meridian plane of volume yield surface have the phenomenon that its slope reduces with mean stress increase；From Feng Pu
Sand (Soil Constitutive Relation research [D] Dalian University of Technology of the Qin Liman based on energy dissipation, 2006.), certain earth dam sand
(Wei Song, Zhu Jungao, Wang Junjie wait the steady state strength unconsolidated-undrained triaxial test of sand to study [J] rock mechanics and work to soil
Journey journal, 2005,24 (22): 4151-4157.), Nanjing sand (Nanjing Zhu Jianqun, Kong Lingwei, Zhong Fangjie sand strength characteristic with it is quiet
State liquefaction phenomenon analyzes [J] rock-soil mechanics, 2008,29 (6): 1461-1465.) triaxial test in observe the slope with flat
The phenomenon that equal stress increases and increases；From Fujian standard sand, (Guo Ying, Han Jie are at quadrat method and stress path to close thin in saturation
Sand CU shear property influence [J] geotechnical engineering journal, 2016,38 (s2): 79-84.) constant mean stress triaxial test see
The slope is observed to increase with mean stress and first reduce the phenomenon that increasing afterwards；From the Nanjing sand (south Zhu Jianqun, Kong Lingwei, Zhong Fangjie
Capital sand strength characteristic and static liquefaction phenomenon analysis [J] rock-soil mechanics, 2008,29 (6): 1461-1465.) triaxial test see
Observe the slope with mean stress increase and the phenomenon that first increases and then decreases.From Fujian standard sand (Ding Hao, Huang Bo, Chen Yunmin,
Research [J] geotechnical engineering journal of back-pressure setting and shearing strength in equal saturated sand triaxial test, 2012,34 (7):
1313-1319.) (Guo Ying, Han Jie influence [J] ground to fine sand CU shear property close in saturation at quadrat method and stress path
Engineering journal, 2016,38 (s2): 79-84.), the Nanjing sand (Nanjing Zhu Jianqun, Kong Lingwei, Zhong Fangjie sand strength characteristic and static
Liquefaction phenomenon analyze [J] rock-soil mechanics, 2008,29 (6): 1461-1465.) triaxial test, it is also observed that volume yield surface
Cut swollen part and the intersection of meridian plane be not straight line.
Describing yield surface of the material in π plane has Huo Ke-Bo Lang item with the theory that mean stress increases non-linear expansion
Part (Hoek E., Carranza-Torres C., Corkum B..Hoek-Brown failure criterion-
2002edition[C]//Proceedings of the Fifth North American Rock Mechanics
Symposium.Toronto, 2002:18-22.), desai model (Desai C.S., Gallagher R.H..Mechanics
Of Engineering Materials [M] .London:John Wiley and Sons, 1984.), ladd enclosed type list is bent
Take surface model (Kim M.K., Lade P.V..Single hardening constitutive model for
frictional materials:I.Plastic potential Function[J].Computers&Geotechnics,
1988,5(4):307-324.)(Lade P.V.,Kim M.K..Single hardening constitutive model
for frictional materials II.Yield critirion and plastic work contours[J]
.Computers&Geotechnics, 1988,6 (1): 13-29.), ladd two yield surface model (Lade P.V..Elasto-
plastic stress-strain theory for Cohesionless soil with curved yield surfaces
[J] .International Journal ofSolids&Structures, 1977,13 (11): 1019-1035.), " Nan Shui "
Model (elastic-plastic analysis [J] Chinese science A volumes of (mathematics, physics, astronomy, skills of Shen Zhujiang Soft Soil Consolidation deformation
Subject), 1985,28 (11): 1049-1060.), " rear work " model (multiple yield surface theory and strain of Zheng Ying people's ground
Space Theory [the C] // Shenyang rock mechanics new development, 1989.), etc..Wherein " rear work " model application is wider, and shearing is bent
The condition of clothes describes shear yielding face and increases non-linear expansion with mean stress, and the speed of expansion declines with the increase of mean stress
Subtract, but shear yielding face of the rock-soil material in π plane can not be described and increase non-linear acceleration expansion with mean stress.Simultaneously should
Shear yielding condition describes the origin that shear yielding face passes through meridian plane, this cuts for the rock-soil material of higher cohesive strength for having
The regression effect for cutting yield surface is not good enough.In addition the volume yield condition of " rear work " model describe volume yield surface cut swollen part with
The intersection of meridian plane is straight line, this causes the regression effect of the volume yield surface of rock-soil material not good enough.
Chinese invention patent application 201611094782.5 discloses a kind of measuring method of metal material yield surface, uses
Pre-stretching-torsional deflection load path measures subsequent yield surface Evolution.This method is not suitable for rock-soil material.Ground material
The shear yielding face of material increases with mean stress and is expanded, and metal material does not have this property usually, and the document is not also examined
Consider this property.Shear yielding can not only occur for rock-soil material, but also volume surrender can occur, and metal material does not have this usually
Kind property, the document do not account for this property yet.
Chinese invention patent application 201710312003.2 discloses a kind of cross tensile pre-deformation load measurement yield surface
Method, using other direction after a direction pre-tension deformation redraw deformation load path measure yield surface.This method is not
Suitable for rock-soil material.The shear yielding face of rock-soil material increases with mean stress and is expanded, and metal material does not have this usually
Kind property, the document do not account for this property yet.Shear yielding can not only occur for rock-soil material, but also volume can occur and bend
Clothes, metal material do not have this property usually, and the document does not account for this property yet.
Chinese invention patent application 201710611974.7 discloses a kind of point of predetermined period lattice material yield surface
Analysis method considers the coupling effect of internal structure axle power and moment of flexure when material actual loading, obtains the period first with theory deduction
Property lattice material representative volume element yield condition, then utilize finite element analysis software, programming realize high-volume total calculation.It should
Method is not suitable for rock-soil material.The shear yielding face of rock-soil material increases with mean stress and is expanded, and the document does not account for
This property.Shear yielding can not only occur for rock-soil material, but also volume surrender can occur, and the document does not account for this property
Matter.
Summary of the invention
The object of the present invention is to provide the measuring method in a kind of rock-soil material shear yielding face and volume yield surface, shearing is bent
Taking face and volume yield surface can judge that rock-soil material is surrendered after stress with the presence or absence of shear yielding or volume in engineering, with
Just corresponding measure is taken, prevents material from generating destruction, causes across the accident of collapsing.
The present invention reaches measurement rock-soil material shear yielding face and volume yield surface by constant mean stress triaxial test
Purpose, this need triaxial tester control in test mean stress be steady state value.Wherein the mean stress is known
Concept, refer to the average value of three principal stresses of material.The occurrence for the mean stress that triaxial tester controls in test
It is equal with the occurrence of the mean stress of rock-soil material in Practical Project, and the mean stress for the overall process tested is steady state value,
This technology is the prior art.
The present invention reaches above-mentioned purpose by the following technical programs: a kind of rock-soil material shear yielding face and volume yield surface
Measuring method, determination step, volume yield surface including shear yielding face cut the determination step and volume yield surface of contracting part
The determination step for cutting swollen part, when it is constant that triaxial tester, which can control mean stress,
The determination step in shear yielding face are as follows:
The explanation of symbol in following steps: fsFor shear yielding function, work as fsShear yielding occurs when >=0, works as fsWhen < 0
Shear yielding does not occur；ξsFor opposite deviatoric stress, defined by formula (2)；HsFor shear hardening parameter；P is mean stress；KsFor reality
Shearing isotropic hardening coefficient when the mean stress of border is defined by formula (3)；S is deviatoric stress tensor；αsFor inclined back stress tensor, when
Consider α when kinematic hardeningsFor variable, the α when not considering kinematic hardeningsIt is 0；Shearing when for benchmark mean stress etc. is to hard
Change coefficient, when considering isotropic hardeningFor variable, when not considering isotropic hardeningFor the constant of setting；BsIt is fixed for formula (4)
The quadratic polynomial of justice；CA、CB、CCFor shear yielding conditional parameter, pass through the different constant mean stress triaxial tests of at least three
Carry out recurrence determination；Q is generalized shear stress；For General architecture；σ1For big principal stress；σ3For minor principal stress；ε1It is answered for master greatly
Become；ε3For small principal strain.
(1) form of shear yielding function is formula (1), formula (2), formula (3) and formula (4), according to " earthwork test rule "
SL237-1999 respectively carries out material by the different constant mean stresses of at least three using constant mean stress triaxial test
Corresponding monotonic loading test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature, solid
Knot and drainage condition.
ξs=s- αs(Hs) (2)
Bs=CAp2+CBp+CC (4)
(2) it according to " earthwork test rule " SL237-1999, acquires each of constant mean stress triaxial test and averagely answers
The data of power condition, and it is converted into principal stress σ1、σ3With principal strain ε1、ε3Data.
(3) according to formula (5) and formula (6) by σ1、σ3、ε1And ε3It is converted into each mean stress conditionRelationship is bent
Line.
Q=| σ1-σ3| (5)
(4) within the scope of the mean stress of engineer application, select one of mean stress as benchmark mean stress, phase
It answersWhen relation curve is benchmark mean stressRelation curve.
(5) in the range of strain of engineer application, one of them is selectedAs reference shear hardening parameter.
(6) the corresponding q of the reference shear hardening parameter of each mean stress is substituted into the K in formula (7)s；Benchmark is averagely answered
The corresponding q of the reference shear hardening parameter of power is substituted into formula (7)P when by each mean stress substitutes into formula (7).Form line
Property equation group, the quantity of linear equation are equal with the quantity of constant mean stress triaxial test.
(7) system of linear equations is solved with the method for solving inconsistent equation group, obtains shear yielding conditional parameter CA、CB、CC。
(8) by shear yielding conditional parameter CA、CB、CCIn generation, returns formula (1), formula (3) and formula (4), obtains the shearing of rock-soil material
Yield condition.
(9) by benchmark mean stress the horizontal corresponding q of each shear hardening parameter is substituted into respectively in formula (7) whenBy CA、
CB、CCValue and substitute into formula (7).Using p as horizontal axis variable, KsIt is that formula (7) draw on meridian plane for longitudinal axis variable, obtains ground
The regression curve in the shear yielding face of material.
