Prediction method of excess pore water pressure in saturated soil under critical state

Abstract

The present invention discloses a method for predicting the excess pore water pressure of saturated soil under a critical state. Specifically, based on the critical state soil mechanics theory and the third law of the critical state line, the average effective stress of the soil under the critical state and the porosity of the soil under the critical state are calculated, a relationship between the excess pore water pressure of the soil under the critical state and the average effective stress of the soil under the critical state is established, a related relationship is calculated, a functional expression of the excess pore water pressure is established, and an excess pore water pressure prediction equation is established using the functional expression of the excess pore water pressure, the initial effective confining pressure of the soil, and the porosity of the soil under the critical state. The present invention solves the problem in the prior art of insufficient accuracy of the relationship model between the average effective stress, deviatoric stress and porosity ratio of the soil established by the traditional critical state soil mechanics method.

Description

Technical Field

[0001] The invention belongs to the technical field of monitoring and prediction of water conservancy projects and geotechnical projects, and particularly relates to a method for predicting excess pore water pressure of saturated soil under a critical state. Background Art

[0002] In the past few decades, many earthquakes have occurred around the world, and natural disasters caused by soil liquefaction during earthquakes are common. Traditional critical state soil mechanics methods have failed to fully consider the influence of excess pore water pressure when studying the critical state of saturated sand. Excess pore water pressure is a key mechanical indicator under undrained shear conditions and is crucial for understanding the mechanical behavior of saturated sand.

[0003] Currently, traditional critical state soil mechanics methods can be used to establish a relationship model between the average effective stress, deviatoric stress, and porosity of soil in the critical state. Although this model has achieved certain results in describing the mechanical behavior of soil, it still suffers from insufficient model accuracy and weak adaptability. In addition, in undrained triaxial shear tests, for soil specimens with the same porosity level, the smaller the initial average effective stress of the specimen, the greater the undrained shear dilatancy potential of the specimen. However, the occurrence of actual liquefaction mainly depends on the initial porosity and is independent of the initial average effective stress. When the initial porosity is less than the intercept porosity, how to predict the excess pore water pressure in the critical state based on the initial conditions of the specimen remains a key issue that needs to be addressed. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the excess pore water pressure of saturated soil under a critical state, which solves the technical problems in the prior art that the relationship model between the average effective stress, deviatoric stress and porosity ratio of soil established by the traditional critical state soil mechanics method is insufficiently accurate, and when the initial porosity ratio of the soil sample is less than the intercept porosity ratio in an undrained triaxial shear test, the excess pore water pressure under the critical state cannot be predicted by the initial conditions of the sample.

[0005] The technical solution adopted by the present invention is a method for predicting excess pore water pressure of saturated soil under a critical state, the method comprising:

[0006] Step S1: Calculate the average effective stress of the soil under critical state based on the critical state soil mechanics theory and the third law of critical state line , porosity ratio of soil under critical state ;

[0007] Step S2: Establish the excess pore water pressure of soil under critical state in undrained triaxial shear test based on state soil mechanics theory and the average effective stress of soil at critical state The functional relationship of Functional relationship of

[0008] Step S3: Establish the excess pore water pressure of the soil under the critical state in the undrained triaxial shear test Function expressions;

[0009] Step S4: Use the excess pore water pressure under the critical state of the soil obtained in step S3 Function expression and initial effective confining pressure of soil , porosity ratio of soil under critical state The prediction equation of excess pore water pressure of saturated soil under critical state is established.

[0010] Furthermore, the specific operations of step S1 are as follows:

[0011] Step S101: Calculate the void ratio intercept of the soil under critical state based on the undrained triaxial shear test data and the slope of the critical state line in the power law model ;

[0012] Step S102: According to the porosity intercept of the soil under critical state The slope of the critical state line in the power law model , calculate the void ratio of soil under critical state , the average effective stress of soil at critical state , the expression is as follows:

[0013] (1)

[0014] Where: is the reference atmospheric pressure, is the porosity intercept of soil at critical state, is the average effective stress of soil under critical state, is the slope of the critical state line in the power law model, is the calibration constant for sandy soil, which is taken as 0.7;

[0015] (2)

[0016] Step S103: Set the critical soil mechanics constant transition parameter to , using the porosity ratio of the soil under critical state obtained in step S102 The average effective stress of soil at critical state , establish the void ratio of soil under critical state and the average effective stress of soil at critical state Transition parameters of critical soil mechanics constants The function expression between them is as follows:

[0017] (3).

