A method for constructing a soft soil creep constitutive model considering stress ratio

Abstract

The invention relates to a method for constructing a soft soil creep constitutive model considering stress ratio. Firstly, creep tests under different combinations of confining pressures and axial pressures, as well as triaxial compressive strength tests under various confining pressures, are carried out to obtain mechanical parameters such as strain duration curves, compressive strength, and equivalent stress; then, fitting is performed for different strain duration curves to obtain creep constitutive equation parameters; then, a curve of stress state related parameter C2 and corresponding stress ratio is drawn and fitted; finally, for the equivalent strain rate duration curve corresponding to each creep test, an equivalent stress-time-equivalent strain rate three-dimensional curve is drawn, and an equation is fitted to obtain a creep constitutive model that can reflect the stress state, and a creep constitutive model whose strain ratio satisfies a quadratic parabola is obtained in combination with examples, which more scientifically reveals the characteristics of soft soil creep, provides a theoretical basis for more accurately predicting creep under different stress states, and is applicable to the research on constitutive models of geotechnical engineering materials such as various soft soils and soft rocks.

Description

Technical Field

[0001] The invention relates to a method for constructing a soft soil creep constitutive model taking stress ratio into consideration, and belongs to the technical field of geotechnical engineering constitutive model research. Background Art

[0002] The stress-strain relationship of rock and soil is related to time in some cases. Such properties are collectively referred to as the rheological properties of rock. The creep property in the rheological properties is one of the main factors affecting the deformation and failure of geotechnical engineering construction. Studying the creep law of rock and soil and constructing a creep constitutive model are currently important theoretical foundations for predicting the deformation and failure of geotechnical engineering structures during operation. They are also important core technologies for improving the safety design of engineering structures throughout their life cycle and decision-making on maintenance plans. However, it is difficult to effectively reflect the influence of stress state on creep in the current creep constitutive model, and there is no analytical method to effectively construct a creep constitutive equation that can reflect the stress state. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a method for constructing a soft soil creep constitutive model taking stress ratio into consideration, thereby providing a theoretical basis for more accurately predicting creep under different stress states.

[0004] In order to solve the above technical problems, the present invention adopts the following technical solution: The present invention designs a method for constructing a soft soil creep constitutive model considering stress ratio, comprising the following steps A to F:

[0005] Step A. Based on each preset confining pressure and at least three preset different axial pressures corresponding to the preset confining pressure that do not exceed the ultimate axial pressure, a creep test is performed on the target type sample soft soil to obtain the axial strain duration curve and the circumferential strain duration curve corresponding to each creep test; and based on each preset confining pressure, a triaxial compressive strength test is performed on the target type sample soft soil to obtain the ultimate compressive strength value under each preset confining pressure and the corresponding ultimate equivalent stress;

[0006] Step B. For each creep test, use the following formula (1):

[0007]

[0008] Obtain the equivalent stress σ corresponding to the creep test e , where σ1 represents the maximum principal stress on the three groups of opposite surfaces of the regular hexahedron micro-element in the soft soil specimen in the creep test, σ3 represents the minimum principal stress on the three groups of opposite surfaces of the regular hexahedron micro-element in the soft soil specimen in the creep test, and σ2 represents the residual principal stress on the three groups of opposite surfaces of the regular hexahedron micro-element in the soft soil specimen in the creep test except σ1 and σ2;

[0009] For each creep test, the following formula (2) is used:

[0010]

[0011] Obtain the equivalent strain ε corresponding to the duration of each test in the creep test e , forming the equivalent strain duration curves corresponding to each creep test, where v′ represents Poisson’s ratio, ε1 represents the strain corresponding to σ1, ε3 represents the strain corresponding to σ3, and ε2 represents the strain corresponding to σ2;

[0012] Step C. for each creep test, according to the value of the equivalent strain duration curve, using the difference method, obtain the duration curve of the equivalent strain rate corresponding to each creep test;

[0013] Step D: According to the generalized exponential function as shown in the following formula (3), the time curve of the equivalent strain rate under the creep test corresponding to the intermediate confining pressure and the intermediate axial pressure is fitted.