Volume yield surface cuts the determination step of contracting part:
The explanation of symbol in following steps: fv1For oval volume yield function, work as fv1Volume surrender occurs when >=0, works as fv1
Volume surrender does not occur when < 0；P is mean stress；HvFor volume hardening parameter；Q is generalized shear stress；Yv1For practical principal stress
Volume yield stress when poor is defined by formula (9)；Δ p is the increment of mean stress, is positive load as Δ p > 0, as Δ p
It is Opposite side loading when < 0；Volume yield stress when for deviator stress being 0 is defined by formula (10)；Bv1For formula (11) definition
Quadratic polynomial；αvFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；CG、CH、CIFor
Oval volume yield condition parameter is returned by the actual measurement volume yield surface of at least three difference hardening parameter level and is determined；σ1For
Big principal stress；σ3For minor principal stress；P ' is effective mean stress；U is pore water pressure.
(1) form of oval volume yield function is formula (8), formula (9), formula (10) and formula (11), according to " soil test is advised
Journey " SL237-1999, using the triaxial test not drained, respectively by the strain of at least three difference constant volume to material progress
Corresponding monotonic loading test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature.
Wherein: the α when considering kinematic hardeningvFor variable,The α when not considering kinematic hardeningvIt is 0, formula (8)
The case where when only calculating Δ p > 0 with formula (10).
(2) according to " earthwork test rule " SL237-1999, the data of each bulk strain condition of triaxial test are acquired,
And it is converted into principal stress σ1、σ3, principal strain ε1、ε3With the data of pore water pressure u.
(3) according to formula (5), formula (12) and formula (13) by σ1、σ3Each bulk strain item on meridian plane is converted into u
Q-p ' relation curve of part, the curve are the volume yield surface of each confining pressure condition and the intersection of meridian plane.
Q=| σ1-σ3| (5)
P=(σ1+2σ3)/3 (12)
P '=p-u (13)
(4) the volume yield surface on q-p ' relation curve of each bulk strain condition cut contracting part selection one
Representative characteristic point in shape, this feature point is not in p ' reference axis.
(5) by deviator stress be 0 when q-p ' relation curve on point abscissa substitute into formula (14) inIt will remove
Deviator stress is that the volume yield surface on q-p ' relation curve outside 0 cuts the abscissa of the selected characteristic point in contracting part
Y in substitution formula (14)v1；Volume yield surface on q-p ' relation curve in addition to deviator stress is 0 is cut selected by contracting part
A characteristic point ordinate substitute into formula (14).Form system of linear equations, the quantity of linear equation and different hardening parameter water
The quantity of flat actual measurement volume yield surface is equal.
(6) system of linear equations is solved with the method for solving inconsistent equation group, obtains oval volume yield condition parameter CG、CH、
CI。
(7) by oval volume yield condition parameter CG、CH、CIIn generation, returns formula (8), formula (9), formula (10) and formula (11), obtains rock
The oval volume yield condition of soil material.
(8) by deviator stress be 0 when volume yield surface on p substitute into formula (14) inBy CG、CH、CIValue and substitution
Formula (14).Using q as longitudinal axis variable, Yv1It is that formula (14) draw on meridian plane for horizontal axis variable, the volume for obtaining rock-soil material is bent
Cut the regression curve of contracting part in the face of clothes.
Volume yield surface cuts the determination step of swollen part:
The explanation of symbol in following steps: fv2For hyperbola volume yield function, work as fv2Volume surrender occurs when >=0, when
fv2Volume surrender does not occur when < 0；P is mean stress；HvFor volume hardening parameter；Q is generalized shear stress；Yv2It is answered for practical master
Volume yield stress when power difference is defined by formula (16)；Δ p is the increment of mean stress, is positive load as Δ p > 0, when
It is Opposite side loading when Δ p < 0；Volume yield stress when for deviator stress being 0 is defined by formula (10)；Bv2It is fixed for formula (17)
The quadratic polynomial of justice；αvFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；CD、CE、CF.
For hyperbola volume yield condition parameter, is returned and determined by the actual measurement volume yield surface of at least three difference hardening parameter level；
σ1For big principal stress；σ3For minor principal stress；P ' is effective mean stress；U is pore water pressure.
(1) form of hyperbola volume yield function is formula (15), formula (16), formula (10) and formula (17), according to " geotechnique tries
Test regulation " SL237-1999, using the triaxial test not drained, respectively by the strain of at least three difference constant volume to material
Carry out corresponding monotonic loading test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature
Degree.
Wherein: the α when considering kinematic hardeningvFor variable,The α when not considering kinematic hardeningvIt is 0, formula (15)
The case where when only calculating Δ p > 0 with formula (10).
(2) according to " earthwork test rule " SL237-1999, the data of each bulk strain condition of triaxial test are acquired,
And it is converted into principal stress σ1、σ3, principal strain ε1、ε3With the data of pore water pressure u.
(3) according to formula (5), formula (12) and formula (13) by σ1、σ3Each bulk strain item on meridian plane is converted into u
Q-p ' relation curve of part, the curve are the volume yield surface of each confining pressure condition and the intersection of meridian plane.
Q=| σ1-σ3| (5)
P=(σ1+2σ3)/3 (12)
P '=p-u (13)
(4) the volume yield surface on q-p ' relation curve of each confining pressure condition cuts swollen part selection one in shape
Upper representative characteristic point, this feature point is not in p ' reference axis.
(5) by deviator stress be 0 when q-p ' relation curve on point abscissa substitute into formula (18) inIt will remove
Deviator stress is that the volume yield surface on q-p ' relation curve outside 0 cuts the abscissa of the selected characteristic point in swollen part
Y in substitution formula (18)v2；Volume yield surface on q-p ' relation curve in addition to deviator stress is 0 is cut selected by swollen part
A characteristic point ordinate substitute into formula (18).Form system of linear equations, the quantity of linear equation and different hardening parameter water
The quantity of flat actual measurement volume yield surface is equal.
(6) system of linear equations is solved with the method for solving inconsistent equation group, obtains hyperbola volume yield condition parameter CD、
CE、CF。
(7) by hyperbola volume yield condition parameter CD、CE、CFIn generation, returns formula (15), formula (16), formula (10) and formula (17), obtains
To the hyperbola volume yield condition of rock-soil material.
(8) by deviator stress be 0 when volume yield surface on p substitute into formula (18) inBy CD、CE、CFValue and substitution
Formula (18).Using q as longitudinal axis variable, Yv2It is that formula (18) draw on meridian plane for horizontal axis variable, the volume for obtaining rock-soil material is bent
Cut the regression curve of swollen part in the face of clothes.
When it is constant that triaxial tester, which is unable to control mean stress, surveyed using equivalent constant mean stress triaxial (test) method
Determine shear yielding face,
The step of equivalent constant mean stress triaxial (test) method measurement shear yielding face are as follows:
The explanation of symbol in following steps: fsFor shear yielding function, work as fsShear yielding occurs when >=0, works as fsWhen < 0
Shear yielding does not occur；ξsFor opposite deviatoric stress, defined by formula (2)；HsFor shear hardening parameter；P is mean stress；KsFor reality
Shearing isotropic hardening coefficient when the mean stress of border is defined by formula (3)；S is deviatoric stress tensor；αsFor inclined back stress tensor, when
Consider α when kinematic hardeningsFor variable, the α when not considering kinematic hardeningsIt is 0；Shearing when for benchmark mean stress etc. is to hard
Change coefficient, when considering isotropic hardeningFor variable, when not considering isotropic hardeningFor the constant of setting；BsIt is fixed for formula (4)
The quadratic polynomial of justice；CA、CB、CCFor shear yielding conditional parameter, pass through the different constant mean stress triaxial tests of at least three
Carry out recurrence determination；Q is generalized shear stress；For General architecture；σ1For big principal stress；σ3For minor principal stress；ε1It is answered for master greatly
Become；ε3For small principal strain.
(1) form of shear yielding function is formula (1), formula (2), formula (3) and formula (4), according to " earthwork test rule "
SL237-1999 respectively carries out material by least three difference constant confining pressure corresponding dull using conventional triaxial compression test
Load test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature, consolidation and draining
Condition.
ξs=s- αs(Hs) (2)
Bs=CAp2+CBp+CC (4)
(2) according to " earthwork test rule " SL237-1999, each confining pressure condition of conventional triaxial compression test is acquired
Data, and it is converted into principal stress σ1、σ3With principal strain ε1、ε3Data.
(3) according to formula (5) and formula (6) by σ1、σ3、ε1And ε3It is converted into each confining pressure conditionRelation curve.
Q=| σ1-σ3| (5)
(4) according to formula (5) and formula (12) by σ1And σ3It is converted into q-p relation curve of the dull load on meridian plane.
P=(σ1+2σ3)/3 (12)
(5) interpolation is carried out to the shear hardening parameter equipotentiality point of q-p relation curve on meridian plane and extrapolation, formation is cut
Cut hardening parameter equipotential lines.
(6) it within the scope of the mean stress of every stress path of conventional triaxial compression test, is set separately equivalent constant
Mean stress triaxial test stress path line, the line are parallel with meridian plane axis of ordinates.
(7) shear hardening parameter equipotential lines intersects with the equivalent constant mean stress triaxial test stress path line of setting,
The intersection point of two kinds of lines, that is, equivalent constant mean stress triaxial test stress path characteristic point.
(8) within the scope of the mean stress of engineer application, wherein an equivalent constant mean stress triaxial test is answered for selection
The mean stress of power path line is as benchmark mean stress.
(9) in the range of strain of engineer application, selection wherein shear hardening parameter equipotential linesIt is cut as reference
Cut hardening parameter.
(10) in the range of equivalent constant mean stress triaxial test stress path characteristic point, by the ginseng of each mean stress
Examine the K that the corresponding q of shear hardening parameter is substituted into formula (7)s；By the corresponding q of reference shear hardening parameter of benchmark mean stress
In substitution formula (7)P when by each mean stress substitutes into formula (7).Formed system of linear equations, the quantity of linear equation with etc.
The quantity for imitating constant mean stress triaxial test is equal.
(11) system of linear equations is solved with the method for solving inconsistent equation group, obtains shear yielding conditional parameter CA、CB、CC。
(12) by shear yielding conditional parameter CA、CB、CCIn generation, returns formula (1), formula (3) and formula (4), obtains cutting for rock-soil material
Cut yield condition.
(13) by benchmark mean stress the horizontal corresponding q of each shear hardening parameter is substituted into respectively in formula (7) whenIt will
CA、CB、CCValue and substitute into formula (7).Using p as horizontal axis variable, KsIt is that formula (7) draw on meridian plane for longitudinal axis variable, obtains rock
The regression curve in the shear yielding face of soil material.
