CN109580388A - A kind of measuring method in rock-soil material shear yielding face and volume yield surface - Google Patents

Abstract

The measuring method in a kind of rock-soil material shear yielding face and volume yield surface is related to metering of solids deformation technology field.In order to judge the stress surrender of rock-soil material, shear yielding face is fitted using quadratic polynomial, using oval and hyperbolic fit volume yield surface.Parametric regression is carried out to quadratic polynomial shear yielding condition by constant mean stress triaxial test and conventional triaxial compression test；Parametric regression is carried out to oval and hyperbola volume yield condition by the constant mean stress triaxial test and conventional triaxial compression test that do not drain.The regression curve of yield surface is drawn according to shear yielding condition, volume yield condition and relevant parameter.According to the specific response in engineering of shear yielding condition and volume yield condition, evaluate whether rock-soil material occurs shear yielding or volume surrender.This method can judge that rock-soil material, with the presence or absence of surrender, to take corresponding measure, prevents material from generating destruction, cause across the accident of collapsing after stress in engineering.

Description

A kind of measuring method in rock-soil material shear yielding face and volume yield surface

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: f_sFor shear yielding function, work as f_sShear yielding occurs when >=0, works as f_sWhen < 0 Shear yielding does not occur；ξ_sFor opposite deviatoric stress, defined by formula (2)；H_sFor shear hardening parameter；P is mean stress；K_sFor reality Shearing isotropic hardening coefficient when the mean stress of border is defined by formula (3)；S is deviatoric stress tensor；α_sFor inclined back stress tensor, when Consider α when kinematic hardening_sFor variable, the α when not considering kinematic hardening_sIt 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；B_sIt is fixed for formula (4) The quadratic polynomial of justice；C_A、C_B、C_CFor 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.

ξ_s=s- α_s(H_s) (2)

B_s=C_Ap²+C_Bp+C_C (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 C_A、C_B、C_C。

(8) by shear yielding conditional parameter C_A、C_B、C_CIn 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 C_A、 C_B、C_CValue and substitute into formula (7).Using p as horizontal axis variable, K_sIt 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: f_v1For oval volume yield function, work as f_v1Volume surrender occurs when >=0, works as f_v1 Volume surrender does not occur when < 0；P is mean stress；H_vFor volume hardening parameter；Q is generalized shear stress；Y_v1For 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)；B_v1For formula (11) definition Quadratic polynomial；α_vFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；C_G、C_H、C_IFor 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 hardening_vFor variable,The α when not considering kinematic hardening_vIt 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 C_G、C_H、 C_I。

(7) by oval volume yield condition parameter C_G、C_H、C_IIn 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 C_G、C_H、C_IValue and substitution Formula (14).Using q as longitudinal axis variable, Y_v1It 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: f_v2For hyperbola volume yield function, work as f_v2Volume surrender occurs when >=0, when f_v2Volume surrender does not occur when < 0；P is mean stress；H_vFor volume hardening parameter；Q is generalized shear stress；Y_v2It 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)；B_v2It is fixed for formula (17) The quadratic polynomial of justice；α_vFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；C_D、C_E、C_F. 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 hardening_vFor variable,The α when not considering kinematic hardening_vIt 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 C_D、 C_E、C_F。

(7) by hyperbola volume yield condition parameter C_D、C_E、C_FIn 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 C_D、C_E、C_FValue and substitution Formula (18).Using q as longitudinal axis variable, Y_v2It 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: f_sFor shear yielding function, work as f_sShear yielding occurs when >=0, works as f_sWhen < 0 Shear yielding does not occur；ξ_sFor opposite deviatoric stress, defined by formula (2)；H_sFor shear hardening parameter；P is mean stress；K_sFor reality Shearing isotropic hardening coefficient when the mean stress of border is defined by formula (3)；S is deviatoric stress tensor；α_sFor inclined back stress tensor, when Consider α when kinematic hardening_sFor variable, the α when not considering kinematic hardening_sIt 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；B_sIt is fixed for formula (4) The quadratic polynomial of justice；C_A、C_B、C_CFor 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.