[0018] Furthermore, in step S103, the critical state soil mechanics constant transition parameter The natural logarithm form of the function expression is as follows:

[0019] (4).

[0020] Furthermore, the specific operations of step S2 are as follows:

[0021] Step S201: Based on the total stress in the effective stress theory , effective stress , ultra-clean pore water pressure The functional relationship between them is shown in formula (5). The undrained stress path in the true liquefaction model, flow liquefaction model, limited liquefaction model, and undrained stable response model is analyzed to establish the excess pore water pressure under the critical state of the soil. The function expression is shown in formula (6):

[0022] (5)

[0023] (6)

[0024] in: is the average total stress of soil under critical state, is the average effective stress of soil under critical state, is the excess pore water pressure in the critical state of soil, is the total stress, is the effective stress, is the ultra-clean pore water pressure;

[0025] Step S202: Establishing a standard triaxial shear test The gradient equation of the total stress path on the surface is expressed as follows:

[0026] (7)

[0027] in: Standard triaxial shear test The total stress path gradient of the surface, is the deviatoric stress of soil at the critical state, is the average total stress in the critical state of soil, is the initial confining pressure;

[0028] Step S203: The standard triaxial shear test result obtained in step S202 is Substitute the total stress path gradient equation into the excess pore water pressure under the critical state of the soil established in step S201 Function expression, get the excess pore water pressure under the first critical state of soil Function expressions, as follows:

[0029] (8)

[0030] in: is the initial effective confining pressure of soil;

[0031] Step S204: The functional expression of the critical state line in the plane is shown in formula (9), The functional expression of the critical state line in the plane is substituted into the first excess pore water pressure Function expressions, eliminating variables , the excess pore water pressure under the second critical state of soil is obtained function expressions, Functional expression of the critical state line in the plane and excess pore water pressure in the second critical state of soil The function expressions are as follows:

[0032] (9)

[0033] (10)

[0034] in: is the slope of the traditional critical state line;

[0035] Assume that the excess pore water pressure under the critical state of the second soil mass is The gradient in the function expression is , the excess pore water pressure under the third critical state of soil is obtained Function expression, the function expression is as follows:

[0036] (11)

[0037] gradient k The function expression is:

[0038] (12)

[0039] The excess pore water pressure in the third soil critical state All variables in the function expression are divided by ,get Functional relationship;

[0040] (13)

[0041] in: is the initial effective confining pressure of soil under critical state.

[0042] Furthermore, the specific operations of step S3 are as follows:

[0043] The porosity ratio of the soil under critical state obtained in step S103 is and the average effective stress of soil at critical state Transition parameters of critical soil mechanics constants The function expression between The excess pore water pressure of soil under critical state in undrained triaxial shear test is obtained by functional relationship Function expression:

[0044] (14).

[0045] Furthermore, the specific operations of step S4 are as follows:

[0046] Step S401: Assume that the void ratio of the soil under the critical state in the undrained triaxial shear test is Equal to the initial porosity of the soil , its function expression is shown in formula (15), critical state soil mechanics constant transition parameter Equal to the initial void ratio parameter of the soil under critical state , its function expression is shown in formula (16):

[0047] (15)

[0048] (16)

[0049] in: is the initial porosity parameter of soil under critical state;

[0050] Step S402: Substitute the function expression obtained in step S401 into the excess pore water pressure under the third critical state of the soil obtained in step S204. Function expression to obtain the excess pore water pressure under the critical state of soil Prediction Model:

[0051] (17)

[0052] in: are the state parameters under initial conditions.

[0053] The beneficial effects of the present invention are as follows: the present invention combines the porosity ratio with the critical state soil mechanics framework. and mean effective stress Excess pore water pressure increment and mean effective stress The relationship between the two is combined to obtain a prediction model for describing the excess pore water pressure in the critical state in the undrained triaxial shear test, which solves the technical problems of insufficient model accuracy in the existing technology and the inability to predict the excess pore water pressure in the critical state through the initial conditions of the sample when the initial porosity of the soil sample is less than the intercept porosity ratio in the undrained triaxial shear test. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 any creative work.