Parameter measured by the measuring method in the rock-soil material shear yielding face and volume yield surface is in evaluation ground
The application in material shear yielding face, applying step are as follows:
(1) it is restrained to be connected kinematic hardening, in the algorithm inclined back stress tensor αsIt is expressed as
αs.n+1=αs.n+Δαs.n+1 (19)
Wherein: subscriptnRefer to an increment；Subscriptn+1Refer to this increment；Symbol Δ refers to that the variable is increment；When t is
Between；It is restrained from specific kinematic hardening,
(2) it is restrained to be connected isotropic hardening, in the algorithm isotropic hardening coefficient when benchmark confining pressureIt is expressed as
Wherein:It is restrained from specific isotropic hardening,
(3) shear yielding condition is checked
Work as fs.n+1Shear yielding occurs for this increment when >=0；Work as fs.n+1Shear yielding does not occur for this increment when < 0.
Parameter measured by the measuring method in the rock-soil material shear yielding face and volume yield surface is in evaluation ground
The application of material volume yield surface, applying step are as follows:
(1) it is restrained to be connected kinematic hardening, in the algorithm inclined back stress tensor αvIt is expressed as
αv.n+1=αv.n+Δαv.n+1 (24)
Wherein: subscriptnRefer to an increment；Subscriptn+1Refer to this increment；Symbol Δ refers to that the variable is increment；When t is
Between；It is restrained from specific kinematic hardening,
(2) it is restrained to be connected isotropic hardening, in the algorithm isotropic hardening coefficient when benchmark deviator stressIt is expressed as
Wherein:It is restrained from specific isotropic hardening,
(3) oval volume yield condition and hyperbola volume yield condition are checked
Work as fv1.n+1>=0 and fv2.n+1Volume surrender occurs for this increment when >=0；Volume does not occur for this increment in the wrong when remaining situation
Clothes.
Technical principle of the invention:
I, shear yielding condition
There is test result to show, the shear yielding face of rock-soil material has the trend for being not passed through meridian plane origin and puts down in π
Increase the characteristic of non-linear expansion on face with mean stress.Also test result shows, rock-soil material is different constant average
The shape of shear hardening curve when stress triaxial test be it is similar, i.e., the subsequent shear yielding of two different mean stresses is answered
The proportionate relationship that power is always kept constant.Based on the above-mentioned fact, following quadratic polynomial shear yielding condition can be used and describe rock
The shear yielding face of soil material.
Wherein: fsFor shear yielding function；ξsFor opposite deviatoric stress, defined by formula (2)；HsFor shear hardening parameter；P is
Mean stress；KsShearing isotropic hardening coefficient when for actual average stress, the i.e. broad sense in actual average yield stress are cut
Stress (q) is defined by formula (3).
ξs=s- αs(Hs) (2)
Wherein: s is deviatoric stress tensor；αsFor inclined back stress tensor, the α when considering kinematic hardeningsFor variable, when not considering
α when kinematic hardeningsIt is 0.
Wherein:Shearing isotropic hardening coefficient when for benchmark mean stress, i.e., it is wide when benchmark mean stress is surrendered
Adopted shear stress (q), when considering isotropic hardeningFor variable, when not considering isotropic hardeningFor the constant of setting；BsFor with
The related coefficient of mean stress is defined by formula (4).
Bs=CAp2+CBp+CC (4)
Wherein: CA、CB、CCFor shear yielding conditional parameter, by the different constant mean stress triaxial tests of at least three into
Row, which returns, to be determined.
Formula (1), formula (2), formula (3) and formula (4) are the quadratic polynomial shear yielding condition of rock-soil material.Wherein formula (3)
It is with the meaning of formula (4), it, can when the subsequent shear yield stress and actual average stress when benchmark mean stress are known
To predict subsequent shear yield stress when actual average stress.
II, ellipse volume yield condition
Zheng Ying people etc. (1989) propose " rear work " model oval volume yield condition be mainly used for description soil cut contracting
Effect is
Wherein: q is generalized shear stress；For plastic volumetric strainFunction.Formula (32) can be write as yield function
General type be
Wherein: fv1For oval volume yield function.The long axis of oval yield condition and the ratio of short axle can be expressed as
There is test result to show, cut the contracting part and the intersection of meridian plane of the volume yield surface of rock-soil material have its slope
The phenomenon that increasing with mean stress and changing.If using oval yield condition, this phenomenon can be described as Bv1With mean stress
Increase and changes.Based on the above-mentioned fact, formula (11) description B can be usedv1Change with mean stress.
Wherein:Volume yield stress when for deviator stress being 0, i.e., the p surrendered when deviator stress is 0 namely ellipse
The long axis of round yield conditionIt is defined by formula (10)；HvFor volume hardening parameter；CG、CH、CIFor oval volume yield condition ginseng
Number is constant, is returned and is determined by the actual measurement ellipse volume yield surface of at least three difference hardening parameter level.
Wherein: αvFor ball back stress tensor；The α when considering kinematic hardeningvFor variable, the α when not considering kinematic hardeningvFor
0；Volume isotropic hardening coefficient when for deviator stress being 0.When considering kinematic hardening,When not considering to be servo-actuated
When hardening, the case where when formula (10) only calculates Δ p > 0, and αvIt is 0.If in formula (5)WithIt indicates, then convolution (34)
It obtains
Wherein: Yv1Volume yield stress when for practical deviator stress, is exclusively used in oval volume yield condition, such as formula (9)
It is shown；Δ p is the increment of mean stress, is positive load when Δ p > 0, and when Δ p < 0 is Opposite side loading.It is servo-actuated hard when not considering
When change, the case where when formula (8) only calculates Δ p > 0.
Formula (11), formula (10), formula (8) and formula (9) are the improvement ellipse volume yield condition of rock-soil material.Wherein formula (11)
It does improved meaning with formula (9) to be, subsequent volume yield stress when deviator stress is 0 and when practical deviator stress
When generalized shear stress is known, subsequent volume yield stress when practical deviator stress can be predicted.
III, hyperbola volume yield condition
There is test result to show, the cut swollen part and the intersection of meridian plane of the volume yield surface of rock-soil material are not straight line,
Its shape and hyperbola are more like.Based on above-mentioned observation, the volume yield surface that following hyperbola describes rock-soil material can be used
Cut swollen part.
Wherein:For hyp real semiaxis,For hyp imaginary semi-axis.Then hyperbola volume yield condition can indicate
For
Wherein: fv2For hyperbola volume yield function, work as fv2Volume surrender occurs when >=0, works as fv2Not generating body when < 0
Product surrender；Yv2Volume yield stress when for practical deviator stress, is exclusively used in hyperbola volume yield condition, by formula (36) institute
Show；
The real semiaxis of hyperbola yield condition and the ratio of imaginary semi-axis can be expressed as
Wherein: Bv2For the inverse of the slope of hyperbola asymptote.
There is test result to show, the slope of the limiting condition line of the volume yield surface of rock-soil material has to be increased with mean stress
And the sign changed.That is Bv2It is to change with mean stress.Based on above-mentioned observation, formula (17) description B can be usedv2With
Mean stress variation.
Wherein: CD、CE、CFFor hyperbola volume yield condition parameter, it is constant, passes through at least three difference hardening parameter water
Flat actual measurement hyperbola volume yield surface, which returns, to be determined.According toAs hyperbola focal length, then
Joint type (36), formula (37) and formula (38) obtain
Formula (15), formula (17) and formula (16) are the hyperbola volume yield condition of rock-soil material.Wherein formula (17) and formula
(16) meaning is, generalized shear stress when subsequent volume yield stress when deviator stress is 0 and practical deviator stress
When being known, subsequent volume yield stress when practical deviator stress can be predicted.
The beneficial effects of the present invention are:
(1) due to the quadratic polynomial that shear yielding function is mean stress, i.e. formula (4) bs=CAp2+CBp+CC, shear and bend
Taking conditional regression curve can either expand with the non-linear deceleration of mean stress, can also expand with the non-linear acceleration of mean stress；
(2) since shear yielding face can be not passed through the origin of meridian plane, for there is the native regression effect of higher cohesive strength
It is good；
(3) what improved oval volume yield condition can describe the volume yield surface of rock-soil material cuts contracting part and meridian
The intersection in face has the phenomenon that its slope changes with mean stress and changed；
(4) what hyperbola volume yield condition can describe the volume yield surface of rock-soil material cuts swollen part and meridian plane
Not the phenomenon that intersection is not straight line；
(5) acquisition pattern of parameter is simple, only needs conventional triaxial compression test.
(6) by equivalent constant mean stress triaxial test, when it is constant that triaxial tester, which is unable to control mean stress,
Also shear yielding condition can be measured.
(7) near in benchmark mean stress and with reference to shear hardening parameter, the error of shear yield stress is said less than 5%
The regression effect in bright shear yielding face is good.
(8) in low deviator stress, the error of oval volume yield stress illustrates oval volume yield surface less than 5%
Regression effect is good.
(9) in high deviator stress, the error of hyperbola volume yield stress illustrates that hyperbola volume is surrendered less than 5%
The regression effect in face is good.
Constant mean stress triaxial test, the normal triaxial pressure of Fujian standard sand of the above-mentioned beneficial effect from Fujian standard sand
Contracting is tested, the conventional triaxial compression test of Nanjing sand is confirmed.
Detailed description of the invention
Fig. 1 is that generalized shear stress-General architecture relationship test of the constant mean stress triaxial test of Fujian standard sand is bent
Line.
Fig. 2 is the shearing subsequent yield surface of the constant mean stress triaxial test of Fujian standard sand.
Fig. 3 is the volume subsequent yield surface of the constant mean stress triaxial test of Fujian standard sand.
Fig. 4 is generalized shear stress-General architecture relationship trial curve of Fujian standard sand conventional triaxial compression test.
Fig. 5 is the schematic diagram that equivalent constant mean stress triaxial test generates stress path.
Fig. 6 is the shearing subsequent yield surface of Fujian standard sand conventional triaxial compression test.
Fig. 7 is the volume subsequent yield surface of Fujian standard sand conventional triaxial compression test.
Fig. 8 is generalized shear stress-General architecture relationship trial curve of Nanjing sand conventional triaxial compression test.
Fig. 9 is the shearing subsequent yield surface of Nanjing sand conventional triaxial compression test.
Figure 10 is the volume subsequent yield surface of Nanjing sand conventional triaxial compression test.
Specific embodiment
Technical solution of the present invention is described in further detail below in conjunction with drawings and examples.