ξ_s=s- α_s(H_s) (2)

B_s=C_Ap²+C_Bp+C_C (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 C_A、C_B、C_C。

(12) by shear yielding conditional parameter C_A、C_B、C_CIn 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 C_A、C_B、C_CValue and substitute into formula (7).Using p as horizontal axis variable, K_sIt 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 α_sIt is expressed as

α_s.n+1=α_s.n+Δα_s.n+1 (19)

Wherein: subscript_nRefer to an increment；Subscript_n+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 f_s.n+1Shear yielding occurs for this increment when >=0；Work as f_s.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 α_vIt is expressed as

α_v.n+1=α_v.n+Δα_v.n+1 (24)

Wherein: subscript_nRefer to an increment；Subscript_n+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 f_v1.n+1>=0 and f_v2.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: f_sFor shear yielding function；ξ_sFor opposite deviatoric stress, defined by formula (2)；H_sFor shear hardening parameter；P is Mean stress；K_sShearing 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).

ξ_s=s- α_s(H_s) (2)

Wherein: s is deviatoric stress tensor；α_sFor inclined back stress tensor, the α when considering kinematic hardening_sFor variable, when not considering α when kinematic hardening_sIt 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；B_sFor with The related coefficient of mean stress is defined by formula (4).

B_s=C_Ap²+C_Bp+C_C (4)

Wherein: C_A、C_B、C_CFor 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: f_v1For 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 B_v1With mean stress Increase and changes.Based on the above-mentioned fact, formula (11) description B can be used_v1Change 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)；H_vFor volume hardening parameter；C_G、C_H、C_IFor 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: α_vFor ball back stress tensor；The α when considering kinematic hardening_vFor variable, the α when not considering kinematic hardening_vFor 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 α_vIt is 0.If in formula (5)WithIt indicates, then convolution (34) It obtains

Wherein: Y_v1Volume 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: f_v2For hyperbola volume yield function, work as f_v2Volume surrender occurs when >=0, works as f_v2Not generating body when < 0 Product surrender；Y_v2Volume 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: B_v2For 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 B_v2It is to change with mean stress.Based on above-mentioned observation, formula (17) description B can be used_v2With Mean stress variation.

Wherein: C_D、C_E、C_FFor 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) b_s=C_Ap²+C_Bp+C_C, 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: f_sFor shear yielding function, work as f_sShear yielding occurs when >=0, works as f_sWhen < 0 Shear yielding does not occur；ξ_sFor opposite deviatoric stress, defined by formula (2)；H_sFor shear hardening parameter；P is mean stress；K_sFor reality Shearing isotropic hardening coefficient when the mean stress of border is defined by formula (3)；S is deviatoric stress tensor；α_sFor inclined back stress tensor, when Consider α when kinematic hardening_sFor variable, the α when not considering kinematic hardening_sIt 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；B_sIt is fixed for formula (4) The quadratic polynomial of justice；C_A、C_B、C_CFor 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.

ξ_s=s- α_s(H_s) (2)

B_s=C_Ap²+C_Bp+C_C (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 C_A、C_B、C_C。

The shear yielding conditional parameter of Fujian standard sand are as follows: C_A=0.1793, C_B=-4.7938, C_C=0.0341.

(8) by shear yielding conditional parameter C_A、C_B、C_CIn 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 C_A、 C_B、C_CValue and substitute into formula (7).Using p as horizontal axis variable, K_sIt 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 α_sIt is expressed as

α_s.n+1=α_s.n+Δα_s.n+1 (19)

Wherein: subscript_nRefer to an increment；Subscript_n+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 α_s.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 f_s.n+1Shear yielding occurs for this increment when >=0；Work as f_s.n+1Shear yielding does not occur for this increment when < 0.

