Method for correcting parameters of Duncan-Chang model of soil body under complex stress condition

Abstract

The invention discloses a Duncan-Chang model parameter correction method for a soil body under a complex stress condition, and belongs to the technical field of water conservancy and hydropower engineering informatization system construction.The Duncan-Chang model parameter correction method comprises the steps that S1, according to different strength criteria, cohesive force expressions under different stress states are obtained; and S2, based on an incremental generalized Hooke's law, considering deformation generated by the effect of small principal stress difference in large principal strain superposition of the Duncan-Tensile model under the influence of medium principal stress, introducing stress state parameters, and correcting deformation modulus parameters. A natural loess consolidation drainage shear test is carried out under the true triaxial condition, the strength and deformation characteristics of a loess body in a complex stress state are revealed, the influence rule of principal stress on strength parameters is discussed from the strength parameter internal friction angle of a material under the true triaxial stress, and the stability of the loess consolidation drainage shear test is improved. The problem that the predicted tangent deformation modulus error is large due to the fact that an existing Duncan-Chang model does not consider the influence of the principal stress is solved, and the accuracy of the predicted tangent deformation modulus is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of civil engineering calculation, and in particular relates to a Duncan-Chang model parameter correction method for soil under complex stress conditions. Background Art

[0002] The nonlinearity of stress-strain relationship is one of the basic deformation characteristics of soil, and the nonlinear elastic model is widely used in the engineering community because of its simple model, fewer parameters and good description of the process of soil deformation under stress. The most classic of these is the Duncan-Zhang nonlinear elastic model, which is widely used in practical engineering due to its simple theory and easy calculation process.

[0003] However, the model does not consider the influence of the change of intermediate principal stress on the shear action of soil, which is inconsistent with the deformation law of soil under the condition of the increase of intermediate principal stress in actual engineering. Since the Duncan-Zhang model fails to consider the influence of intermediate principal stress, the predicted tangent deformation modulus error is large. If the most original model formula is applied arbitrarily without considering the test conditions, it may cause unsafe or uneconomical engineering. Therefore, it is necessary to modify the most original model so that engineers can more accurately obtain parameters that can correctly characterize material properties. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that the existing Duncan-Zhang model fails to consider the influence of the intermediate principal stress, resulting in a large error in the predicted tangent deformation modulus, and proposes a Duncan-Zhang model parameter correction method for soil under complex stress conditions. By carrying out a natural loess consolidation drainage shear test under true triaxial conditions, the strength and deformation characteristics of the loess body in a complex stress state are revealed, and starting from the internal friction angle of the strength parameter of the material under true triaxial stress, the influence of the intermediate principal stress on the strength parameter is explored, and based on the generalized Hooke's law, it is introduced into the Duncan-Zhang EB model parameters, which solves the problem that the existing Duncan-Zhang model fails to consider the influence of the intermediate principal stress, resulting in a large error in the predicted tangent deformation modulus, and improves the accuracy of the predicted tangent deformation modulus.

[0005] In order to solve the above technical problems, the present invention provides a method for correcting parameters of the Duncan-Zhang model for soil under complex stress conditions, comprising the following steps:

[0006] S1. According to different strength criteria, the relationship function between the internal friction angle and the stress state is derived, and then the cohesion expression under different stress states is obtained;

[0007] S2. Based on the incremental generalized Hooke's law, the deformation caused by the superposition of the large principal strain and the difference between the intermediate and small principal stresses of the Duncan-Zhang model under the influence of the intermediate principal stress is considered, and the influence of the strength parameters under the influence of the intermediate principal stress on the Duncan-Zhang model under the true triaxial actual stress state is considered. The stress state parameters are introduced to correct the deformation modulus parameters.