Embodiment 1
The present embodiment is one of the measuring method of rock-soil material shear yielding of the present invention face and volume yield surface
Application example, it is steady state value that triaxial tester, which can control mean stress, at this time, uses Fujian standard sand for test material, including
The measurement that determination step, the volume yield surface in shear yielding face cut the determination step of contracting part and volume yield surface cuts swollen part walks
Suddenly.
The determination step in shear yielding face are as follows:
The explanation of symbol in following steps: fsFor shear yielding function, work as fsShear yielding occurs when >=0, works as fsWhen < 0
Shear yielding does not occur；ξsFor opposite deviatoric stress, defined by formula (2)；HsFor shear hardening parameter；P is mean stress；KsFor reality
Shearing isotropic hardening coefficient when the mean stress of border is defined by formula (3)；S is deviatoric stress tensor；αsFor inclined back stress tensor, when
Consider α when kinematic hardeningsFor variable, the α when not considering kinematic hardeningsIt is 0；Shearing when for benchmark mean stress etc. is to hard
Change coefficient, when considering isotropic hardeningFor variable, when not considering isotropic hardeningFor the constant of setting；BsIt is fixed for formula (4)
The quadratic polynomial of justice；CA、CB、CCFor shear yielding conditional parameter, pass through the different constant mean stress triaxial tests of at least three
Carry out recurrence determination；Q is generalized shear stress；For General architecture；σ1For big principal stress；σ3For minor principal stress；ε1It is answered for master greatly
Become；ε3For small principal strain.
(1) form of shear yielding function is formula (1), formula (2), formula (3) and formula (4), according to " earthwork test rule "
SL237-1999 respectively carries out material by the different constant mean stresses of at least three using constant mean stress triaxial test
Corresponding monotonic loading test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature, solid
Knot and drainage condition.
ξs=s- αs(Hs) (2)
Bs=CAp2+CBp+CC (4)
The condition that the present embodiment passes through 3 constant mean stresses of difference respectively carries out 3 dullnesses to Fujian standard sand sample
Load test.Soil sample relative density is 0.5.Sample is cylinder, diameter 39.1mm, a height of 80mm.3 constant mean stresses
Respectively 0.1MPa, 0.2MPa and 0.3MPa.The condition of dullness load is identical as the loading environment of Practical Project, such as loading speed
For 6kPa/min, room temperature is waited to consolidation and is drained.
(2) it according to " earthwork test rule " SL237-1999, acquires each of constant mean stress triaxial test and averagely answers
The data of power condition, and it is converted into principal stress σ1、σ3With principal strain ε1、ε3Data.
(3) according to formula (5) and formula (6) by σ1、σ3、ε1And ε3It is converted into each mean stress conditionRelationship is bent
Line.
Q=| σ1-σ3| (5)
The constant mean stress triaxial test of Fujian standard sandRelationship trial curve is shown in Fig. 1.
(4) within the scope of the mean stress of engineer application, select one of mean stress as benchmark mean stress, phase
It answersWhen relation curve is benchmark mean stressRelation curve.
(5) in the range of strain of engineer application, one of them is selectedAs reference shear hardening parameter.
SelectionAs reference shear hardening parameter.
(6) the corresponding q of the reference shear hardening parameter of each mean stress is substituted into the K in formula (7)s；Benchmark is averagely answered
The corresponding q of the reference shear hardening parameter of power is substituted into formula (7)P when by each mean stress substitutes into formula (7).Form line
Property equation group, the quantity of linear equation are equal with the quantity of constant mean stress triaxial test.
It samples to obtain generalized shear stress (q) from the constant mean stress triaxial test of the consolidation draining of Fujian standard sand and be shown in Table
1。
Generalized shear stress/MPa of 1 Fujian standard sand of table
System of linear equations is
(7) system of linear equations is solved with the method for solving inconsistent equation group, obtains shear yielding conditional parameter CA、CB、CC。
The shear yielding conditional parameter of Fujian standard sand are as follows: CA=0.1793, CB=-4.7938, CC=0.0341.
(8) by shear yielding conditional parameter CA、CB、CCIn generation, returns formula (1), formula (3) and formula (4), obtains the shearing of rock-soil material
Yield condition.The shear yielding function of Fujian standard sand are as follows:
(9) by benchmark mean stress the horizontal corresponding q of each shear hardening parameter is substituted into respectively in formula (7) whenBy CA、
CB、CCValue and substitute into formula (7).Using p as horizontal axis variable, KsIt is that formula (7) draw on meridian plane for longitudinal axis variable, obtains ground
The regression curve in the shear yielding face of material.The horizontal corresponding shearing subsequent yield surface of obtained each shear hardening parameter is returned,
See Fig. 2；The scatterplot of the horizontal corresponding shearing subsequent yield surface of each shear hardening parameter obtained from test, is shown in Fig. 2.It can from Fig. 2
See, shear yielding face is expanded with the non-linear acceleration of mean stress, and does not pass through the origin of meridian plane.Near 0.2MPa confining pressure
When,When neighbouring, the regression effect in shear yielding face is good, and error is less than 5%.
Parameter measured by the measuring method in the rock-soil material shear yielding face and volume yield surface is in evaluation ground
The application in material shear yielding face, applying step are as follows:
(1) it is restrained to be connected kinematic hardening, in the algorithm inclined back stress tensor αsIt is expressed as
αs.n+1=αs.n+Δαs.n+1 (19)
Wherein: subscriptnRefer to an increment；Subscriptn+1Refer to this increment；Symbol Δ refers to that the variable is increment；When t is
Between；It is restrained from specific kinematic hardening.If a upper increment transmits αs.n=[0.1,0.2,0.15,0.01,0.01,0.01]
MPa；This incrementΔ t=0.1s；Then this increment
(2) it is restrained to be connected isotropic hardening, in the algorithm isotropic hardening coefficient when benchmark confining pressureIt is expressed as
Wherein:It is restrained from specific isotropic hardening.If a upper increment transmitsThis incrementThen this increment
(3) shear yielding condition is checked
Work as fs.n+1Shear yielding occurs for this increment when >=0；Work as fs.n+1Shear yielding does not occur for this increment when < 0.
If this increment ssn+1=[1,1,1,0,0,0] MPa, p=0.3MPa；The then shear yielding of this increment Fujian standard sand
Condition are as follows:This increment is cut
Cut surrender.
Volume yield surface cuts the determination step of contracting part:
The explanation of symbol in following steps: fv1For oval volume yield function, work as fv1Volume surrender occurs when >=0, works as fv1
Volume surrender does not occur when < 0；P is mean stress；HvFor volume hardening parameter；Q is generalized shear stress；Yv1For practical principal stress
Volume yield stress when poor is defined by formula (9)；Δ p is the increment of mean stress, is positive load as Δ p > 0, as Δ p
It is Opposite side loading when < 0；Volume yield stress when for deviator stress being 0 is defined by formula (10)；Bv1It is defined for formula (11)
Quadratic polynomial；αvFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；CG、CH、CIFor ellipse
Volume yield condition parameter is returned by the actual measurement volume yield surface of at least three difference hardening parameter level and is determined；σ1It is main greatly
Stress；σ3For minor principal stress；P ' is effective mean stress；U is pore water pressure.
(1) form of oval volume yield function is formula (8), formula (9), formula (10) and formula (11), according to " soil test is advised
Journey " SL237-1999, using the triaxial test not drained, respectively by the strain of at least three difference constant volume to material progress
Corresponding monotonic loading test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature.
Wherein: the α when considering kinematic hardeningvFor variable,The α when not considering kinematic hardeningvBe 0, formula (8) and
The case where when formula (10) only calculates Δ p > 0.The condition that the present embodiment passes through 3 different constant volume strains respectively marks Fujian
Quasi- sand sample carries out 3 monotonic loading tests.Soil sample relative density is 0.5.Sample is cylinder, and diameter 39.1mm is a height of
80mm.3 constant confining pressures are respectively 0.2MPa, 0.3MPa and 0.4MPa.The condition of dullness load and the load item of Practical Project
Part is identical, if loading speed is 6kPa/min, room temperature.
(2) according to " earthwork test rule " SL237-1999, the data of each bulk strain condition of triaxial test are acquired,
And it is converted into principal stress σ1、σ3, principal strain ε1、ε3With the data of pore water pressure u.
(3) according to formula (5), formula (12) and formula (13) by σ1、σ3Each bulk strain item on meridian plane is converted into u
Q-p ' relation curve of part, the curve are the volume yield surface of each confining pressure condition and the intersection of meridian plane.
Q=| σ1-σ3| (5)
P=(σ1+2σ3)/3 (12)
P '=p-u (13)
Q-p ' relationship trial curve that Fujian standard sand does not drain constant mean stress triaxial test is shown in Fig. 3.
(4) the volume yield surface on q-p ' relation curve of each bulk strain condition cut contracting part selection one
Representative characteristic point in shape, this feature point is not in p ' reference axis.Fujian standard sand volume yield surface feature points
According to being shown in Table 2.
2 Fujian standard sand volume yield surface characteristic point data of table/MPa
(5) by deviator stress be 0 when q-p ' relation curve on point abscissa substitute into formula (14) inIt will remove
Deviator stress is that the volume yield surface on q-p ' relation curve outside 0 cuts the abscissa of the selected characteristic point in contracting part
Y in substitution formula (14)v1；Volume yield surface on q-p ' relation curve in addition to deviator stress is 0 is cut selected by contracting part
A characteristic point ordinate substitute into formula (14).Form system of linear equations, the quantity of linear equation and different hardening parameter water
The quantity of flat actual measurement volume yield surface is equal.
System of linear equations is
(6) system of linear equations is solved with the method for solving inconsistent equation group, obtains oval volume yield condition parameter CG、CH、
CI。
The oval volume yield condition parameter of Fujian standard sand are as follows: CG=-26.9447, CH=15.2498, CI=-
1.6947。
(7) by oval volume yield condition parameter CG、CH、CIIn generation, returns formula (8), formula (9), formula (10) and formula (11), obtains rock
The oval volume yield condition of soil material.The oval volume yield condition of Fujian standard sand are as follows:
(8) by deviator stress be 0 when volume yield surface on p substitute into formula (14) inBy CG、CH、CIValue and substitution
Formula (14).Using q as longitudinal axis variable, Yv1It is that formula (14) draw on meridian plane for horizontal axis variable, the volume for obtaining rock-soil material is bent
Cut the regression curve of contracting part in the face of clothes.The obtained corresponding volume subsequent yield surface of each mean stress is returned, sees Fig. 3；From test
The corresponding volume subsequent yield surface of obtained each mean stress, is shown in Fig. 3.It can be seen from figure 3 that the volume yield surface in low deviator stress
The regression effect for cutting contracting part is good, and error is less than 5%.