[0014]

[0015] Obtain the values ​​of parameters C1, C2, C3, and C4, and fix the values ​​of C1, C3, and C4. According to formula (3), fit the duration curve of the equivalent strain rate under each creep test respectively, and then obtain the value of parameter C2 corresponding to each creep test, where: represents the equivalent strain rate, t represents the duration of the test, and e represents a mathematical constant;

[0016] Step E. For each creep test, the stress ratio corresponding to each creep test is formed according to the ratio of the equivalent stress corresponding to the creep test to the ultimate equivalent stress corresponding to the ultimate compressive strength value under confining pressure corresponding to the creep test; then, the parameter C2 value corresponding to each creep test is fitted with the stress ratio according to the quadratic parabola function as shown in the following formula (4):

[0017] C2=A1x 2 +A2x+A3 (4)

[0018] Get the values ​​of parameters A1, A2, A3, where σ e Indicates the equivalent stress corresponding to the creep test; It indicates the ultimate equivalent stress corresponding to the ultimate compressive strength value under the confining pressure corresponding to the creep test;

[0019] Step F. Based on equations (3) and (4), for the equivalent strain rate duration curves corresponding to each creep test, a three-dimensional curve of equivalent stress-time-equivalent strain rate is drawn, and a three-dimensional fitting is performed. Combined with the example, the creep constitutive model of the soft soil specimen with a strain ratio satisfying the quadratic parabola is obtained as follows:

[0020]

[0021] The method for constructing a soft soil creep constitutive model considering stress ratio described in the present invention adopts the above technical solution and has the following technical effects compared with the prior art:

[0022] (1) The method for constructing a soft soil creep constitutive model considering stress ratio designed by the present invention firstly carries out creep tests under different combinations of confining pressure and axial pressure, as well as triaxial compressive strength tests under various confining pressures, to obtain mechanical parameters such as strain duration curve, compressive strength, and equivalent stress; then, for different strain duration curves, the creep constitutive equation of the generalized exponential equation is used for fitting to obtain the creep constitutive equation parameters; then, a curve of the stress state related parameter C2 and the corresponding stress ratio is drawn, and a suitable equation is used for fitting according to the shape of the curve. In this example, a quadratic parabola function is used for fitting; finally, for the equivalent strain rate duration curve corresponding to each creep test, a three-dimensional curve of equivalent stress-time-equivalent strain rate is drawn, and an equation is fitted to obtain a creep constitutive model that can reflect the stress state. Combined with the example, a creep constitutive model with a strain ratio satisfying a quadratic parabola is obtained, which more scientifically reveals the characteristics of soft soil creep, provides a theoretical basis for more accurate prediction of creep under different stress states, and is applicable to the study of constitutive models of various geotechnical engineering materials such as soft soil and soft rock. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a module structure diagram of the method for constructing a soft soil creep constitutive model considering stress ratio designed by the present invention;

[0024] Figure 2 is the axial strain duration curve in the application embodiment of the present invention;

[0025] Figure 3 is the axial strain rate duration curve in the application embodiment of the present invention;

[0026] Figure 4 is the equivalent effect strain duration curve in the application embodiment of the present invention;

[0027] Figure 5 is the equivalent effect strain rate duration curve in the application embodiment of the present invention;

[0028] Figure 6 is the equivalent effect strain rate fitting curve in the application embodiment of the present invention;

[0029] Figure 7 is the relationship curve between C2 and stress ratio in the application embodiment of the present invention;

[0030] Figure 8 is the fitting curve of C2 and stress ratio in the application example of the present invention;

[0031] Fig. 9is a schematic diagram of a three-dimensional surface fitting result in an application embodiment of the present invention;

[0032] Fig.10 It is a comparison curve between the predicted value and the measured value of the traditional viscoelastic Nishihara creep constitutive equation in the application embodiment of the present invention;

[0033] Fig.11 is a comparison curve between the predicted value and the measured value of the creep constitutive equation fitted by the generalized exponential equation in the application embodiment of the present invention;

[0034] Fig.12 is a comparison curve between the predicted value and the measured value of the soft soil creep constitutive equation considering the stress ratio in the application embodiment of the present invention;

[0035] Fig.13 It is a schematic diagram comparing the prediction results of different constitutive equations in the application examples of the present invention. DETAILED DESCRIPTION

[0036] The specific implementation modes of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0037] The present invention designs a method for constructing a soft soil creep constitutive model considering stress ratio. In practical applications, Figure 1 As shown, the following steps A to F are specifically performed.