[0055] Figure 1 is a flow chart of the present invention;

[0056] Figure 2 The present invention Schematic diagram of three regions divided by different mechanical responses under undrained triaxial shear conditions in a plane;

[0057] Figure 3 Figure 2 is a graph of predicted and measured excess pore water pressure during undrained triaxial shear of four clean sands at different initial states. DETAILED DESCRIPTION

[0058] 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 embodiments described 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 efforts are within the scope of protection of the present invention.

[0059] like Figure 1 The flow chart of the method for predicting excess pore water pressure of saturated soil under critical state proposed by the present invention includes: Step S1: Calculate the average effective stress of soil under critical state based on critical state soil mechanics theory and the third law of critical state line , porosity ratio of soil under critical state ; Step S2: Establish the excess pore water pressure of soil under critical state in undrained triaxial shear test based on state soil mechanics theory and the average effective stress of soil at critical state Functional relationship, calculation Step S3: Establish the excess pore water pressure of soil under critical state in undrained triaxial shear test Function expression; Step S4: Use the excess pore water pressure under the critical state of the soil obtained in step S3 Function expression and initial effective confining pressure of soil , porosity ratio of soil under critical state There are four steps including establishing the prediction equation of excess pore water pressure of saturated soil under critical state.

[0060] The specific operations of step S1 are as follows:

[0061] Step S101: Calculate the void ratio intercept of the soil under critical state based on the undrained triaxial shear test data and the slope of the critical state line in the power law model ;

[0062] Step S102: According to the porosity intercept of the soil under critical state The slope of the critical state line in the CSL power law model proposed by Li and Wang (1998) is , calculate the void ratio of soil under critical state , the average effective stress of soil at critical state The expression is as follows:

[0063] (1)

[0064] Where: is the reference atmospheric pressure, is the void ratio intercept of soil at critical state, is the average effective stress of soil under critical state, is the slope of the critical state line in the power law model, is the calibration constant for sandy soil, which is taken as 0.7;

[0065] (2)

[0066] Step S103: Set the critical soil mechanics constant transition parameter to , using the porosity ratio of the soil under critical state obtained in step S102 The average effective stress of soil at critical state , establish the porosity ratio of soil under critical state The average effective stress of the soil at the critical state Transition parameters of critical soil mechanics constants The function expression between them is as follows:

[0067] (3)

[0068] The transition parameter of the critical state soil mechanics constant in step S103 The natural logarithm form of the function expression is as follows:

[0069] (4)

[0070] The specific operations of step S2 are as follows:

[0071] Step S201: Based on the total stress in the effective stress theory , effective stress , ultra-clean pore water pressure The functional relationship between them is shown in formula (5). The undrained stress path in the true liquefaction model, flow liquefaction model, limited liquefaction model, and undrained stable response model is analyzed to establish the excess pore water pressure under the critical state of the soil. The function expression is shown in formula (6):

[0072] (5)

[0073] (6)

[0074] in: is the average total stress of soil under critical state, is the average effective stress of soil under critical state, is the excess pore water pressure in the critical state of soil, is the total stress, is the effective stress, is the ultra-clean pore water pressure;

[0075] Step S202: Establishing a standard triaxial shear test The gradient equation of the total stress path on the surface is expressed as follows:

[0076] (7)

[0077] in: Standard triaxial shear test The total stress path gradient of the surface, is the deviatoric stress of soil at the critical state, is the average total stress in the critical state of soil, is the initial confining pressure.

[0078] Step S203: The standard triaxial shear test result obtained in step S202 is Substitute the total stress path gradient equation into the excess pore water pressure under the critical state of the soil established in step S201 Function expression, get the excess pore water pressure under the first critical state of soil Function expressions, as follows:

[0079] (8)

[0080] in: is the initial effective confining pressure of soil, is the deviatoric stress at the critical state;

[0081] Step S204: The functional expression of the critical state line in the plane is shown in formula (9), The functional expression of the critical state line in the plane is substituted into the first excess pore water pressure Function expressions, eliminating variables , the excess pore water pressure under the second critical state of soil is obtained function expressions, Functional expression of the critical state line in the plane and excess pore water pressure in the second critical state of soil The function expressions are as follows:

[0082] (9)

[0083] (10)

[0084] in: is the slope of the traditional critical state line;

[0085] Assume that the excess pore water pressure under the critical state of the second soil mass is The gradient in the function expression is , the excess pore water pressure under the third critical state of soil is obtained Function expression, the function expression is as follows:

[0086] (11)

[0087] In soil mechanics, the standard triaxial shear test is a commonly used geotechnical test used to study the shear strength characteristics of soil. The surface is a stress state representation plane commonly used in the analysis of triaxial shear test results. is the effective mean stress, is the deviatoric stress.

