A model construction method considering the strain hardening and softening characteristics of the reinforcement-soil interface

Abstract

The present invention discloses a model construction method considering the strain hardening and softening characteristics of the reinforcement-soil interface, including: setting the normal stress as a single variable, obtaining a plurality of shear stress-shear displacement curves under different normal stress levels through a pull-out test on the soil sample to be tested; and establishing a model according to the influence of the normal stress on the reinforcement-soil interface characteristics and the change characteristics of the interface shear stress during the shearing process. The model considering the strain hardening and softening characteristics of the reinforcement-soil interface constructed by the present invention can more accurately predict the reinforcement-soil interface characteristics under different stress states, with high efficiency and low cost.

Description

Technical Field

[0001] The invention belongs to the technical field of civil engineering and relates to a model construction method taking into account the strain hardening and softening characteristics of a reinforcement-soil interface. Background Art

[0002] The interaction between geosynthetics and soil is a common problem in roadbed engineering. However, due to the obvious stiffness difference between the reinforcement and soil, the mechanical properties of the contact interface between the two media are significantly different from those of the soil far away from the interface. In actual engineering, under the action of external forces, the contact interface between geogrid and soil will show characteristics such as strain hardening and strain softening.

[0003] For the constitutive model of the reinforcement-soil interface, the Mohr-Coulomb linear elastic constitutive model is commonly used. Although this model has certain practicality, the mechanical behavior of the actual reinforcement-soil interface usually shows nonlinear characteristics. In 1971, Clough and Duncan conducted a direct shear test on the sand-concrete slab interface and proposed the Clough-Duncan model, a hyperbolic relationship model between shear stress and relative displacement, based on the test results. This model is often used to describe the characteristic relationship between the reinforcement-soil interface, but it can only reflect the monotonically increasing characteristics of shear stress with the increase of shear strain. When the shear stress-strain curve of the reinforcement-soil interface softens, the Clough-Duncan hyperbolic model is no longer applicable for studying the shear stress-displacement relationship. A large number of test results show that strain softening will occur on the contact surface during the shear process. Even for the same set of shear tests, when the normal stress is large, the contact surface will show a hardening curve, and when the normal stress is small, the contact surface will show a softening curve. However, it is difficult to effectively reflect the influence of stress state on the reinforcement-soil interface characteristics in the current reinforcement-soil interface model, and there is no effective interface model analysis method that can simultaneously reflect both strain softening and strain hardening stress states. Summary of the invention

[0004] In order to solve the above problems, the present invention provides a model construction method that takes into account the strain hardening and softening characteristics of the reinforcement-soil interface. The constructed model can more accurately predict the reinforcement-soil interface characteristics under different stress states with high efficiency and low cost.

[0005] The technical solution adopted by the present invention is a model construction method considering the strain hardening and softening characteristics of the reinforcement-soil interface, comprising the following steps:

[0006] S1, setting the normal stress as a single variable, and obtaining shear stress-shear displacement curves at multiple different normal stress levels through a pull-out test on the soil sample to be tested;

[0007] S2, according to the normal stress σ nThe influence of the reinforcement-soil interface characteristics and the change characteristics of the interface shear stress during shearing are established. Among them, δ represents shear displacement, τ represents shear stress, and a, b, and c are model parameters;

[0008] in, G represents the initial shear modulus, δ p represents the peak shear displacement, τ p represents the peak shear stress.

[0009] Furthermore, in S2, the method for determining the model parameter c is:

[0010] Model Find partial derivatives: Initial shear modulus Right now

[0011] Furthermore, in S2, the method for determining the model parameter a is:

[0012] When the shear stress reaches its peak value, the corresponding peak shear displacement but

[0013] Furthermore, in S2, the method for determining the model parameter b is:

[0014] When the shear stress reaches its peak, according to the model get: Will Substitute into the model get τ p is the peak shear stress;

[0015] Furthermore, the initial shear modulus G and the normal stress σ n The relationship between them is: Where Pa is atmospheric pressure, M and n are fitting parameters;

[0016] Peak shear stress τ p and normal stress σ n The relationship between them is: c sg is the cohesion of the soil, is the internal friction angle;

[0017] When shear displacement δ>δ p When the shear displacement increases, the shear stress gradually decreases after reaching the peak value. r Where δ r >δ p , take the corresponding residual shear stress as τr ; δ r = kδ p , k is a dimensionless parameter; the introduction of the damage ratio R f Definition of residual shear stress τ r and peak shear stress τ p The relationship between: τ r =R f τ p ; and then get:

[0018] The c of the soil samples of the same soil type sg , M, n, k and Pa, and different normal stresses σ n The corresponding R f , substitute and The initial shear modulus G and peak shear displacement δ are obtained. p and peak shear stress τ p , and then determine the model parameters a, b, c.