Volume yield surface cuts the determination step of swollen part:
The explanation of symbol in following steps: fv2For hyperbola volume yield function, work as fv2Volume surrender occurs when >=0, when
fv2Volume surrender does not occur when < 0；P is mean stress；HvFor volume hardening parameter；Q is generalized shear stress；Yv2It is answered for practical master
Volume yield stress when power difference is defined by formula (16)；Δ p is the increment of mean stress, is positive load as Δ p > 0, when
It is Opposite side loading when Δ p < 0；Volume yield stress when for deviator stress being 0 is defined by formula (10)；Bv2It is fixed for formula (17)
The quadratic polynomial of justice；αvFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；CD、CE、CF.
For hyperbola volume yield condition parameter, is returned and determined by the actual measurement volume yield surface of at least three difference hardening parameter level；
σ1For big principal stress；σ3For minor principal stress；P ' is effective mean stress；U is pore water pressure.
(1) form of hyperbola volume yield function is formula (15), formula (16), formula (10) and formula (17), according to " geotechnique tries
Test regulation " SL237-1999, using the triaxial test not drained, respectively by the strain of at least three difference constant volume to material
Carry out corresponding monotonic loading test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature
Degree.
Wherein: the α when considering kinematic hardeningvFor variable,The α when not considering kinematic hardeningvIt is 0, formula (15)
The case where when only calculating Δ p > 0 with formula (10).The present embodiment passes through the condition of 3 different constant volume strains to Fujian respectively
Normal sand sample carries out 3 monotonic loading tests.Soil sample relative density is 0.5.Sample is cylinder, and diameter 39.1mm is high
For 80mm.3 constant confining pressures are respectively 0.2MPa, 0.3MPa and 0.4MPa.The condition of dullness load and the load of Practical Project
Condition is identical, if loading speed is 6kPa/min, room temperature.
(2) according to " earthwork test rule " SL237-1999, the data of each bulk strain condition of triaxial test are acquired,
And it is converted into principal stress σ1、σ3, principal strain ε1、ε3With the data of pore water pressure u.
(3) according to formula (5), formula (12) and formula (13) by σ1、σ3Each bulk strain item on meridian plane is converted into u
Q-p ' relation curve of part, the curve are the volume yield surface of each confining pressure condition and the intersection of meridian plane.
Q=| σ1-σ3| (5)
P=(σ1+2σ3)/3 (12)
P '=p-u (13)
Q-p ' relationship trial curve that Fujian standard sand does not drain constant mean stress triaxial test is shown in Fig. 3.
(4) the volume yield surface on q-p ' relation curve of each confining pressure condition cuts swollen part selection one in shape
Upper representative characteristic point, this feature point is not in p ' reference axis.Fujian standard sand volume yield surface characteristic point data is shown in
Table 2.
(5) by deviator stress be 0 when q-p ' relation curve on point abscissa substitute into formula (18) inIt will remove
Deviator stress is that the volume yield surface on q-p ' relation curve outside 0 cuts the abscissa of the selected characteristic point in swollen part
Y in substitution formula (18)v2；Volume yield surface on q-p ' relation curve in addition to deviator stress is 0 is cut selected by swollen part
A characteristic point ordinate substitute into formula (18).Form system of linear equations, the quantity of linear equation and different hardening parameter water
The quantity of flat actual measurement volume yield surface is equal.
System of linear equations is
(6) system of linear equations is solved with the method for solving inconsistent equation group, obtains hyperbola volume yield condition parameter CD、
CE、CF。
The hyperbola volume yield condition parameter of Fujian standard sand are as follows: CD=-0.2777, CE=0.1220, CF=
0.6395。
(7) by hyperbola volume yield condition parameter CD、CE、CFIn generation, returns formula (15), formula (16), formula (10) and formula (17), obtains
To the hyperbola volume yield condition of rock-soil material.The hyperbola volume yield condition of Fujian standard sand are as follows:
(8) by deviator stress be 0 when volume yield surface on p substitute into formula (18) inBy CD、CE、CFValue and substitution
Formula (18).Using q as longitudinal axis variable, Yv2It is that formula (18) draw on meridian plane for horizontal axis variable, the volume for obtaining rock-soil material is bent
Cut the regression curve of swollen part in the face of clothes.The obtained corresponding volume subsequent yield surface of each mean stress is returned, sees Fig. 3；From test
The corresponding volume subsequent yield surface of obtained each mean stress, is shown in Fig. 3.It can be seen from figure 3 that the volume yield surface in high deviator stress
The regression effect for cutting swollen part is good, and error is less than 5%.
Parameter measured by the measuring method in the rock-soil material shear yielding face and volume yield surface is in evaluation ground
The application of material volume yield surface, applying step are as follows:
(1) it is restrained to be connected kinematic hardening, in the algorithm inclined back stress tensor αvIt is expressed as
αv.n+1=αv.n+Δαv.n+1 (24)
Wherein: subscriptnRefer to an increment；Subscriptn+1Refer to this increment；Symbol Δ refers to that the variable is increment；When t is
Between；It is restrained from specific kinematic hardening.If a upper increment transmits αv.n=0.1MPa；This incrementThen this increment
(2) it is restrained to be connected isotropic hardening, in the algorithm isotropic hardening coefficient when benchmark deviator stressIt is expressed as
Wherein:It is restrained from specific isotropic hardening.If a upper increment transmitsThis incrementThen this increment
(3) oval volume yield condition and hyperbola volume yield condition are checked
Work as fv1.n+1>=0 and fv2.n+1Volume surrender occurs for this increment when >=0；Volume does not occur for this increment in the wrong when remaining situation
Clothes.
If this increment pn+1=1MPa, q=0.0015MPa, Δ p > 0；Then the volume of this increment Fujian standard sand surrenders item
Part are as follows:
fv2.n+1=| pn+1|-Yv2.n+1=| 1 | volume does not occur and bends for-(- 20.1998)=increment of 21.1998MPa > 0
Clothes.
Embodiment 2
It is another with the measuring method of volume yield surface that the present embodiment is rock-soil material shear yielding of the present invention face
A application example, it is steady state value that triaxial tester, which is unable to control mean stress, at this time, uses Fujian standard sand for test material, is wrapped
Include the determination step in shear yielding face, volume yield surface cuts the determination step of contracting part and volume yield surface cuts the measurement of swollen part
Step.
The step of equivalent constant mean stress triaxial (test) method measurement shear yielding face are as follows:
The explanation of symbol in following steps: fsFor shear yielding function, work as fsShear yielding occurs when >=0, works as fsWhen < 0
Shear yielding does not occur；ξsFor opposite deviatoric stress, defined by formula (2)；HsFor shear hardening parameter；P is mean stress；KsFor reality
Shearing isotropic hardening coefficient when the mean stress of border is defined by formula (3)；S is deviatoric stress tensor；αsFor inclined back stress tensor, when
Consider α when kinematic hardeningsFor variable, the α when not considering kinematic hardeningsIt is 0；Shearing when for benchmark mean stress etc. is to hard
Change coefficient, when considering isotropic hardeningFor variable, when not considering isotropic hardeningFor the constant of setting；BsIt is fixed for formula (4)
The quadratic polynomial of justice；CA、CB、CCFor shear yielding conditional parameter, pass through the different constant mean stress triaxial tests of at least three
Carry out recurrence determination；Q is generalized shear stress；For General architecture；σ1For big principal stress；σ3For minor principal stress；ε1It is answered for master greatly
Become；ε3For small principal strain.
(1) form of shear yielding function is formula (1), formula (2), formula (3) and formula (4), according to " earthwork test rule "
SL237-1999 respectively carries out material by least three difference constant confining pressure corresponding dull using conventional triaxial compression test
Load test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature, consolidation and draining
Condition.
ξs=s- αs(Hs) (2)
Bs=CAp2+CBp+CC (4)
The condition that the present embodiment passes through 4 different constant confining pressures respectively carries out 4 dull loads to Fujian standard sand sample
Test.Soil sample relative density is 0.6.Sample is cylinder, diameter 39.1mm, a height of 80mm.4 constant confining pressures are respectively
0.05MPa, 0.1MPa, 0.15MPa and 0.2MPa.The condition of dullness load is identical as the loading environment of Practical Project, such as loads
Rate is 0.08mm/min, and room temperature is waited to consolidation and drained.
(2) according to " earthwork test rule " SL237-1999, each confining pressure condition of conventional triaxial compression test is acquired
Data, and it is converted into principal stress σ1、σ3With principal strain ε1、ε3Data.
(3) according to formula (5) and formula (6) by σ1、σ3、ε1And ε3It is converted into each confining pressure conditionRelation curve.
Q=| σ1-σ3| (5)
Fujian standard sand conventional triaxial compression testRelationship trial curve is shown in Fig. 4.
(4) according to formula (5) and formula (12) by σ1And σ3It is converted into q-p relation curve of the dull load on meridian plane.
P=(σ1+2σ3)/3 (12)
(5) interpolation is carried out to the shear hardening parameter equipotentiality point of q-p relation curve on meridian plane and extrapolation, formation is cut
Cut hardening parameter equipotential lines.
(6) it within the scope of the mean stress of every stress path of conventional triaxial compression test, is set separately equivalent constant
Mean stress triaxial test stress path line, the line are parallel with meridian plane axis of ordinates.
(7) shear hardening parameter equipotential lines intersects with the equivalent constant mean stress triaxial test stress path line of setting,
The intersection point of two kinds of lines, that is, equivalent constant mean stress triaxial test stress path characteristic point.Equivalent constant mean stress triaxial test
The schematic diagram that method generates stress path is shown in Fig. 5.
It samples to obtain generalized shear stress (q) from the conventional triaxial compression test of the draining of Fujian standard sand and is shown in Table 3.
Actual measurement generalized shear stress (q)/MPa of 3 Fujian standard sand conventional triaxial compression test of table
The generalized shear stress (q) of the equivalent constant mean stress triaxial test of the Fujian standard sand of generation is shown in Table 4.
Generalized shear stress (q)/MPa of the equivalent constant mean stress triaxial test of 4 Fujian standard sand of table
(8) within the scope of the mean stress of engineer application, wherein an equivalent constant mean stress triaxial test is answered for selection
The mean stress of power path line is as benchmark mean stress.Select 0.2343MPa as benchmark mean stress.