[0088] gradient k The function expression is:

[0089] (12)

[0090] The excess pore water pressure in the third soil critical state All variables in the function expression are divided by get Functional relationship;

[0091] (13)

[0092] in: is the initial effective confining pressure of soil under critical state.

[0093] Formula (13) can also be written as shown in formula (19):

[0094] (19)

[0095] in: is the normalized excess pore water pressure with respect to the initial effective confining pressure at the critical state, is the normalized mean effective stress with respect to the initial effective confining pressure at the critical state.

[0096] The specific operations of step S3 are as follows:

[0097] The porosity ratio of the soil under critical state obtained in step S103 is and the average effective stress of soil at critical state Transition parameters of critical soil mechanics constants The function expression between The excess pore water pressure of soil under critical state in undrained triaxial shear test is obtained by functional relationship Function expression:

[0098] (14)

[0099] The specific operations of step S4 are as follows:

[0100] Step S401: Assume that the void ratio of the soil under the critical state in the undrained triaxial shear test is Equal to the initial porosity of the soil , its function expression is shown in formula (15), critical state soil mechanics constant transition parameter Equal to the initial void ratio parameter of the soil under critical state , its function expression is shown in formula (16):

[0101] (15)

[0102] (16)

[0103] in: is the initial porosity parameter of soil under critical state;

[0104] Step S402: Substitute the function expression obtained in step S401 into the excess pore water pressure under the third soil critical state obtained in step S204. Function expression to obtain the excess pore water pressure under the critical state of soil Prediction Model:

[0105] (17)

[0106] in: are the state parameters under initial conditions.

[0107] More specific: Figure 2 This invention is Schematic diagram of three regions divided by different mechanical responses under undrained triaxial shear conditions in a plane. The prediction model (17) of excess pore water pressure under critical state can also be obtained from (16) and Figure 2 Description composition.

[0108] Figure 2 For specimens with initial conditions S1 and S2, or other conditions in Region III, the undrained triaxial shear test will terminate the critical steady state at T1 and T2, respectively. For specimens with initial conditions S3, which has a lower mean effective stress, and S4, which has a higher mean effective stress, the undrained triaxial shear test will terminate the critical steady state at the same state T3 along the critical state line. For specimens with initial conditions S3 or other conditions in Region I, the undrained triaxial shear test will exhibit an undrained stable response. For specimens with initial conditions S4 or other conditions in Region II, the undrained triaxial shear test will exhibit an undrained unstable response.

[0109] Figure 2 Where S1 is the first initial condition, S2 is the second initial condition, S3 is the third initial condition, S4 is the fourth initial condition, T1 is the first critical state, T2 is the second critical state, and T3 is the third critical state.

[0110] When the initial porosity is greater than the trigger porosity for true liquefaction, true liquefaction should occur under undrained triaxial shear. Therefore, when the initial porosity is greater than the intercept porosity of the critical state line, the excess pore water pressure should be equal to the initial effective confining pressure.

[0111] Transition parameters of critical soil mechanical constants The exponential form of the function expression is as follows:

[0112] (18)

[0113] This application carried out four groups of drained monotonic triaxial shear tests and four groups of undrained monotonic triaxial shear tests. The test objects were four different sand remolded specimens, namely Pearl River Sand (ZRS), Leighton Buzzard Sand (LBS), Quartz Sand A (QSA), and Quartz Sand B (QSB). The specimens were uniformly 38 mm in diameter and 76 mm in height. They were prepared using the wet ramming method and under-compaction technology. During the monotonic triaxial shear process, the shear strain rate parameter of each specimen was controlled at 0.5% height / min.