[0008] Preferably, the S1 comprises:

[0009] S11. In the SMP strength criterion expression, the relationship between the first stress invariant, the second stress invariant and the third stress invariant and different stresses is determined by the following formulas:

[0010] I 1 =σ 1 +σ 2 +σ 3 ;I 3 =σ 1 σ 2 σ 3 ;

[0011]

[0012] Among them, σ 1 , σ 2 , σ 3 I represents the major principal stress, the intermediate principal stress and the minor principal stress respectively. 1 and I 3 represent the first and third stress invariants, J 2 is the second deviatoric stress invariant;

[0013] S12. Based on the SMP strength criterion, the failure surface under three-dimensional stress conditions is expressed by the relationship between major principal stress, medium principal stress and minor principal stress, and the expression is:

[0014]

[0015] Among them, k f constants determined experimentally;

[0016] S13, according to the Mohr-Coulomb criterion

[0017] in, is the anisotropic friction angle, is the cohesion of soil under axisymmetric compression conditions; c 0 is the friction angle of soil under axisymmetric compression conditions;

[0018] S14. Introducing the relationship between major principal stress, intermediate principal stress and minor principal stress into the equation in S13, we obtain

[0019]

[0020] in, b σ is the ratio of the intermediate principal stress; λ is the soil property parameter related to the strength index cohesion and friction angle; is the internal friction angle;

[0021] S15. According to each strength criterion, there is a cone surface of different shapes in the principal stress space. For isotropic materials, the vertex of the cone is the same for different strength criteria, and the expression of cohesion under different stress states is obtained.

[0022] Preferably, the relationship between the major principal stress, the intermediate principal stress and the minor principal stress in S14 is represented by a stress state parameter, which is as follows:

[0023]

[0024] Preferably, the cohesion expression under different stress states is specifically expressed as follows:

[0025]

[0026] in, is the cohesion under different stress states.

[0027] Preferably, S2 comprises the following steps:

[0028] S21. According to the incremental generalized Hooke's law, consider dσ in the triaxial test 2 =dσ 3 = 0 and the minor principal stress and stress state parameters are constant under different stress paths. Among them, ε 1 is the major principal strain; μ t is the tangent Poisson's ratio; E t is the tangent deformation modulus;

[0029] S22, Substitute the stress state parameters into the equation in S21 to obtain

[0030] S23. Continuing the basic idea of ​​the Duncan-Zhang model, considering the hyperbolic curves obtained under different consolidation pressure conditions, we get Among them, a is the intercept; b is the slope;

[0031] S24. In the true triaxial test, ε 1 =0,E t =E i ,but Among them, E i is the initial deformation modulus;

[0032] S25. In the true triaxial test, based on the idea of ​​replacing Poisson's ratio with volume modulus, and considering the growth effect of the difference between major and minor principal stresses and the difference between intermediate and minor principal stresses, Poisson's ratio is calculated, and then the relationship between initial deformation modulus and volume modulus is obtained;

[0033] S26. Considering that the stress difference of the original loess at the time of failure is smaller than the stress difference limit value, the failure ratio is expressed as:

[0034] Among them, R f The value is between 0.75 and 1.0, which is consistent with σ 3 irrelevant;(σ 1 -σ 3 ) f is the stress difference, (σ 1 -σ 3 ) u is the stress difference limit; R f is the destruction ratio;

[0035] S27, combined with S26 and according to the SMP strength criterion, the shear strength expression is obtained;

[0036] S28. According to the relationship function between internal friction angle and stress state and the cohesion expression, under the same confining pressure conditions and different stress state parameter values, ε 1 / (σ 1 -σ 3 ) and ε 1 The slope and intercept are different. Based on the above conditions, the deformation modulus parameters are corrected to obtain the modified Duncan-Zhang nonlinear model expression.

[0037] Preferably, the shear strength expression is:

[0038]

[0039] Preferably, the modified Duncan-Zhang nonlinear model expression is:

[0040]

[0041] Where B is the volume modulus.