If this increment s_sn+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: f_v1For oval volume yield function, work as f_v1Volume surrender occurs when >=0, works as f_v1 Volume surrender does not occur when < 0；P is mean stress；H_vFor volume hardening parameter；Q is generalized shear stress；Y_v1For 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)；B_v1It is defined for formula (11) Quadratic polynomial；α_vFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；C_G、C_H、C_IFor 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 hardening_vFor variable,The α when not considering kinematic hardening_vBe 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 C_G、C_H、 C_I。

The oval volume yield condition parameter of Fujian standard sand are as follows: C_G=-26.9447, C_H=15.2498, C_I=- 1.6947。

(7) by oval volume yield condition parameter C_G、C_H、C_IIn 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 C_G、C_H、C_IValue and substitution Formula (14).Using q as longitudinal axis variable, Y_v1It 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: f_v2For hyperbola volume yield function, work as f_v2Volume surrender occurs when >=0, when f_v2Volume surrender does not occur when < 0；P is mean stress；H_vFor volume hardening parameter；Q is generalized shear stress；Y_v2It 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)；B_v2It is fixed for formula (17) The quadratic polynomial of justice；α_vFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；C_D、C_E、C_F. 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 hardening_vFor variable,The α when not considering kinematic hardening_vIt 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 C_D、 C_E、C_F。

The hyperbola volume yield condition parameter of Fujian standard sand are as follows: C_D=-0.2777, C_E=0.1220, C_F= 0.6395。

(7) by hyperbola volume yield condition parameter C_D、C_E、C_FIn 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 C_D、C_E、C_FValue and substitution Formula (18).Using q as longitudinal axis variable, Y_v2It 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 α_vIt is expressed as

α_v.n+1=α_v.n+Δα_v.n+1 (24)

Wherein: subscript_nRefer to an increment；Subscript_n+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 α_v.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 f_v1.n+1>=0 and f_v2.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 p_n+1=1MPa, q=0.0015MPa, Δ p > 0；Then the volume of this increment Fujian standard sand surrenders item Part are as follows:

f_v2.n+1=| p_n+1|-Y_v2.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: f_sFor shear yielding function, work as f_sShear yielding occurs when >=0, works as f_sWhen < 0 Shear yielding does not occur；ξ_sFor opposite deviatoric stress, defined by formula (2)；H_sFor shear hardening parameter；P is mean stress；K_sFor reality Shearing isotropic hardening coefficient when the mean stress of border is defined by formula (3)；S is deviatoric stress tensor；α_sFor inclined back stress tensor, when Consider α when kinematic hardening_sFor variable, the α when not considering kinematic hardening_sIt 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；B_sIt is fixed for formula (4) The quadratic polynomial of justice；C_A、C_B、C_CFor 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.

ξ_s=s- α_s(H_s) (2)

B_s=C_Ap²+C_Bp+C_C (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 C_A、C_B、C_C。

The shear yielding conditional parameter of Fujian standard sand are as follows: C_A=0.2889, C_B=-4.3259, C_C=-0.0341.

(12) by shear yielding conditional parameter C_A、C_B、C_CIn 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 C_A、C_B、C_CValue and substitute into formula (7).Using p as horizontal axis variable, K_sIt 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 α_sIt is expressed as

α_s.n+1=α_s.n+Δα_s.n+1 (19)

Wherein: subscript_nRefer to an increment；Subscript_n+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 α_s.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 f_s.n+1Shear yielding occurs for this increment when >=0；Work as f_s.n+1Shear yielding does not occur for this increment when < 0.

If this increment s_sn+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: f_v1For oval volume yield function, work as f_v1Volume surrender occurs when >=0, works as f_v1 Volume surrender does not occur when < 0；P is mean stress；H_vFor volume hardening parameter；Q is generalized shear stress；Y_v1For 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)；B_v1For formula (11) definition Quadratic polynomial；α_vFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；C_G、C_H、C_IFor 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 hardening_vFor variable,The α when not considering kinematic hardening_vBe 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 C_G、C_H、 C_I。

The oval volume yield condition parameter of Fujian standard sand are as follows: C_G=-8.0176, C_H=2.6323, C_I=0.6412.