[0038] Step A. Based on the 100 kPa confining pressure, and the corresponding 130 kPa axial pressure, 190 kPa axial pressure, 250 kPa axial pressure, and 310 kPa axial pressure that do not exceed the ultimate axial pressure, a creep test is performed on the target type sample soft soil to obtain the axial strain duration curve, the circumferential strain duration curve, the axial strain rate duration curve, and the circumferential strain rate duration curve corresponding to each creep test, wherein the axial strain duration curve corresponding to each creep test is as follows: Figure 2 As shown in the figure, the axial strain rate time curves corresponding to each creep test are shown in the figure Figure 3 shown.

[0039] And based on the confining pressure of 100 kPa, a triaxial compressive strength test was performed on the target type sample soft soil, and the ultimate compressive strength value of 660 kPa under the confining pressure of 100 kPa and the corresponding ultimate equivalent stress of 560 kPa were obtained.

[0040] Next, step B to step D are performed, and for different strain duration curves, the creep constitutive equation of the generalized exponential equation is used for fitting to obtain the parameters of the creep constitutive equation.

[0041] Step B. Use generalized shear stress for each creep test according to the following formula (1):

[0042]

[0043] Obtain the equivalent stress σ corresponding to the creep test e , where σ1 represents the maximum principal stress on the three opposite surfaces of the regular hexahedron micro-elements in the soft soil specimen in the creep test, σ3 represents the minimum principal stress on the three opposite surfaces of the regular hexahedron micro-elements in the soft soil specimen in the creep test, and σ2 represents the residual principal stress on the three opposite surfaces of the regular hexahedron micro-elements in the soft soil specimen in the creep test except σ1 and σ2.

[0044] The generalized shear strain is further adopted for each creep test according to the following formula (2):

[0045]

[0046] Obtain the equivalent strain ε corresponding to the duration of each test in the creep test e , constituting the equivalent strain duration curves corresponding to each creep test, wherein v′ represents the Poisson's ratio, specifically, it is equal to 0.35, ε1 represents the strain corresponding to σ1, ε3 represents the strain corresponding to σ3, and ε2 represents the strain corresponding to σ2.

[0047] According to the above creep tests in which the confining pressure of 100 kPa corresponds to the axial pressure of 130 kPa, 190 kPa, 250 kPa and 310 kPa, the corresponding equivalent stresses are 30 kPa, 90 kPa, 150 kPa and 210 kPa respectively. The corresponding equivalent strain duration curves are as follows: Figure 4 shown.

[0048] Step C: for each creep test, according to the value of the equivalent strain duration curve, a difference method is used to obtain the duration curve of the equivalent strain rate corresponding to each creep test.

[0049] In practical applications, according to the above creep tests where the confining pressure of 100 kPa corresponds to axial pressure of 130 kPa, axial pressure of 190 kPa, axial pressure of 250 kPa, and axial pressure of 310 kPa, the corresponding equivalent effect strain rate duration curves are as follows: Figure 5 shown.

[0050] Step D: According to the generalized exponential function as shown in the following formula (3), the time curve of the equivalent strain rate under the creep test corresponding to the intermediate confining pressure and the intermediate axial pressure is fitted.

[0051]

[0052] Obtain the values ​​of parameters C1, C2, C3, and C4, and fix the values ​​of C1, C3, and C4. According to formula (3), fit the duration curve of the equivalent strain rate under each creep test respectively, and then obtain the value of parameter C2 corresponding to each creep test, where: represents the equivalent strain rate, t represents the test duration, and e represents a mathematical constant.