[0019] Furthermore, the cohesion c sg and internal friction angle Method for determining:

[0020] The shear strength envelope of the reinforcement-soil interface is drawn according to the shear stress-shear displacement curve in S1. The horizontal coordinate of the shear strength envelope of the reinforcement-soil interface is the normal stress σ n , the ordinate is the peak shear stress τ p ; Cohesion c sg is the ordinate intercept of the shear strength envelope of the reinforcement-soil interface, is the slope of the shear strength envelope of the reinforcement-soil interface.

[0021] The beneficial effects of the present invention are:

[0022] In the prior art, in order to obtain the shear stress-shear displacement curve of the same soil sample under different stress states, it is usually necessary to conduct a separate test for each stress state. This method has the problems of complicated steps, long test cycle, low operating efficiency, etc., especially in the scenario where a large amount of data is required for interface characteristic analysis, it significantly increases the manpower and time costs. The present invention can effectively solve the above problems by analyzing, summarizing and modeling the test results of the same soil sample under a finite stress state, thereby deriving the shear stress-shear displacement curve under other stress states, without the need to conduct separate tests for each stress state. This not only simplifies the test steps and improves the test efficiency, but also reduces the test cost and improves the overall efficiency and accuracy of interface characteristic research. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0024] Figure 1 It is a schematic diagram of the shear stress-shear displacement relationship of the model of the embodiment of the present invention.

[0025] Figure 2 1 is a shear stress-shear displacement relationship diagram under different normal stresses of an embodiment of the present invention.

[0026] Figure 3 It is the shear strength envelope of the interface between clay and geogrid in the embodiment of the present invention.

[0027] Figure 4 This is the model verification effect diagram. DETAILED DESCRIPTION

[0028] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments 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.

[0029] Embodiment, a model construction method considering the strain hardening and softening characteristics of the reinforcement-soil interface, comprising the following steps:

[0030] S1, set the normal stress as a single variable, and obtain the shear stress-shear displacement (τ-δ) curves at six levels of normal stress of 0 kPa, 10 kPa, 20 kPa, 40 kPa, 60 kPa and 80 kPa through the pull-out test, see Figure 2 ;

[0031] S2, according to the normal stress σ n The influence law of the reinforcement-soil interface characteristics and the change characteristics of the interface shear stress during shearing process. Specifically, according to the phenomenon in the pull-out test: the reinforcement-soil interface characteristics show strain softening characteristics when the normal stress is small, and strain hardening characteristics when the normal stress is large, a model is established Among them, δ represents shear displacement, τ represents shear stress, and a, b, and c are model parameters.

[0032] S21, cohesion c sg and internal friction angle Method for determining:

[0033] Draw the shear strength envelope τ of the reinforcement-soil interface based on the τ-δ curve test results of S1 p -σ n ,See Figure 3 , using the Mohr-Coulomb criterion: The fitting result is c sg =20.21kPa, τ p is the peak shear stress (kPa), σ n is the normal stress (kPa). Cohesion c sg is the ordinate intercept of the shear strength envelope of the reinforcement-soil interface, is the slope of the shear strength envelope of the reinforcement-soil interface.

[0034] S22, normal stress σ n = 10kPa as an example, the parameters M, n, k, R are determined by the corresponding τ-δ curve f ;

[0035] (1) According to the experimental curve fitting parameter c = 0.1299; δ represents shear displacement, τ represents shear stress; the relationship between shear stress and shear displacement of the model is as follows Figure 1 shown.