(7) by oval volume yield condition parameter C_G、C_H、C_IIn 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 C_G、C_H、C_IValue and substitution Formula (14).Using q as longitudinal axis variable, Y_v1It 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: f_v2For hyperbola volume yield function, work as f_v2Volume surrender occurs when >=0, when f_v2Volume surrender does not occur when < 0；P is mean stress；H_vFor volume hardening parameter；Q is generalized shear stress；Y_v2It 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)；B_v2It is fixed for formula (17) The quadratic polynomial of justice；α_vFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；C_D、C_E、C_F. 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 hardening_vFor variable,The α when not considering kinematic hardening_vIt 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 C_D、 C_E、C_F。

The hyperbola volume yield condition parameter of Fujian standard sand are as follows: C_D=-5.2951, C_E=1.1163, C_F= 0.6343。

(7) by hyperbola volume yield condition parameter C_D、C_E、C_FIn 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 C_D、C_E、C_FValue and substitution Formula (18).Using q as longitudinal axis variable, Y_v2It 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 α_vIt is expressed as

α_v.n+1=α_v.n+Δα_v.n+1 (24)

Wherein: subscript_nRefer to an increment；Subscript_n+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 α_v.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 f_v1.n+1>=0 and f_v2.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 p_n+1=1MPa, q=0.0015MPa, Δ p < 0；Then the volume of this increment Fujian standard sand surrenders item Part are as follows:

f_v2.n+1=Y_v2.n+1-|p_n+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: f_sFor shear yielding function, work as f_sShear yielding occurs when >=0, works as f_sWhen < 0 Shear yielding does not occur；ξ_sFor opposite deviatoric stress, defined by formula (2)；H_sFor shear hardening parameter；P is mean stress；K_sFor reality Shearing isotropic hardening coefficient when the mean stress of border is defined by formula (3)；S is deviatoric stress tensor；α_sFor inclined back stress tensor, when Consider α when kinematic hardening_sFor variable, the α when not considering kinematic hardening_sIt 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；B_sIt is fixed for formula (4) The quadratic polynomial of justice；C_A、C_B、C_CFor 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.

ξ_s=s- α_s(H_s) (2)

B_s=C_Ap²+C_Bp+C_C (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 C_A、C_B、C_C。

The shear yielding conditional parameter of Nanjing sand are as follows: C_A=-3.6027, C_B=-6.2193, C_C=0.0533.

(12) by shear yielding conditional parameter C_A、C_B、C_CIn 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 C_A、C_B、C_CValue and substitute into formula (7).Using p as horizontal axis variable, K_sIt 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 α_sIt is expressed as

α_s.n+1=α_s.n+Δα_s.n+1 (19)

Wherein: subscript_nRefer to an increment；Subscript_n+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 α_s.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 f_s.n+1Shear yielding occurs for this increment when >=0；Work as f_s.n+1Shear yielding does not occur for this increment when < 0.

If this increment s_sn+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: f_v1For oval volume yield function, work as f_v1Volume surrender occurs when >=0, works as f_v1 Volume surrender does not occur when < 0；P is mean stress；H_vFor volume hardening parameter；Q is generalized shear stress；Y_v1For 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)；B_v1For formula (11) definition Quadratic polynomial；α_vFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；C_G、C_H、C_IFor 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 hardening_vFor variable,The α when not considering kinematic hardening_vBe 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 C_G、C_H、 C_I。

The oval volume yield condition parameter of Nanjing sand are as follows: C_G=87.7545, C_H=-21.1092, C_I=1.2392.

(7) by oval volume yield condition parameter C_G、C_H、C_IIn 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 C_G、C_H、C_IValue and substitution Formula (14).Using q as longitudinal axis variable, Y_v1It 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: f_v2For hyperbola volume yield function, work as f_v2Volume surrender occurs when >=0, when f_v2Volume surrender does not occur when < 0；P is mean stress；H_vFor volume hardening parameter；Q is generalized shear stress；Y_v2It 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)；B_v2It is fixed for formula (17) The quadratic polynomial of justice；α_vFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；C_D、C_E、C_F. 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 hardening_vFor variable,The α when not considering kinematic hardening_vIt 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 C_D、 C_E、C_F。

The hyperbola volume yield condition parameter of Nanjing sand are as follows: C_D=-12.8960, C_E=2.6531, C_F=0.6198.