[0042] Beneficial effects of the present invention:

[0043] 1. This scheme conducts consolidation and drainage shear tests on natural loess under true triaxial conditions to reveal the strength and deformation characteristics of loess in complex stress states. Starting from the internal friction angle, a strength parameter of the material under true triaxial stress, the influence of the intermediate principal stress on the strength parameters is explored. Based on the generalized Hooke's law, it is introduced into the Duncan-Zhang EB model parameters, solving the problem that the existing Duncan-Zhang model fails to consider the influence of the intermediate principal stress, resulting in a large error in the predicted tangent deformation modulus, thereby improving the accuracy of the predicted tangent deformation modulus.

[0044] 2. The Duncan-Zhang model used in this scheme is a typical EB model. It is based on the stress-strain curve obtained from the conventional triaxial consolidation and drainage test to determine the model parameters. It has good prediction results for normal consolidated remolded soil, but is also often used in deformation simulation of various geotechnical materials such as saturated, unsaturated sand, silty clay, etc. Since the Duncan-Zhang model fails to consider the influence of the intermediate principal stress, the predicted tangent deformation modulus has a large error. Based on this problem, the present invention modifies the Duncan-Zhang model by considering the strength parameters affected by the intermediate principal stress, and finally provides theoretical support for calculating the Duncan-Zhang model parameters according to the test results in engineering, and provides a scientific basis for decision makers. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Other features, objects and advantages of the present invention will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings. The drawings are only for the purpose of illustrating preferred embodiments and are not to be considered as limiting the present invention. Also, the same reference symbols are used throughout the drawings to represent the same parts.

[0046] Figure 1 It is a flow chart of the Duncan-Zhang model parameter correction method for soil under complex stress conditions according to the present invention;

[0047] Figure 2 True triaxial test σ 3 =50kPa when the principal stress difference and the major principal strain curve;

[0048] Figure 3 is the true triaxial test σ 3 =100kPa when the principal stress difference and the major principal strain curve;

[0049] Figure 4 is the true triaxial test σ 3 =150kPa when the principal stress difference and the major principal strain curve;

[0050] Figure 5 is the true triaxial test σ 3 =200kPa when the principal stress difference and the major principal strain relationship curve;

[0051] Figure 6 is 3 =Comparison chart of the predicted curve of the corrected model and the measured results when 50 kPa;

[0052] Figure 7 is 3 =Comparison chart of the predicted curve of the corrected model and the measured results when 100 kPa;

[0053] Figure 8 is 3 =Comparison chart of the predicted curve of the corrected model and the measured results when 150 kPa;

[0054] Fig. 9 is 3 =200kPa when the correction model prediction curve and the measured results are compared. DETAILED DESCRIPTION

[0055] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific implementation method described herein is only an optimal embodiment of the present invention, which is only used to explain the present invention and does not limit the scope of protection of the present invention. All other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0056] Example 1: Figure 1 As shown in FIG, the Duncan-Zhang model parameter correction method for soil under complex stress conditions includes the following steps:

[0057] Based on the SMP criterion, which is the most reasonable failure criterion for describing the strength of clay at present, the relationship function between the internal friction angle of soil and the stress state is derived; according to each criterion, it is a cone surface of different shapes in the principal stress space. For isotropic materials, the vertex of the cone is the same for different strength criteria, and the cohesion expression under different stress states can be obtained; through the incremental generalized Hooke's law, the deformation caused by the superposition of the large principal strain and the difference between the intermediate and small principal stresses of the Duncan-Zhang EB model is proposed, and the parameter determination method of the Duncan-Zhang EB model with different intermediate principal stress ratios is proposed; according to the internal friction angle and cohesion determined by the SMP criterion under the stress path, the deformation modulus parameters of the Duncan-Zhang model under the true triaxial actual stress state are corrected by considering the strength parameters affected by the intermediate principal stress.