[0053] In practical applications, according to the above creep tests where the confining pressure of 100 kPa corresponds to axial pressure of 130 kPa, axial pressure of 190 kPa, axial pressure of 250 kPa, and axial pressure of 310 kPa, the corresponding equivalent strain rate fitting curves are as follows: Figure 6 As shown, and on the basis of fixing the values ​​of C1, C3, and C4, the C2 obtained as described above are -0.05124, -0.10105, -0.11492, and -0.11058 respectively.

[0054] Step E. For each creep test, the stress ratio corresponding to each creep test is formed according to the ratio of the equivalent stress corresponding to the creep test to the ultimate equivalent stress corresponding to the ultimate compressive strength value under confining pressure corresponding to the creep test; according to the above embodiment, the curve between the parameter C2 value corresponding to each creep test and the stress ratio is as follows: Figure 7 shown.

[0055] Therefore, the quadratic parabola function is fitted with the parameter C2 value and stress ratio corresponding to each creep test as shown in the following formula (4):

[0056] C2=A1x 2 +A2x+A3 (4)

[0057] Get the values ​​of parameters A1, A2, A3, where σ e Indicates the equivalent stress corresponding to the creep test; It represents the ultimate equivalent stress corresponding to the ultimate compressive strength value under the confining pressure corresponding to the creep test.

[0058] According to the above embodiment, the curve of the fitting parameter C2 value and the stress ratio in step E is as follows: Figure 8 As shown, formula (4) is updated as follows:

[0059] C2=1.13833x 2 -0.66169x-0.02173

[0060] Step F. Based on equations (3) and (4), the stress exponential parameter in the generalized exponential equation is improved to be a function of the stress ratio (a quadratic parabola function in this example). For the equivalent strain rate duration curve corresponding to each creep test, a three-dimensional curve of equivalent stress-time-equivalent strain rate is drawn. The improved generalized exponential equation (the exponential parameter of stress is an equation containing the stress ratio) is used for three-dimensional fitting. Combined with the example, the creep constitutive model of the soft soil specimen with a strain ratio satisfying the quadratic parabola is obtained as follows:

[0061]

[0062] In practical applications, the creep constitutive model of soft soil samples obtained above was verified and found to have certain advantages over other constitutive models.

[0063] According to the above embodiment, step E is performed here, and the surface fitting is as follows: Fig. 9 As shown, the creep constitutive model of the soft soil specimen is finally obtained as follows:

[0064]

[0065] In practical applications, in order to further verify the rationality of the constitutive equation constructed by the method designed in the present invention, it is compared with the traditional viscoelastic Nishihara creep constitutive equation and other creep constitutive equations fitted by generalized exponential equations. The traditional viscoelastic Nishihara creep constitutive equation is: The comparison curve between the predicted value and the measured value is as follows: Fig.10 shown.

[0066] The creep constitutive equation fitted by the generalized exponential equation is as follows:

[0067]

[0068] The comparison curve between the predicted value and the measured value is as follows: Fig.11 shown.

[0069] The soft soil creep constitutive equation considering the stress ratio is as follows:

[0070]

[0071] The comparison curve between the predicted value and the measured value is as follows: Fig.12 shown.

[0072] Based on this, the prediction results of the above different constitutive equations are compared, such as Fig.13 As shown, by comparing and analyzing the measured values ​​with the predicted values ​​of the equation, compared with the traditional viscoelastic Nishihara creep constitutive equation and the creep constitutive equation fitted by the generalized exponential equation, the predicted values ​​of the present invention are closest to the measured values ​​and are more reasonable, and can be used to predict the long-term creep of soft soil in actual engineering.