(7) by hyperbola volume yield condition parameter C_D、C_E、C_FIn 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 C_D、C_E、C_FValue and substitution Formula (18).Using q as longitudinal axis variable, Y_v2It 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 α_vIt is expressed as

α_v.n+1=α_v.n+Δα_v.n+1 (24)

Wherein: subscript_nRefer to an increment；Subscript_n+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 α_v.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 f_v1.n+1>=0 and f_v2.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 p_n+1=1MPa, q=0.0015MPa, Δ p > 0；The then volume yield condition of this increment Nanjing sand are as follows:

f_v2.n+1=| p_n+1|-Y_v2.n+1=| 1 | volume surrender occurs for-(- 21.6579)=increment of 22.6579MPa > 0.

Claims (4)

1. the measuring method in a kind of rock-soil material shear yielding face and volume yield surface, which is characterized in that including shear yielding face Determination step and volume yield surface determination step, when triaxial tester can in test control mean stress be it is constant When,

The determination step in shear yielding face are as follows:

The explanation of symbol in following steps: f_sFor shear yielding function, work as f_sShear yielding occurs when >=0, works as f_s0 Shi Bufa of < Raw shear yielding；ξ_sFor opposite deviatoric stress, defined by formula (2)；H_sFor shear hardening parameter；P is mean stress；K_sIt is practical flat Shearing isotropic hardening coefficient when equal stress is defined by formula (3)；S is deviatoric stress tensor；α_sFor inclined back stress tensor, work as consideration α when kinematic hardening_sFor variable, the α when not considering kinematic hardening_sIt is 0；Shearing isotropic hardening system when for benchmark mean stress Number, when considering isotropic hardeningFor variable, when not considering isotropic hardeningFor the constant of setting；B_sIt is defined for formula (4) Quadratic polynomial；C_A、C_B、C_CFor shear yielding conditional parameter, carried out by the different constant mean stress triaxial tests of at least three It returns and determines；Q is generalized shear stress；For General architecture；σ₁For big principal stress；σ₃For minor principal stress；ε₁For major principal strain；ε₃ For 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, using constant mean stress triaxial test, material is carried out by least three different constant mean stresses respectively corresponding single Load test is adjusted, the condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature, consolidation and row Water bar part,

ξ_s=s- α_s(H_s) (2)

B_s=C_Ap²+C_Bp+C_C (4)

(2) according to " earthwork test rule " SL237-1999, each mean stress item of constant mean stress triaxial test is acquired The data of part, 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 conditionRelation curve,

Q=| σ₁-σ₃| (5)

(4) within the scope of the mean stress of engineer application, select one of mean stress as benchmark mean stress, accordinglyWhen 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；By the ginseng of benchmark mean stress The corresponding q of shear hardening parameter is examined to substitute into formula (7)P when by each mean stress substitutes into formula (7), forms linear equation Group, the quantity of linear equation is 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 C_A、C_B、C_C,

(8) by shear yielding conditional parameter C_A、C_B、C_CIn generation, returns formula (1), formula (3) and formula (4), obtains the shear yielding of rock-soil material Condition,

(9) by benchmark mean stress the horizontal corresponding q of each shear hardening parameter is substituted into respectively in formula (7) whenBy C_A、C_B、C_C Value and substitute into formula (7), using p as horizontal axis variable, K_sIt is that formula (7) draw on meridian plane for longitudinal axis variable, obtains rock-soil material Shear yielding face regression curve,

Volume yield surface cuts the determination step of contracting part:

The explanation of symbol in following steps: f_v1For oval volume yield function, work as f_v1Volume surrender occurs when >=0, works as f_v1< 0 When do not occur volume surrender；P is mean stress；H_vFor volume hardening parameter；Q is generalized shear stress；Y_v1For practical deviator stress When volume yield stress, by formula (9) define；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)；B_v1It is defined for formula (11) Quadratic polynomial；α_vFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；C_G、C_H、C_IFor 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 " earthwork test rule " SL237-1999 respectively carries out material by the strain of at least three difference constant volume corresponding using the triaxial test not drained The condition of monotonic loading test, dullness load is identical as the loading environment of Practical Project, including loading speed, temperature,

Wherein: the α when considering kinematic hardening_vFor variable,The α when not considering kinematic hardening_vIt is 0, formula (8) and formula (10) only calculate Δ p > 0 when the case where,