[0058] The above-mentioned Duncan-Zhang model parameter correction method for soil under complex stress conditions derives the relationship function between the internal friction angle and the stress state of the soil under actual complex stress state as follows:

[0059] In the strength criterion expression, σ 1 , σ 2 , σ3 represent the major principal stress, the intermediate principal stress and the minor principal stress respectively, c is the cohesion, is the internal friction angle, I 1 and I 3 represent the first and third stress invariants, J 2 is the second deviatoric stress invariant, and its relationship with the principal stress can be determined by the following formulas:

[0060] I 1 =σ 1 +σ 2 +σ 3 ;I 3 =σ 1 σ 2 σ 3 ;

[0061] The SMP strength criterion takes into account the influence of the intermediate principal stress and establishes a strength formula for soil under three-dimensional stress conditions. This strength criterion assumes that the material is damaged when the ratio of shear stress to normal stress reaches a certain value, and the failure surface under this three-dimensional stress condition is called the SMP spatial sliding surface, which is expressed as:

[0062]

[0063] where k f is a constant determined experimentally.

[0064] According to the Mohr-Coulomb criterion:

[0065]

[0066] Introducing the stress state parameter b in the above formula σ :

[0067]

[0068] We can get:

[0069]

[0070] Where:

[0071]

[0072] The above-mentioned Duncan-Zhang model parameter correction method for soil under complex stress conditions is a cone surface of different shapes in the principal stress space according to each criterion. For isotropic materials, the apex of the cone is the same for different strength criteria. The cohesion expression under different stress states can be obtained as follows:

[0073]

[0074] The above-mentioned Duncan-Zhang model parameter correction method for soil under complex stress conditions, through the incremental generalized Hooke's law, according to the strength parameters determined by the various criteria considering the influence of the intermediate principal stress obtained in the previous article, is based on the deformation caused by the large principal strain superimposed on the intermediate and small principal stress differences of the Duncan-Zhang EB model. The method is as follows:

[0075] According to the incremental generalized Hooke's law:

[0076]

[0077] In conventional triaxial tests, because dσ 2 =dσ 3 =0, so:

[0078]

[0079] This embodiment is based on σ 3 and b σ The results are obtained under different stress paths with constants, so:

[0080]

[0081] Substituting the stress state parameters into the above formula, we get:

[0082]

[0083] Following the basic idea of ​​the Duncan-Zhang model, it is assumed that different consolidation pressures σ 3 The obtained (σ 1 -σ 3 )-ε 1 The curve is a hyperbola, and we can determine:

[0084]

[0085] At the start of the experiment, ε 1 =0,E t =E i ,but

[0086]

[0087] Because there are some inconveniences in using Poisson's ratio in calculations, Duncan et al. proposed using the volume modulus B instead of Poisson's ratio μ t In the true triaxial test, the growth effect of the major and minor principal stress differences and the medium and minor principal stress differences are considered at the same time, and the volume deformation modulus corresponding to the stress level of 0.7 is used. , so the bulk modulus is:

[0088]

[0089] Therefore, Poisson's ratio μ t It can be calculated by the following relationship:

[0090]

[0091] Initial deformation modulus μ i The relationship with the volume modulus B is:

[0092]

[0093] The stress difference of the original loess at the time of failure (σ 1 -σ 3 ) J , which is always greater than the stress difference limit value (σ 1 -σ 3 ) u Small, the damage ratio R J It is expressed as:

[0094]

[0095] R J The value is generally between 0.75 and 1.0, which is actually the same as σ 3 It is irrelevant, so according to the SMP criterion, the shear strength can be expressed as:

[0096]

[0097] The above-mentioned Duncan-Zhang model parameter correction method for soil under complex stress conditions, based on the internal friction angle and cohesion determined by the SMP criterion under the stress path, corrects the deformation modulus parameters of the Duncan-Zhang model under the true triaxial actual stress state by considering the strength parameters affected by the intermediate principal stress. e In the case of ε 1 / (σ 1 -σ 3 ) and ε 1 The slope b and intercept a are different. After sorting, the modified Duncan-Zhang nonlinear model can be expressed as:

[0098]

[0099] Where: E t is the tangent deformation modulus, μ t is the tangent Poisson's ratio, b σ is the ratio of the intermediate principal stress, B is the volume modulus, E i is the initial deformation modulus, R f is the destruction ratio, is the internal friction angle, For cohesion.