[0036] (2) Model Find partial derivatives: Initial shear modulus Right now

[0037] (3) For the equation Take the logarithm of both sides: Pa is atmospheric pressure, taken as =101 kPa, and the fitting parameters are obtained as M=0.107, n=0.147; σ n is a whole, representing the normal stress; the "n" in the nth power is a dimensionless parameter;

[0038] (4) When the shear stress reaches its peak value, the corresponding shear displacement δ p for: but

[0039] (5) Substitute into the model have to Will Substitution get

[0040] (6) When shear displacement δ>δ p When the shear displacement increases, the shear stress gradually decreases after reaching the peak value. r (δr >δ p ), the corresponding residual shear stress is taken as τ r By introducing the destruction ratio R f To define the residual shear stress τ r and peak shear stress τ p The relationship between:

[0041]

[0042] In this embodiment, k=1.6, at this time R f is 0.925.

[0043] Where: G is the initial shear modulus; M and n are dimensionless parameters; σ n is the normal stress (kPa); Pa is the atmospheric pressure (kPa); τ p is the peak shear stress (kPa); c sg is the cohesion (kPa); is the internal friction angle (°); δ p is the peak shear displacement (mm); δ r is the residual shear displacement (mm); R f is the destruction ratio; k is a dimensionless parameter with a value range of (1, ∞).

[0044] The value of k is not fixed. r The selected position is related to the calculation convenience. The k value is the same under different normal stresses. f Method for determination: Determine c sg , After the parameters of M, n, Pa, a δ r The value corresponds to a k value, which is greater than δ p Select δ r , through the normal stress σ n = 10kPa corresponding τ-δ curve ( Figure 2 ) is fitted to obtain the normal stress σ n = R corresponding to 10 kPa f ; According to the same method, the model parameters under different normal stresses are obtained, as shown in Table 1:

[0045] Table 1 Model parameters under different normal stresses

[0046]

[0047] When R f When it is large enough, it will no longer change with the increase of normal stress. As shown in Table 1, when R f When it is 0.985, it can be considered that when k is 1.6, R f No longer changes.

[0048] When the soil type and external conditions (water content, compaction, etc.) are the same, the parameters M, n, Pa, c sg , The values ​​of and k remain unchanged, R f It only changes with the normal stress. Assuming that a lot of soil is taken on site, and a part of the soil is taken for the pull-out test, the soil pile is suitable for the method of the embodiment of the present invention.

[0049] The parameter (c sg , M, n, k, R f , Pa), substitute into the following formula to determine the parameters a, b, c, Then, the strain hardening and softening characteristics of the reinforcement-soil interface are considered through the model, and the model fitting effect is shown in Figure 4 , the fitting effects are all over 0.9.

[0050] Table 2 Different normal stress σ n The parameters a, b, c under

[0051] Normal stress(kPa) a b c 0 0.008255 -0.01981 0.175439 10 0.000955 0.008633 0.129991 20 0.000378 0.01016 0.117382 40 8.1E-05 0.01232 0.105996 60 8.16E-06 0.011528 0.099855 80 5.49E-07 0.009802 0.095715

[0052] In Table 2, “8.1E-05” means 8×10 -5 .

[0053] Given the shear stress-shear displacement curve under 0-40kPa, the parameter c can be obtained through S2 sg , M, n, k, R f , Pa, through the known parameters and normal stress σ n , the model parameters a, b, c at 60kPa and 80Pa can be obtained, thereby deriving the test curve. From the indoor test, the fitting effect of the actual curve and the predicted curve is very close, and the fitting effect exceeds 0.9.

[0054] The derivation process:

[0055]

[0056] δ r = kδ p Substituting into formula (1) we get:

[0057]

[0058] Will Substituting into formula (2) we get:

[0059]

[0060] Will and Substituting into formula (3), we get:

[0061]

[0062] Solving formula (4) yields:

[0063] The reinforcement-soil interface shear stress calculation formula disclosed in the Chinese patent with publication number CN 115976899 A cannot simultaneously characterize the strain softening and hardening characteristics of the reinforcement-soil interface; the reinforcement-soil interface shear displacement curve under different moisture content conditions is obtained through indoor interface shear test, and then the interface shear type is determined according to the evolution trend of the reinforcement-soil interface shear displacement curve, and then the reinforcement-soil interface parameters are obtained by fitting the test data with the calculation formula, that is, the interface parameters can only be obtained by fitting a set of parameters through a set of test data, and the parameter acquisition process is relatively difficult.