(2) according to " earthwork test rule " SL237-1999, the data of each bulk strain condition of triaxial test are acquired, and are turned Change principal stress σ into₁、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 condition on meridian plane is converted into u Q-p ' relation curve, 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 cuts contracting part selection one in shape Upper representative characteristic point, this feature point 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 be answered except master Power difference be 0 outside q-p ' relation curve on volume yield surface cut the selected characteristic point in contracting part abscissa substitution Y in formula (14)_v1；Volume yield surface on q-p ' relation curve in addition to deviator stress is 0 is cut into contracting part selected one The ordinate of a characteristic point substitutes into formula (14), forms system of linear equations, the quantity of linear equation and different hardening parameters levels The quantity for surveying 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 C_G、C_H、C_I,

(7) by oval volume yield condition parameter C_G、C_H、C_IIn generation, returns formula (8), formula (9), formula (10) and formula (11), obtains ground material The oval volume yield condition of material,

(8) by deviator stress be 0 when volume yield surface on p substitute into formula (14) in Y_v ^*；By C_G、C_H、C_IValue and substitute into formula (14), using q as longitudinal axis variable, Y_v1It is that formula (14) draw on meridian plane for horizontal axis variable, obtains the volume surrender of rock-soil material The regression curve of contracting part is cut in face,

Volume yield surface cuts the determination step of swollen part:

The explanation of symbol in following steps: f_v2For hyperbola volume yield function, work as f_v2Volume surrender occurs when >=0, works as f_v2< Volume surrender does not occur when 0；P is mean stress；H_vFor volume hardening parameter；Q is generalized shear stress；Y_v2For practical deviator stress When volume yield stress, by formula (16) define；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)；B_v2For formula (17) definition Quadratic polynomial；α_vFor ball back stress tensor；Volume isotropic hardening coefficient when for deviator stress being 0；C_D、C_E、C_F.For Hyperbola volume yield condition parameter is returned by the actual measurement volume yield surface of at least three difference hardening parameter level and is determined；σ₁ For 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 " 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 The condition of corresponding monotonic loading test, dullness load is identical as the loading environment of Practical Project, including loading speed, temperature,

Wherein: the α when considering kinematic hardening_vFor variable,The α when not considering kinematic hardening_vIt is 0, formula (15) and formula (10) only calculate Δ p > 0 when the case where,

(2) according to " earthwork test rule " SL237-1999, the data of each bulk strain condition of triaxial test are acquired, and are turned Change principal stress σ into₁、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 condition on meridian plane is converted into u Q-p ' relation curve, 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 is cut swollen part selection one and is had in shape Representational characteristic point, this feature point 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 be answered except master Power difference be 0 outside q-p ' relation curve on volume yield surface cut the selected characteristic point in swollen part abscissa substitute into Y in formula (18)_v2；Volume yield surface on q-p ' relation curve in addition to deviator stress is 0 is cut into swollen part selected one The ordinate of a characteristic point substitutes into formula (18), forms system of linear equations, the quantity of linear equation and different hardening parameters levels The quantity for surveying 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 C_D、C_E、 C_F,

(7) by hyperbola volume yield condition parameter C_D、C_E、C_FIn generation, returns formula (15), formula (16), formula (10) and formula (17), obtains rock The hyperbola volume yield condition of soil material,

(8) by deviator stress be 0 when volume yield surface on p substitute into formula (18) inBy C_D、C_E、C_FValue and substitute into formula (18), using q as longitudinal axis variable, Y_v2It is that formula (18) draw on meridian plane for horizontal axis variable, obtains the volume surrender of rock-soil material Cut the regression curve of swollen part in face.

2. the measuring method in rock-soil material shear yielding described in claim 1 face and volume yield surface, which is characterized in that when three Shaft experiment instrument is unable to control in test mean stress when being constant, is cut using equivalent constant mean stress triaxial (test) method measurement Yield surface is cut,

The step of equivalent constant mean stress triaxial (test) method measurement shear yielding face are as follows:

The explanation of symbol in following steps: f_sFor shear yielding function, work as f_sShear yielding occurs when >=0, works as f_s0 Shi Bufa of < Raw shear yielding；ξ_sFor opposite deviatoric stress, defined by formula (2)；H_sFor shear hardening parameter；P is mean stress；K_sIt is practical flat Shearing isotropic hardening coefficient when equal stress is defined by formula (3)；S is deviatoric stress tensor；α_sFor inclined back stress tensor, work as consideration α when kinematic hardening_sFor variable, the α when not considering kinematic hardening_sIt is 0；Shearing isotropic hardening system when for benchmark mean stress Number, when considering isotropic hardeningFor variable, when not considering isotropic hardeningFor the constant of setting；B_sIt is defined for formula (4) Quadratic polynomial；C_A、C_B、C_CFor shear yielding conditional parameter, carried out by the different constant mean stress triaxial tests of at least three It returns and determines；Q is generalized shear stress；For General architecture；σ₁For big principal stress；σ₃For minor principal stress；ε₁For major principal strain；ε₃ For 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, using conventional triaxial compression test, corresponding dull load examination is carried out to material by least three difference constant confining pressure respectively It tests, the condition of dullness load is identical as the loading environment of Practical Project, including loading speed, temperature, consolidation and drainage condition,

ξ_s=s- α_s(H_s) (2)

B_s=C_Ap²+C_Bp+C_C (4)

(2) according to " earthwork test rule " SL237-1999, the data of each confining pressure condition of conventional triaxial compression test are acquired, 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 and extrapolation are carried out to the shear hardening parameter equipotentiality point of q-p relation curve on meridian plane, it is hard forms shearing Change 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 average Stress triaxial test stress path line, the line is 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, and two kinds The intersection point of line, that is, equivalent constant mean stress triaxial test stress path characteristic point,

(8) within the scope of the mean stress of engineer application, a wherein equivalent constant mean stress triaxial test stress road is selected The mean stress of radial line as benchmark mean stress,

(9) in the range of strain of engineer application, selection wherein shear hardening parameter equipotential linesIt is hard as reference shearing Change parameter,

(10) in the range of equivalent constant mean stress triaxial test stress path characteristic point, the reference of each mean stress is cut Cut the K that the corresponding q of hardening parameter is substituted into formula (7)_s；The corresponding q of the reference shear hardening parameter of benchmark mean stress is substituted into In formula (7)P when by each mean stress substitutes into formula (7), forms system of linear equations, the quantity of linear equation and equivalent perseverance The quantity for determining 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 C_A、C_B、C_C,

(12) by shear yielding conditional parameter C_A、C_B、C_CIn generation, returns formula (1), formula (3) and formula (4), and the shearing for obtaining rock-soil material is bent Condition is taken,

(13) by benchmark mean stress the horizontal corresponding q of each shear hardening parameter is substituted into respectively in formula (7) whenBy C_A、C_B、 C_CValue and substitute into formula (7), using p as horizontal axis variable, K_sIt is that formula (7) draw on meridian plane for longitudinal axis variable, obtains rock-soil material Shear yielding face regression curve.

3. parameter measured by measuring method of the rock-soil material shear yielding described in claim 1 face with volume yield surface is being commented The application in valence rock-soil material shear yielding face, which is characterized in that applying step are as follows:

(1) it is restrained to be connected kinematic hardening, in the algorithm inclined back stress tensor α_sIt is expressed as

α_s.n+1=α_s.n+Δα_s.n+1 (19)

Wherein: subscript_nRefer to an increment；Subscript_n+1Refer to this increment；Symbol Δ refers to that the variable is increment；T is the time； 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 f_s.n+1Shear yielding occurs for this increment when >=0；Work as f_s.n+1Shear yielding does not occur for this increment when < 0.

4. parameter measured by measuring method of the rock-soil material shear yielding described in claim 1 face with volume yield surface is being commented The application of valence rock-soil material volume yield surface, which is characterized in that applying step is,

(1) it is restrained to be connected kinematic hardening, in the algorithm inclined back stress tensor α_vIt is expressed as

α_v.n+1=α_v.n+Δα_v.n+1 (24)

Wherein: subscript n refers to an increment；Subscript n+1 refers to this increment；Symbol Δ refers to that the variable is increment；T is the time；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 f_v1.n+1>=0 and f_v2.n+1Volume surrender occurs for this increment when >=0；Volume surrender does not occur for this increment when remaining situation.