[0114] Based on the above monotonic triaxial shear test, the initial effective confining pressure of each reshaped specimen during triaxial shear is obtained: Compared with the porosity ratio after consolidation under initial conditions , the initial effective confining pressure of each reshaped specimen in triaxial shear Compared with the porosity ratio after consolidation under initial conditions Substituting the excess pore water pressure prediction equation of soil under critical state shown in formula (17) into the predicted value of excess pore water pressure of soil under critical state of each reshaped specimen, the excess pore water pressure of soil under critical state of each reshaped specimen was obtained. Then, the excess pore water pressure of soil under critical state of each reshaped specimen was measured, and the results are shown in Table 1-4.

[0115] Table 1 Predicted values of excess pore water pressure Δ of QSA sand under critical state u cs Compared with the measured value of excess pore water pressure

[0116] ;

[0117] Table 2 Predicted values of excess pore water pressure Δ of QSB sand under critical state u cs Compared with the measured value of excess pore water pressure

[0118] ;

[0119] Table 3 Predicted values of excess pore water pressure Δ of ZRS sand under critical state u cs Compared with the measured value of excess pore water pressure

[0120] ;

[0121] Table 4 Prediction value of excess pore water pressure Δ of LBS sand under critical state u cs Compared with the measured value of excess pore water pressure

[0122] .

[0123] Each test is represented by the code “XXX-a-CIDb” or “XXX-a-CIUb”, where CID and CIU stand for consolidated isotropic shear, drained shear and consolidated isotropic undrained shear, respectively; XXX is the code for sand, a is the initial effective confining pressure, and b is the test number.

[0124] like Figure 3 As shown in the figure, the predicted excess pore water pressure of each specimen of each sand and the test results can basically be fitted into a straight line, which proves that the value predicted by the model is highly consistent with the measured data.

[0125] like Figure 3 As shown in the figure, when the excess pore water pressure is less than -300 kPa, the model-predicted excess pore water pressure is less than the corresponding measured value. This is because the solubility of carbon dioxide and air decreases with the applied back pressure. During the undrained shear process, when the excess pore water pressure is less than the saturation back pressure applied to the prepared specimen, the physical pore pressure of the current specimen becomes negative, the saturation level is severely reduced, and the specimen's saturation state changes from saturated to unsaturated.

[0126] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A method for predicting excess pore water pressure of saturated soil under critical state, characterized in that: Follow these steps: Step S1: Based on the critical state soil mechanics theory and the third law of critical state line, calculate the average effective stress p′ of the soil under the critical state cs , the void ratio e of soil under critical state cs ; Step S2: Based on the state soil mechanics theory, establish the excess pore water pressure Δu of the soil under the critical state in the undrained triaxial shear test cs and the average effective stress p′ of soil at critical state cs Functional relationship, calculate Δu cs -p′ cs Functional relationship of Step S3: Establish the excess pore water pressure Δu at the fourth critical state of the soil in the undrained triaxial shear test cs4 Function expressions; The specific operations of step S3 are: The porosity ratio e of soil at critical state cs and the average effective stress p′ of soil at critical state cs The critical soil mechanics constant transition parameter f(e cs ) between the function expression, into Δu cs -p′ cs The excess pore water pressure Δu at the critical state of the fourth soil mass in the undrained triaxial shear test is obtained by the functional relationship cs4 The function expression is: Thu cs4 =s' 3c -kp a f(e cs ) (14); Among them: k is the gradient, p a is the reference atmospheric pressure; Step S4: Using the excess pore water pressure Δu under the fourth soil critical state obtained in step S3 cs4 Function expression and soil initial effective confining pressure σ'3c, soil critical state porosity ratio e cs The prediction equation of excess pore water pressure of saturated soil under critical state is established.

2. The method for predicting excess pore water pressure of saturated soil under critical state according to claim 1, characterized in that: The specific operations of step S1 are: Step S101: Calculate the void ratio intercept e of the soil under critical state based on the undrained triaxial shear test data. Γ and the slope λ of the critical state line in the power law model e ; Step S102: According to the porosity intercept e of the soil under critical state Γ and the slope λ of the critical state line in the power law model e , calculate the void ratio e of soil under critical state cs , the average effective stress p′ of soil at critical state cs The expression is: Where: p a is the reference atmospheric pressure, e Γ is the porosity intercept of soil at critical state, p′ cs is the average effective stress of soil at critical state, λ e is the slope of the critical state line in the power law model, α is the calibration constant for sand, which is taken as 0.7; Step S103: Assume that the critical state soil mechanics constant transition parameter is f(e cs ), using the void ratio e under the critical state of the soil obtained in step S102 cs The average effective stress p′ of soil at critical state cs , establish the void ratio e of soil under critical state cs and the average effective stress p′ of soil at critical state cs The critical soil mechanics constant transition parameter f(e cs ) is the function expression between: p′ cs =p a f(e cs ) (3)。 3. The method for predicting excess pore water pressure of saturated soil under critical state according to claim 2, characterized in that: In step S103, the critical state soil mechanics constant transition parameter f(e cs )The natural logarithm form of the function expression is:

4. The method for predicting excess pore water pressure of saturated soil under critical state according to claim 1, characterized in that: The specific operations of step S2 are: Step S201: Based on the effective stress theory, the functional relationship between the total stress σ, the effective stress σ', and the ultra-clean pore water pressure Δu is: σ=σ'+Δu (5) Analyze the undrained stress path in the true liquefaction model, flow liquefaction model, limited liquefaction model, and undrained stability response model to establish the excess pore water pressure Δu under the critical state of the soil cs The function expression is: Δu cs =p cs -p' cs (6) Where: p cs is the average total stress of soil at critical state, p′ cs is the average effective stress of soil at critical state, Δu cs is the excess pore water pressure under the critical state of soil, σ is the total stress, σ' is the effective stress, and Δu is the excess pore water pressure; Step S202: Establish the total stress path gradient equation of the q–p plane of the standard triaxial shear test as follows: Where: M tsp is the total stress path gradient on the q–p plane of the standard triaxial shear test, q cs is the deviatoric stress of soil at the critical state, p cs is the average total stress of soil at critical state, σ 3c is the initial confining pressure; Step S203: Substitute the total stress path gradient equation of the standard triaxial shear test q–p plane obtained in step S202 into the excess pore water pressure Δu under the critical state of the soil established in step S201. cs Function expression, the excess pore water pressure Δu under the first critical state of soil is obtained cs1 The function expression is: Where: σ'3c is the initial effective confining pressure of the soil; Step S204: The function expression of the critical state line in the q–p' plane is: q cs =M cs p' cs (9) Where: M cs is the slope of the traditional critical state line; Substitute the function expression of the critical state line in the q–p' plane into the excess pore water pressure Δu under the first critical state of soil cs1 Function expression, eliminating variable q cs , the excess pore water pressure Δu under the second critical state of soil is obtained cs2 for: Where: q-p' plane is a stress state representation plane commonly used in the analysis of triaxial shear test results, p' is the effective mean stress, q is the deviatoric stress; Assume that the excess pore water pressure Δu under the critical state of the second soil mass is cs2 The gradient in the function expression is k, and the excess pore water pressure Δu under the third critical state of soil is obtained cs3 The function expression is: Thu cs3 =in' 3c -kp' cs (11) The function expression of gradient k is: The excess pore water pressure Δu under the critical state of the third soil cs3 All variables in the function expression are divided by σ' 3c , we get Δu cs -p′ cs The functional relationship is: Thu cs =-k·p' cs +(σ′ 3c ) cs (13) Where: (σ′ 3c ) cs is the initial effective confining pressure of soil under critical state.

5. The method for predicting excess pore water pressure of saturated soil under critical state according to claim 1 or 4, characterized in that: The specific operations of step S4 are: Step S401: Assume that the void ratio e of the soil under the critical state in the undrained triaxial shear test is cs Equal to the initial porosity ratio e of the soil c , its function expression is: And cs =and c (15) Critical state soil mechanics constant transition parameter f(e cs ) is equal to the initial void ratio parameter f(e) in the critical state of the soil c ), its function expression is: f(e cs )=f(e c ) (16) Where: f(e c ) is the initial void ratio parameter of the soil under critical state; Step S402: Substitute the function expression obtained in step S401 into the excess pore water pressure Δu of the fourth soil mass under the critical state in the undrained triaxial shear test obtained in step S3. cs4 Function expression, the prediction model of excess pore water pressure under critical state of soil is obtained as follows: Where: ψ0 is the state parameter under initial conditions, e Γ is the porosity intercept of soil at critical state, p a is the reference atmospheric pressure and k is the gradient.

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