[0100] Example 2: The soil samples selected for this test were taken from the natural loess of Bailuyuan, Xi'an, Shaanxi Province, which belong to the typical Q3 loess. The soil sampling depth is about 6.5m to 8.0m. This type of soil sample is widely distributed in the Guanzhong Basin and is used as a filling material for foundations, slopes, dam bodies, etc. The soil sample is yellow-brown with a small amount of calcareous nodules inside, belonging to silty clay loess. According to indoor test measurements, the experimental loess controlled particle size d 60 =0.83mm, effective particle size d 10 =0.35mm, middle particle size d 30 =0.38mm, non-uniformity coefficient 2.37, curvature coefficient 0.5, other basic physical properties are shown in Table 1. The test uses a rectangular original specimen with a standard specification of 70mmx70mmx140mm.

[0101] In this test, true triaxial tests were carried out under isotropic consolidation and drainage conditions, and the minor principal stress σ 3 are 50kPa, 100kPa, 150kPa and 200kPa respectively, and the intermediate principal stress ratio coefficient b σ are 0, 0.25, 0.5, 0.75 and 1.0 respectively. At the beginning of the test, isotropic consolidation stress is applied to the specimen simultaneously through the axial rigid and lateral flexible hydraulic bags. After consolidation is completed, the minor principal stress σ is controlled in the shear stage. J and the intermediate principal stress ratio coefficient b σ The intermediate principal stress was kept constant, and the loading deformation rate was 0.05 mm / min in the axial strain control mode until the specimen failure occurred. All the tests in this study were carried out at room temperature (24-27°).

[0102] The stress-strain curves of the original loess under different intermediate principal stress ratios when the minor principal stress is 50 kPa, 100 kPa, 150 kPa and 200 kPa are as follows: Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown in the figure, under the true triaxial stress condition, the overall trend of the original loess stress-strain relationship curve is hardening type, and the peak value of the difference between the major and minor principal stresses and the volume deformation law are basically the same, both of which increase with the initial confining pressure and the intermediate principal stress ratio coefficient b. σ increases with the increase of .

[0103] According to the true triaxial test results of loess mentioned above, the modified Duncan-Zhang nonlinear model formula is used to predict the stress-strain curves of the original loess under different stress paths and compare them with the actual measured data. Figure 6 , Figure 7 , Figure 8 and Fig. 9 As shown, it is obvious that the model after considering the intermediate principal stress is more in line with the actual situation.

[0104] The above specific embodiments are preferred embodiments of the present invention, and are not intended to limit the specific implementation scope of the present invention. The scope of the present invention includes but is not limited to the present specific embodiments. All equivalent changes made in accordance with the shape, structure, and method of the present invention are within the protection scope of the present invention.

Claims

1. A method for modifying the parameters of the Duncan-Zhang model for soil under complex stress conditions, characterized in that: The steps include: S1. According to different strength criteria, the relationship function between the internal friction angle and the stress state is derived, and then the cohesion expression under different stress states is obtained; S2. Based on the incremental generalized Hooke's law, the deformation caused by the superposition of the large principal strain and the difference between the intermediate and small principal stresses of the Duncan-Zhang model under the influence of the intermediate principal stress is considered, and the influence of the strength parameters under the influence of the intermediate principal stress on the Duncan-Zhang model under the true triaxial actual stress state is considered. The stress state parameters are introduced to correct the deformation modulus parameters.