(9) in the range of strain of engineer application, selection wherein shear hardening parameter equipotential linesAs reference
Shear hardening parameter.SelectionAs reference shear hardening parameter.
(10) in the range of equivalent constant mean stress triaxial test stress path characteristic point, by the ginseng of each mean stress
Examine the K that the corresponding q of shear hardening parameter is substituted into formula (7)s；By the corresponding q of reference shear hardening parameter of benchmark mean stress
In substitution formula (7)P when by each mean stress substitutes into formula (7).Formed system of linear equations, the quantity of linear equation with etc.
The quantity for imitating constant mean stress triaxial test is equal.
System of linear equations is
(11) system of linear equations is solved with the method for solving inconsistent equation group, obtains shear yielding conditional parameter CA、CB、CC。
The shear yielding conditional parameter of Fujian standard sand are as follows: CA=0.2889, CB=-4.3259, CC=-0.0341.
(12) by shear yielding conditional parameter CA、CB、CCIn generation, returns formula (1), formula (3) and formula (4), obtains cutting for rock-soil material
Cut yield condition.The shear yielding function of Fujian standard sand are as follows:
(13) by benchmark mean stress the horizontal corresponding q of each shear hardening parameter is substituted into respectively in formula (7) whenIt will
CA、CB、CCValue and substitute into formula (7).Using p as horizontal axis variable, KsIt is that formula (7) draw on meridian plane for longitudinal axis variable, obtains rock
The regression curve in the shear yielding face of soil material.Return the horizontal corresponding subsequent surrender of shearing of obtained each shear hardening parameter
Fig. 6 is seen in face；The scatterplot of the horizontal corresponding shearing subsequent yield surface of each shear hardening parameter obtained from test, is shown in Fig. 6.From Fig. 6
As it can be seen that shear yielding face is expanded with the non-linear acceleration of mean stress, and the origin of meridian plane is not passed through.It is average in 0.2343MPa
When near stress,When neighbouring, the regression effect in good shear yielding face, error is less than 5%.
Parameter measured by the measuring method in the rock-soil material shear yielding face and volume yield surface is in evaluation ground
The application in material shear yielding face, applying step are as follows:
(1) it is restrained to be connected kinematic hardening, in the algorithm inclined back stress tensor αsIt is expressed as
αs.n+1=αs.n+Δαs.n+1 (19)
Wherein: subscriptnRefer to an increment；Subscriptn+1Refer to this increment；Symbol Δ refers to that the variable is increment；When t is
Between；It is restrained from specific kinematic hardening.If a upper increment transmits αs.n=[0.1,0.2,0.15,0.01,0.01,0.01]
MPa；This incrementΔ t=0.1s；Then this increment
(2) it is restrained to be connected isotropic hardening, in the algorithm isotropic hardening coefficient when benchmark confining pressureIt is expressed as
Wherein:It is restrained from specific isotropic hardening.If a upper increment transmitsThis incrementThen this increment
(3) shear yielding condition is checked
Work as fs.n+1Shear yielding occurs for this increment when >=0；Work as fs.n+1Shear yielding does not occur for this increment when < 0.
If this increment ssn+1=[1,1,1,0,0,0] MPa, p=0.3MPa；The then shear yielding of this increment Fujian standard sand
Condition are as follows:This increment is cut
Cut surrender.
Volume yield surface cuts the determination step of contracting part:
The explanation of symbol in following steps: fv1For oval volume yield function, work as fv1Volume surrender occurs when >=0, works as fv1
Volume surrender does not occur when < 0；P is mean stress；HvFor volume hardening parameter；Q is generalized shear stress；Yv1For practical principal stress
Volume yield stress when poor is defined by formula (9)；Δ p is the increment of mean stress, is positive load as Δ p > 0, as Δ p
It is Opposite side loading when < 0；Volume yield stress when for deviator stress being 0 is defined by formula (10)；Bv1For formula (11) definition
Quadratic polynomial；αvFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；CG、CH、CIFor
Oval volume yield condition parameter is returned by the actual measurement volume yield surface of at least three difference hardening parameter level and is determined；σ1For
Big principal stress；σ3For minor principal stress；P ' is effective mean stress；U is pore water pressure.
(1) form of oval volume yield function is formula (8), formula (9), formula (10) and formula (11), according to " soil test is advised
Journey " SL237-1999, using the triaxial test not drained, respectively by the strain of at least three difference constant volume to material progress
Corresponding monotonic loading test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature.
Wherein: the α when considering kinematic hardeningvFor variable,The α when not considering kinematic hardeningvBe 0, formula (8) and
The case where when formula (10) only calculates Δ p > 0.The condition that the present embodiment passes through 3 different constant volume strains respectively marks Fujian
Quasi- sand sample carries out 3 monotonic loading tests.Soil sample relative density is 0.7.Sample is cylinder, and diameter 39.1mm is a height of
80mm.3 constant confining pressures are respectively 0.05MPa, 0.1MPa and 0.15MPa.The condition of dullness load and the load of Practical Project
Condition is identical, if loading speed is 5kPa/min, room temperature.
(2) according to " earthwork test rule " SL237-1999, the data of each bulk strain condition of triaxial test are acquired,
And it is converted into principal stress σ1、σ3, principal strain ε1、ε3With the data of pore water pressure u.
(3) according to formula (5), formula (12) and formula (13) by σ1、σ3Each bulk strain item on meridian plane is converted into u
Q-p ' relation curve of part, the curve are the volume yield surface of each confining pressure condition and the intersection of meridian plane.
Q=| σ1-σ3| (5)
P=(σ1+2σ3)/3 (12)
P '=p-u (13)
Q-p ' relationship trial curve that Fujian standard sand does not drain constant confining pressure triaxial test is shown in Fig. 7.
(4) the volume yield surface on q-p ' relation curve of each bulk strain condition cut contracting part selection one
Representative characteristic point in shape, this feature point is not in p ' reference axis.Fujian standard sand volume yield surface feature points
According to being shown in Table 5.
5 Fujian standard sand volume yield surface characteristic point data of table/MPa
(5) by deviator stress be 0 when q-p ' relation curve on point abscissa substitute into formula (14) inIt will remove
Deviator stress is that the volume yield surface on q-p ' relation curve outside 0 cuts the abscissa of the selected characteristic point in contracting part
Y in substitution formula (14)v1；Volume yield surface on q-p ' relation curve in addition to deviator stress is 0 is cut selected by contracting part
A characteristic point ordinate substitute into formula (14).Form system of linear equations, the quantity of linear equation and different hardening parameter water
The quantity of flat actual measurement volume yield surface is equal.
System of linear equations is
(6) system of linear equations is solved with the method for solving inconsistent equation group, obtains oval volume yield condition parameter CG、CH、
CI。
The oval volume yield condition parameter of Fujian standard sand are as follows: CG=-8.0176, CH=2.6323, CI=0.6412.
(7) by oval volume yield condition parameter CG、CH、CIIn generation, returns formula (8), formula (9), formula (10) and formula (11), obtains rock
The oval volume yield condition of soil material.The oval volume yield condition of Fujian standard sand are as follows:
(8) by deviator stress be 0 when volume yield surface on p substitute into formula (14) inBy CG、CH、CIValue and substitution
Formula (14).Using q as longitudinal axis variable, Yv1It is that formula (14) draw on meridian plane for horizontal axis variable, the volume for obtaining rock-soil material is bent
Cut the regression curve of contracting part in the face of clothes.The obtained corresponding volume subsequent yield surface of each confining pressure is returned, sees Fig. 7；It is obtained from test
The corresponding volume subsequent yield surface of each confining pressure, see Fig. 7.From fig.7, it can be seen that volume yield surface cuts contracting part in low deviator stress
Regression effect it is good, error is less than 5%.
Volume yield surface cuts the determination step of swollen part:
The explanation of symbol in following steps: fv2For hyperbola volume yield function, work as fv2Volume surrender occurs when >=0, when
fv2Volume surrender does not occur when < 0；P is mean stress；HvFor volume hardening parameter；Q is generalized shear stress；Yv2It is answered for practical master
Volume yield stress when power difference is defined by formula (16)；Δ p is the increment of mean stress, is positive load as Δ p > 0, when
It is Opposite side loading when Δ p < 0；Volume yield stress when for deviator stress being 0 is defined by formula (10)；Bv2It is fixed for formula (17)
The quadratic polynomial of justice；αvFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；CD、CE、CF.
For hyperbola volume yield condition parameter, is returned and determined by the actual measurement volume yield surface of at least three difference hardening parameter level；
σ1For big principal stress；σ3For minor principal stress；P ' is effective mean stress；U is pore water pressure.
(1) form of hyperbola volume yield function is formula (15), formula (16), formula (10) and formula (17), according to " geotechnique tries
Test regulation " SL237-1999, using the triaxial test not drained, respectively by the strain of at least three difference constant volume to material
Carry out corresponding monotonic loading test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature
Degree.
Wherein: the α when considering kinematic hardeningvFor variable,The α when not considering kinematic hardeningvIt is 0, formula (15)
The case where when only calculating Δ p > 0 with formula (10).The present embodiment passes through the condition of 3 different constant volume strains to Fujian respectively
Normal sand sample carries out 3 monotonic loading tests.Soil sample relative density is 0.7.Sample is cylinder, and diameter 39.1mm is high
For 80mm.3 constant confining pressures are respectively 0.05MPa, 0.1MPa and 0.15MPa.The condition of dullness load and adding for Practical Project
Carrier strip part is identical, if loading speed is 5kPa/min, room temperature.
(2) according to " earthwork test rule " SL237-1999, the data of each bulk strain condition of triaxial test are acquired,
And it is converted into principal stress σ1、σ3, principal strain ε1、ε3With the data of pore water pressure u.
(3) according to formula (5), formula (12) and formula (13) by σ1、σ3Each bulk strain item on meridian plane is converted into u
Q-p ' relation curve of part, the curve are the volume yield surface of each confining pressure condition and the intersection of meridian plane.
Q=| σ1-σ3| (5)
P=(σ1+2σ3)/3 (12)
P '=p-u (13)
Q-p ' relationship trial curve that Fujian standard sand does not drain constant confining pressure triaxial test is shown in Fig. 7.
(4) the volume yield surface on q-p ' relation curve of each confining pressure condition cuts swollen part selection one in shape
Upper representative characteristic point, this feature point is not in p ' reference axis.Fujian standard sand volume yield surface characteristic point data is shown in
Table 5.