[0073] The method for constructing a soft soil creep constitutive model considering stress ratio designed by the above technical scheme first conducts creep tests under different combinations of confining pressure and axial pressure, as well as triaxial compressive strength tests under various confining pressures, to obtain mechanical parameters such as strain duration curve, compressive strength, and equivalent stress; then, for different strain duration curves, the creep constitutive equation of the generalized exponential equation is used for fitting to obtain the creep constitutive equation parameters; then, a curve of the stress state related parameter C2 and the corresponding stress ratio is drawn, and a suitable equation is used for fitting according to the shape of the curve. In this example, a quadratic parabola function is used for fitting; finally, for the equivalent strain rate duration curve corresponding to each creep test, a three-dimensional curve of equivalent stress-time-equivalent strain rate is drawn, and an equation is fitted to obtain a creep constitutive model that can reflect the stress state. Combined with the example, a creep constitutive model with a strain ratio satisfying a quadratic parabola is obtained, which more scientifically reveals the characteristics of soft soil creep, provides a theoretical basis for more accurate prediction of creep under different stress states, and can be applied to the study of constitutive models of geotechnical engineering materials such as various soft soils and soft rocks.

[0074] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A method for constructing a soft soil creep constitutive model considering stress ratio, characterized in that: The method comprises the following steps A to F: Step A. Based on each preset confining pressure and at least three preset different axial pressures corresponding thereto that do not exceed the ultimate axial pressure, a creep test is performed on the target type sample soft soil to obtain the axial strain duration curve and the circumferential strain duration curve corresponding to each creep test; and performing triaxial compressive strength tests on the target type sample soft soil based on each preset confining pressure, to obtain the ultimate compressive strength value under each preset confining pressure and the corresponding ultimate equivalent stress; Step B. For each creep test, use the following formula (1): Obtain the equivalent stress σ corresponding to the creep test e , where σ1 represents the maximum principal stress on the three groups of opposite surfaces of the regular hexahedron micro-element in the soft soil specimen in the creep test, σ3 represents the minimum principal stress on the three groups of opposite surfaces of the regular hexahedron micro-element in the soft soil specimen in the creep test, and σ2 represents the residual principal stress on the three groups of opposite surfaces of the regular hexahedron micro-element in the soft soil specimen in the creep test except σ1 and σ2; For each creep test, the following formula (2) is used: Obtain the equivalent strain ε corresponding to the duration of each test in the creep test e , forming the equivalent strain duration curves corresponding to each creep test, where v′ represents Poisson’s ratio, ε1 represents the strain corresponding to σ1, ε3 represents the strain corresponding to σ3, and ε2 represents the strain corresponding to σ2; Step C. for each creep test, according to the value of the equivalent strain duration curve, using the difference method, obtain the duration curve of the equivalent strain rate corresponding to each creep test; Step D: According to the generalized exponential function as shown in the following formula (3), the time curve of the equivalent strain rate under the creep test corresponding to the intermediate confining pressure and the intermediate axial pressure is fitted. Obtain the values ​​of parameters C1, C2, C3, and C4, and fix the values ​​of C1, C3, and C4. According to formula (3), fit the duration curve of the equivalent strain rate under each creep test respectively, and then obtain the value of parameter C2 corresponding to each creep test, where: represents the equivalent strain rate, t represents the duration of the test, and e represents a mathematical constant; Step E. For each creep test, the stress ratio corresponding to each creep test is formed according to the ratio of the equivalent stress corresponding to the creep test to the ultimate equivalent stress corresponding to the ultimate compressive strength value under confining pressure corresponding to the creep test; then, the parameter C2 value corresponding to each creep test is fitted with the stress ratio according to the quadratic parabola function as shown in the following formula (4): C2=A1x 2 +A2x+A3 (4) Get the values ​​of parameters A1, A2, A3, where σ e Indicates the equivalent stress corresponding to the creep test; It indicates the ultimate equivalent stress corresponding to the ultimate compressive strength value under the confining pressure corresponding to the creep test; Step F. Based on equations (3) and (4), for the equivalent strain rate duration curves corresponding to each creep test, a three-dimensional curve of equivalent stress-time-equivalent strain rate is drawn, and a three-dimensional fitting is performed. Combined with the example, the creep constitutive model of the soft soil specimen with a strain ratio satisfying the quadratic parabola is obtained as follows:

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