2. The Duncan-Zhang model parameter correction method for soil under complex stress conditions according to claim 1, characterized in that: The S1 includes: S11. In the SMP strength criterion expression, the relationship between the first stress invariant, the second stress invariant and the third stress invariant and different stresses is determined by the following formulas: I1=σ1+σ2+σ3; I3=σ1σ2σ3; Among them, σ1, σ2, σ3 represent the major principal stress, the intermediate principal stress and the minor principal stress respectively, I1 and I3 represent the first and third stress invariants respectively, and J2 is the second deviatoric stress invariant; S12. Based on the SMP strength criterion, the failure surface under three-dimensional stress conditions is expressed by the relationship between major principal stress, medium principal stress and minor principal stress, and the expression is: Among them, k f constants determined experimentally; S13, according to the Mohr-Coulomb criterion in, is the anisotropic friction angle, is the cohesion of soil under axisymmetric compression conditions; c0 is the friction angle of soil under axisymmetric compression conditions; S14. Introducing the relationship between major principal stress, intermediate principal stress and minor principal stress into the equation in S13, we obtain in, b σ is the ratio of the intermediate principal stress; λ is the soil property parameter related to the strength index cohesion and friction angle; is the internal friction angle; S15. According to each strength criterion, there is a cone surface of different shapes in the principal stress space. For isotropic materials, the vertex of the cone is the same for different strength criteria, and the expression of cohesion under different stress states is obtained.

3. The Duncan-Zhang model parameter correction method for soil under complex stress conditions according to claim 1, characterized in that: The relationship between the major principal stress, the intermediate principal stress and the minor principal stress in S14 is represented by the stress state parameters, which are as follows:

4. The Duncan-Zhang model parameter correction method for soil under complex stress conditions according to claim 3 is characterized in that: The cohesion expression under different stress states is specifically expressed as follows: in, is the cohesion under different stress states.

5. The Duncan-Zhang model parameter correction method for soil under complex stress conditions according to claim 1, characterized in that: S2 includes the following steps: S21. According to the incremental generalized Hooke's law, considering the triaxial test under different stress paths with dσ2=dσ3=0 and the minor principal stress and stress state parameters being constant, we can obtain Among them, ε1 is the major principal strain; μ t is the tangent Poisson's ratio; E t is the tangent deformation modulus; S22, Substitute the stress state parameters into the equation in S21 to obtain S23. Continuing the basic idea of ​​the Duncan-Zhang model, considering the hyperbolic curves obtained under different consolidation pressure conditions, we get Among them, a is the intercept; b is the slope; S24. In the true triaxial test, ε1 = 0, E t =E i ,but Among them, E i is the initial deformation modulus; S25. In the true triaxial test, based on the idea of ​​replacing Poisson's ratio with volume modulus, and considering the growth effect of the difference between major and minor principal stresses and the difference between intermediate and minor principal stresses, Poisson's ratio is calculated, and then the relationship between initial deformation modulus and volume modulus is obtained; S26. Considering that the stress difference of the original loess at the time of failure is smaller than the stress difference limit value, the failure ratio is expressed as: Among them, R f The value is between 0.75 and 1.0, and has nothing to do with σ3; (σ1-σ3) f is the stress difference, (σ1-σ3) u is the stress difference limit; R f is the destruction ratio; S27, combined with S26 and according to the SMP strength criterion, the shear strength expression is obtained; S28. According to the relationship function between the internal friction angle and the stress state and the cohesion expression, under the same confining pressure conditions and different stress state parameter values, the slope and intercept of ε1 / (σ1-σ3) and ε1 are different. Based on the above conditions, the deformation modulus parameters are corrected to obtain the corrected Duncan-Zhang nonlinear model expression.

6. The Duncan-Zhang model parameter correction method for soil under complex stress conditions according to claim 5, characterized in that: The shear strength expression is:

7. The Duncan-Zhang model parameter correction method for soil under complex stress conditions according to claim 1, characterized in that: The modified Duncan-Zhang nonlinear model expression is: Where B is the volume modulus.

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