[0064] In the embodiment of the present invention, several groups of pull-out tests under different normal stresses are first performed on the unknown soil sample, and the shear strength envelope τ of the reinforcement-soil interface is drawn according to step S21. p -σ n , and get c sg , According to step S22, M, n, k, R are obtained. f , Pa value; R f The value of the parameter changes with the change of the normal stress. Substituting the parameter into the calculation, the shear stress-shear displacement curve of the same soil sample under the unknown stress state can be obtained. n The influence of the reinforcement-soil interface characteristics and the change characteristics of the interface shear stress during shearing were established. n The connection between It can simultaneously characterize the strain softening and hardening characteristics of the reinforcement-soil interface, and has a good fitting effect. It does not need to separately represent the shear hardening characteristics and softening characteristics, and the model parameters are few. And the normal stress σ is comprehensively considered. n The influence of shear stress on the shear stress and the changing characteristics of the interface shear stress during the shearing process can predict more test curves based on several sets of indoor test data under different normal stresses; it can not only accurately simulate the nonlinear behavior of the reinforcement-soil interface under different stress states, but also effectively reflect the stress-strain response in actual engineering. p ,δ p Respectively with the normal stress σ n Establish a connection and determine the parameters M, n, Pa, k, R based on S2 f , when the normal stress increases to a certain extent, R fIt no longer changes, and there is no need to conduct experiments on this type of experimental soil. Based on these parameters, a, b, and c under different normal stresses can be calculated to predict the shear stress-shear displacement curve of the reinforced soil interface.

[0065] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A model construction method considering the strain hardening and softening characteristics of the reinforcement-soil interface, characterized in that: The following steps are involved: S1, setting the normal stress as a single variable, and obtaining shear stress-shear displacement curves at multiple different normal stress levels through a pull-out test on the soil sample to be tested; S2, according to the normal stress σ n The influence of the reinforcement-soil interface characteristics and the change characteristics of the interface shear stress during shearing are established. Among them, δ represents shear displacement, τ represents shear stress, and a, b, and c are model parameters; in, G represents the initial shear modulus, δ p represents the peak shear displacement, τ p represents the peak shear stress; The initial shear modulus G and the normal stress σ n The relationship between them is: Where Pa is atmospheric pressure, M and n are fitting parameters; Peak shear stress τ p and normal stress σ n The relationship between them is: c sg is the cohesion of the soil, is the internal friction angle; When shear displacement δ>δ p When the shear displacement increases, the shear stress gradually decreases after reaching the peak value. r Where δ r >δ p , take the corresponding residual shear stress as τ r ; δ r = kδ p , k is a dimensionless parameter; the introduction of the damage ratio R f Definition of residual shear stress τ r and peak shear stress τ p The relationship between: τ r =R f τ p ; and then get: The c of the soil samples of the same soil type sg , M, n, k and Pa, and different normal stresses σ n The corresponding R f , substitute and The initial shear modulus G and peak shear displacement δ are obtained. p and peak shear stress τ p , and then determine the model parameters a, b, c.

2. A model construction method considering the strain hardening and softening characteristics of the reinforcement-soil interface according to claim 1, characterized in that: In S2, the method for determining the model parameter c is: Model Find the partial derivative: Initial shear modulus Right now 3. A model construction method considering the strain hardening and softening characteristics of the reinforcement-soil interface according to claim 2, characterized in that: In S2, the method for determining the model parameter a is: When the shear stress reaches its peak value, the corresponding peak shear displacement but 4. A model construction method considering the strain hardening and softening characteristics of the reinforcement-soil interface according to claim 3, characterized in that: In S2, the method for determining the model parameter b is: When the shear stress reaches its peak, according to the model get: Will Substitute into the model get τ p is the peak shear stress; 5. A model construction method considering the strain hardening and softening characteristics of the reinforcement-soil interface according to claim 1, characterized in that: The cohesion c sg and internal friction angle Method for determining: The shear strength envelope of the reinforcement-soil interface is drawn according to the shear stress-shear displacement curve in S1. The horizontal coordinate of the shear strength envelope of the reinforcement-soil interface is the normal stress σ n , the ordinate is the peak shear stress τ p ; Cohesion c sg is the ordinate intercept of the shear strength envelope of the reinforcement-soil interface, is the slope of the shear strength envelope of the reinforcement-soil interface.

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