(5) by deviator stress be 0 when q-p ' relation curve on point abscissa substitute into formula (18) inIt will remove
Deviator stress is that the volume yield surface on q-p ' relation curve outside 0 cuts the abscissa of the selected characteristic point in swollen part
Y in substitution formula (18)v2；Volume yield surface on q-p ' relation curve in addition to deviator stress is 0 is cut selected by swollen part
A characteristic point ordinate substitute into formula (18).Form system of linear equations, the quantity of linear equation and different hardening parameter water
The quantity of flat actual measurement volume yield surface is equal.
System of linear equations is
(6) system of linear equations is solved with the method for solving inconsistent equation group, obtains hyperbola volume yield condition parameter CD、
CE、CF。
The hyperbola volume yield condition parameter of Fujian standard sand are as follows: CD=-5.2951, CE=1.1163, CF=
0.6343。
(7) by hyperbola volume yield condition parameter CD、CE、CFIn generation, returns formula (15), formula (16), formula (10) and formula (17), obtains
To the hyperbola volume yield condition of rock-soil material.The hyperbola volume yield condition of Fujian standard sand are as follows:
(8) by deviator stress be 0 when volume yield surface on p substitute into formula (18) inBy CD、CE、CFValue and substitution
Formula (18).Using q as longitudinal axis variable, Yv2It is that formula (18) draw on meridian plane for horizontal axis variable, the volume for obtaining rock-soil material is bent
Cut the regression curve of swollen part in the face of clothes.The obtained corresponding volume subsequent yield surface of each confining pressure is returned, sees Fig. 7；It is obtained from test
The corresponding volume subsequent yield surface of each confining pressure, see Fig. 7.From fig.7, it can be seen that volume yield surface cuts swollen part in high deviator stress
Regression effect it is good, error is less than 5%.
Parameter measured by the measuring method in the rock-soil material shear yielding face and volume yield surface is in evaluation ground
The application of material volume yield surface, applying step are as follows:
(1) it is restrained to be connected kinematic hardening, in the algorithm inclined back stress tensor αvIt is expressed as
αv.n+1=αv.n+Δαv.n+1 (24)
Wherein: subscriptnRefer to an increment；Subscriptn+1Refer to this increment；Symbol Δ refers to that the variable is increment；T is the time；It is restrained from specific kinematic hardening.If a upper increment transmits αv.n=0.1MPa；This increment
Then this increment
(2) it is restrained to be connected isotropic hardening, in the algorithm isotropic hardening coefficient when benchmark deviator stressIt is expressed as
Wherein:It is restrained from specific isotropic hardening.If a upper increment transmitsThis incrementThen this increment
(3) oval volume yield condition and hyperbola volume yield condition are checked
Work as fv1.n+1>=0 and fv2.n+1Volume surrender occurs for this increment when >=0；Volume does not occur for this increment in the wrong when remaining situation
Clothes.
If this increment pn+1=1MPa, q=0.0015MPa, Δ p < 0；Then the volume of this increment Fujian standard sand surrenders item
Part are as follows:
fv2.n+1=Yv2.n+1-|pn+1|=9.5145 × 10-4| 1 | volume does not occur and bends for 0 increment of=- 0.9990MPa <
Clothes.
Embodiment 3
It is another with the measuring method of volume yield surface that the present embodiment is rock-soil material shear yielding of the present invention face
A application example, it is steady state value that triaxial tester, which is unable to control mean stress, at this time, uses Nanjing sand for test material, including cut
Cut the determination step of yield surface, the measurement that volume yield surface cuts the determination step of contracting part and volume yield surface cuts swollen part walks
Suddenly.
The step of equivalent constant mean stress triaxial (test) method measurement shear yielding face are as follows:
The explanation of symbol in following steps: fsFor shear yielding function, work as fsShear yielding occurs when >=0, works as fsWhen < 0
Shear yielding does not occur；ξsFor opposite deviatoric stress, defined by formula (2)；HsFor shear hardening parameter；P is mean stress；KsFor reality
Shearing isotropic hardening coefficient when the mean stress of border is defined by formula (3)；S is deviatoric stress tensor；αsFor inclined back stress tensor, when
Consider α when kinematic hardeningsFor variable, the α when not considering kinematic hardeningsIt is 0；Shearing when for benchmark mean stress etc. is to hard
Change coefficient, when considering isotropic hardeningFor variable, when not considering isotropic hardeningFor the constant of setting；BsIt is fixed for formula (4)
The quadratic polynomial of justice；CA、CB、CCFor shear yielding conditional parameter, pass through the different constant mean stress triaxial tests of at least three
Carry out recurrence determination；Q is generalized shear stress；For General architecture；σ1For big principal stress；σ3For minor principal stress；ε1It is answered for master greatly
Become；ε3For small principal strain.
(1) form of shear yielding function is formula (1), formula (2), formula (3) and formula (4), according to " earthwork test rule "
SL237-1999 respectively carries out material by least three difference constant confining pressure corresponding dull using conventional triaxial compression test
Load test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature, consolidation and draining
Condition.
ξs=s- αs(Hs) (2)
Bs=CAp2+CBp+CC (4)
The condition that the present embodiment passes through 3 different constant confining pressures respectively carries out 3 monotonic loading tests to Nanjing sand sample.
Soil sample relative density is 0.48.Sample is cylinder, diameter 39.1mm, a height of 80mm.3 constant confining pressures are respectively
0.05MPa, 0.1MPa and 0.2MPa.The condition of dullness load is identical as the loading environment of Practical Project, as loading speed is
0.073mm/min, room temperature are waited to consolidation and are not drained.
(2) according to " earthwork test rule " SL237-1999, each confining pressure condition of conventional triaxial compression test is acquired
Data, and it is converted into principal stress σ1、σ3With principal strain ε1、ε3Data.
(3) according to formula (5) and formula (6) by σ1、σ3、ε1And ε3It is converted into each confining pressure conditionRelation curve.
Q=| σ1-σ3| (5)
Nanjing sand conventional triaxial compression testRelationship trial curve is shown in Fig. 8.
(4) according to formula (5) and formula (12) by σ1And σ3It is converted into q-p relation curve of the dull load on meridian plane.
P=(σ1+2σ3)/3 (12)
(5) interpolation is carried out to the shear hardening parameter equipotentiality point of q-p relation curve on meridian plane and extrapolation, formation is cut
Cut hardening parameter equipotential lines.
(6) it within the scope of the mean stress of every stress path of conventional triaxial compression test, is set separately equivalent constant
Mean stress triaxial test stress path line, the line are parallel with meridian plane axis of ordinates.
(7) shear hardening parameter equipotential lines intersects with the equivalent constant mean stress triaxial test stress path line of setting,
The intersection point of two kinds of lines, that is, equivalent constant mean stress triaxial test stress path characteristic point.Equivalent constant mean stress triaxial test
The schematic diagram that method generates stress path is shown in Fig. 5.
It samples to obtain generalized shear stress (q) from the conventional triaxial compression test of Nanjing sand not drained and is shown in Table 6.
Actual measurement generalized shear stress (q)/MPa of 6 Nanjing sand conventional triaxial compression test of table
The generalized shear stress (q) of the equivalent constant mean stress triaxial test of the Nanjing sand of generation is shown in Table 7.
Generalized shear stress (q)/MPa of the equivalent constant mean stress triaxial test of 7 Nanjing sand of table
(8) within the scope of the mean stress of engineer application, wherein an equivalent constant mean stress triaxial test is answered for selection
The mean stress of power path line is as benchmark mean stress.Select 0.1687MPa as benchmark mean stress.
(9) in the range of strain of engineer application, selection wherein shear hardening parameter equipotential linesAs reference
Shear hardening parameter.SelectionAs reference shear hardening parameter.
(10) in the range of equivalent constant mean stress triaxial test stress path characteristic point, by the ginseng of each mean stress
Examine the K that the corresponding q of shear hardening parameter is substituted into formula (7)s；By the corresponding q of reference shear hardening parameter of benchmark mean stress
In substitution formula (7)P when by each mean stress substitutes into formula (7).Formed system of linear equations, the quantity of linear equation with etc.
The quantity for imitating constant mean stress triaxial test is equal.
System of linear equations is
(11) system of linear equations is solved with the method for solving inconsistent equation group, obtains shear yielding conditional parameter CA、CB、CC。
The shear yielding conditional parameter of Nanjing sand are as follows: CA=-3.6027, CB=-6.2193, CC=0.0533.
(12) by shear yielding conditional parameter CA、CB、CCIn generation, returns formula (1), formula (3) and formula (4), obtains cutting for rock-soil material
Cut yield condition.The shear yielding function of Nanjing sand are as follows:
(13) by benchmark mean stress the horizontal corresponding q of each shear hardening parameter is substituted into respectively in formula (7) whenIt will
CA、CB、CCValue and substitute into formula (7).Using p as horizontal axis variable, KsIt is that formula (7) draw on meridian plane for longitudinal axis variable, obtains rock
The regression curve in the shear yielding face of soil material.Return the horizontal corresponding subsequent surrender of shearing of obtained each shear hardening parameter
Fig. 9 is seen in face；The scatterplot of the horizontal corresponding shearing subsequent yield surface of each shear hardening parameter obtained from test, is shown in Fig. 9.From Fig. 9
As it can be seen that shear yielding face is expanded with the non-linear deceleration of mean stress, and the origin of meridian plane is not passed through.It is average in 0.1687MPa
When near stress,When neighbouring, the regression effect in shear yielding face is good, and error is less than 5%.
Parameter measured by the measuring method in the rock-soil material shear yielding face and volume yield surface is in evaluation ground
The application in material shear yielding face, applying step are as follows:
(1) it is restrained to be connected kinematic hardening, in the algorithm inclined back stress tensor αsIt is expressed as
αs.n+1=αs.n+Δαs.n+1 (19)
Wherein: subscriptnRefer to an increment；Subscriptn+1Refer to this increment；Symbol Δ refers to that the variable is increment；When t is
Between；It is restrained from specific kinematic hardening.If a upper increment transmits αs.n=[0.1,0.2,0.15,0.01,0.01,0.01]
MPa；This incrementΔ t=0.1s；Then this increment
(2) it is restrained to be connected isotropic hardening, in the algorithm isotropic hardening coefficient when benchmark confining pressureIt is expressed as
Wherein:It is restrained from specific isotropic hardening.If a upper increment transmitsThis incrementThen this increment
(3) shear yielding condition is checked
Work as fs.n+1Shear yielding occurs for this increment when >=0；Work as fs.n+1Shear yielding does not occur for this increment when < 0.
If this increment ssn+1=[1,1,1,0,0,0] MPa, p=0.3MPa；The then shear yielding of this increment Fujian standard sand
Condition are as follows:This increment occurs
Shear yielding.
Volume yield surface cuts the determination step of contracting part:
The explanation of symbol in following steps: fv1For oval volume yield function, work as fv1Volume surrender occurs when >=0, works as fv1
Volume surrender does not occur when < 0；P is mean stress；HvFor volume hardening parameter；Q is generalized shear stress；Yv1For practical principal stress
Volume yield stress when poor is defined by formula (9)；Δ p is the increment of mean stress, is positive load as Δ p > 0, as Δ p
It is Opposite side loading when < 0；Volume yield stress when for deviator stress being 0 is defined by formula (10)；Bv1For formula (11) definition
Quadratic polynomial；αvFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；CG、CH、CIFor
Oval volume yield condition parameter is returned by the actual measurement volume yield surface of at least three difference hardening parameter level and is determined；σ1For
Big principal stress；σ3For minor principal stress；P ' is effective mean stress；U is pore water pressure.
(1) form of oval volume yield function is formula (8), formula (9), formula (10) and formula (11), according to " soil test is advised
Journey " SL237-1999, using the triaxial test not drained, respectively by the strain of at least three difference constant volume to material progress
Corresponding monotonic loading test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature.
Wherein: the α when considering kinematic hardeningvFor variable,The α when not considering kinematic hardeningvBe 0, formula (8) and
The case where when formula (10) only calculates Δ p > 0.The present embodiment passes through the condition of 3 different constant volume strains to Nanjing sand respectively
Sample carries out 3 monotonic loading tests.Soil sample relative density is 0.48.Sample is cylinder, and diameter 39.1mm is a height of
80mm.3 constant confining pressures are respectively 0.05MPa, 0.1MPa and 0.2MPa.The condition of dullness load and the load item of Practical Project
Part is identical, if loading speed is 0.073mm/min, room temperature.
(2) according to " earthwork test rule " SL237-1999, the data of each bulk strain condition of triaxial test are acquired,
And it is converted into principal stress σ1、σ3, principal strain ε1、ε3With the data of pore water pressure u.
(3) according to formula (5), formula (12) and formula (13) by σ1、σ3Each bulk strain item on meridian plane is converted into u
Q-p ' relation curve of part, the curve are the volume yield surface of each confining pressure condition and the intersection of meridian plane.
Q=| σ1-σ3| (5)
P=(σ1+2σ3)/3 (12)
P '=p-u (13)
Q-p ' relationship trial curve that Nanjing sand does not drain constant confining pressure triaxial test is shown in Figure 10.
(4) the volume yield surface on q-p ' relation curve of each bulk strain condition cut contracting part selection one
Representative characteristic point in shape, this feature point is not in p ' reference axis.Sand body product yield surface characteristic point data in Nanjing is shown in
Table 8.
8 Nanjing sand body of table accumulates yield surface characteristic point data/MPa
(5) by deviator stress be 0 when q-p ' relation curve on point abscissa substitute into formula (14) inIt will remove
Deviator stress is that the volume yield surface on q-p ' relation curve outside 0 cuts the abscissa of the selected characteristic point in contracting part
Y in substitution formula (14)v1；Volume yield surface on q-p ' relation curve in addition to deviator stress is 0 is cut selected by contracting part
A characteristic point ordinate substitute into formula (14).Form system of linear equations, the quantity of linear equation and different hardening parameter water
The quantity of flat actual measurement volume yield surface is equal.
System of linear equations is
(6) system of linear equations is solved with the method for solving inconsistent equation group, obtains oval volume yield condition parameter CG、CH、
CI。
The oval volume yield condition parameter of Nanjing sand are as follows: CG=87.7545, CH=-21.1092, CI=1.2392.
(7) by oval volume yield condition parameter CG、CH、CIIn generation, returns formula (8), formula (9), formula (10) and formula (11), obtains rock
The oval volume yield condition of soil material.The oval volume yield condition of Fujian standard sand are as follows:
(8) by deviator stress be 0 when volume yield surface on p substitute into formula (14) inBy CG、CH、CIValue and substitution
Formula (14).Using q as longitudinal axis variable, Yv1It is that formula (14) draw on meridian plane for horizontal axis variable, the volume for obtaining rock-soil material is bent
Cut the regression curve of contracting part in the face of clothes.The obtained corresponding volume subsequent yield surface of each confining pressure is returned, sees Figure 10；It is obtained from test
The corresponding volume subsequent yield surface of each confining pressure, see Figure 10.As seen from Figure 10, in low deviator stress, volume yield surface cuts contracting portion
The regression effect divided is good, and error is less than 5%.
Volume yield surface cuts the determination step of swollen part:
The explanation of symbol in following steps: fv2For hyperbola volume yield function, work as fv2Volume surrender occurs when >=0, when
fv2Volume surrender does not occur when < 0；P is mean stress；HvFor volume hardening parameter；Q is generalized shear stress；Yv2It is answered for practical master
Volume yield stress when power difference is defined by formula (16)；Δ p is the increment of mean stress, is positive load as Δ p > 0, when
It is Opposite side loading when Δ p < 0；Volume yield stress when for deviator stress being 0 is defined by formula (10)；Bv2It is fixed for formula (17)
The quadratic polynomial of justice；αvFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；CD、CE、CF.
For hyperbola volume yield condition parameter, is returned and determined by the actual measurement volume yield surface of at least three difference hardening parameter level；
σ1For big principal stress；σ3For minor principal stress；P ' is effective mean stress；U is pore water pressure.
(1) form of hyperbola volume yield function is formula (15), formula (16), formula (10) and formula (17), according to " geotechnique tries
Test regulation " SL237-1999, using the triaxial test not drained, respectively by the strain of at least three difference constant volume to material
Carry out corresponding monotonic loading test.The condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature
Degree.
Wherein: the α when considering kinematic hardeningvFor variable,The α when not considering kinematic hardeningvIt is 0, formula (15)
The case where when only calculating Δ p > 0 with formula (10).The present embodiment passes through the condition of 3 different constant volume strains to Nanjing respectively
Sand sample carries out 3 monotonic loading tests.Soil sample relative density is 0.48.Sample is cylinder, and diameter 39.1mm is a height of
80mm.3 constant confining pressures are respectively 0.05MPa, 0.1MPa and 0.2MPa.The condition of dullness load and the load item of Practical Project
Part is identical, if loading speed is 0.073mm/min, room temperature.
(2) according to " earthwork test rule " SL237-1999, the data of each bulk strain condition of triaxial test are acquired,
And it is converted into principal stress σ1、σ3, principal strain ε1、ε3With the data of pore water pressure u.
(3) according to formula (5), formula (12) and formula (13) by σ1、σ3Each bulk strain item on meridian plane is converted into u
Q-p ' relation curve of part, the curve are the volume yield surface of each confining pressure condition and the intersection of meridian plane.
Q=| σ1-σ3| (5)
P=(σ1+2σ3)/3 (12)
P '=p-u (13)
Q-p ' relationship trial curve that Nanjing sand does not drain constant confining pressure triaxial test is shown in Figure 10.
(4) the volume yield surface on q-p ' relation curve of each confining pressure condition cuts swollen part selection one in shape
Upper representative characteristic point, this feature point is not in p ' reference axis.Sand body product yield surface characteristic point data in Nanjing is shown in Table 8.
(5) by deviator stress be 0 when q-p ' relation curve on point abscissa substitute into formula (18) inIt will remove
Deviator stress is that the volume yield surface on q-p ' relation curve outside 0 cuts the abscissa of the selected characteristic point in swollen part
Y in substitution formula (18)v2；Volume yield surface on q-p ' relation curve in addition to deviator stress is 0 is cut selected by swollen part
A characteristic point ordinate substitute into formula (18).Form system of linear equations, the quantity of linear equation and different hardening parameter water
The quantity of flat actual measurement volume yield surface is equal.
System of linear equations is
(6) system of linear equations is solved with the method for solving inconsistent equation group, obtains hyperbola volume yield condition parameter CD、
CE、CF。
The hyperbola volume yield condition parameter of Nanjing sand are as follows: CD=-12.8960, CE=2.6531, CF=0.6198.
(7) by hyperbola volume yield condition parameter CD、CE、CFIn generation, returns formula (15), formula (16), formula (10) and formula (17), obtains
To the hyperbola volume yield condition of rock-soil material.The hyperbola volume yield condition of Nanjing sand are as follows:
(8) by deviator stress be 0 when volume yield surface on p substitute into formula (18) inBy CD、CE、CFValue and substitution
Formula (18).Using q as longitudinal axis variable, Yv2It is that formula (18) draw on meridian plane for horizontal axis variable, the volume for obtaining rock-soil material is bent
Cut the regression curve of swollen part in the face of clothes.The obtained corresponding volume subsequent yield surface of each confining pressure is returned, sees Figure 10；It is obtained from test
The corresponding volume subsequent yield surface of each confining pressure, see Figure 10.As seen from Figure 10, in high deviator stress, volume yield surface cuts swollen portion
The regression effect divided is good, and error is less than 5%.
Parameter measured by the measuring method in the rock-soil material shear yielding face and volume yield surface is in evaluation ground
The application of material volume yield surface, applying step are as follows:
(1) it is restrained to be connected kinematic hardening, in the algorithm inclined back stress tensor αvIt is expressed as
αv.n+1=αv.n+Δαv.n+1 (24)
Wherein: subscriptnRefer to an increment；Subscriptn+1Refer to this increment；Symbol Δ refers to that the variable is increment；When t is
Between；It is restrained from specific kinematic hardening.If a upper increment transmits αv.n=0.1MPa；This incrementThen this increment
(2) it is restrained to be connected isotropic hardening, in the algorithm isotropic hardening coefficient when benchmark deviator stressIt is expressed as
Wherein:It is restrained from specific isotropic hardening.If a upper increment transmitsThis incrementThen this increment
(3) oval volume yield condition and hyperbola volume yield condition are checked
Work as fv1.n+1>=0 and fv2.n+1Volume surrender occurs for this increment when >=0；Volume does not occur for this increment in the wrong when remaining situation
Clothes.If this increment pn+1=1MPa, q=0.0015MPa, Δ p > 0；The then volume yield condition of this increment Nanjing sand are as follows:
fv2.n+1=| pn+1|-Yv2.n+1=| 1 | volume surrender occurs for-(- 21.6579)=increment of 22.6579MPa > 0.
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