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

Abstract

The invention discloses a method for predicting excess pore water pressure of a saturated soil body in a critical state, which specifically comprises the following steps of: calculating average effective stress in the critical state of the soil body and a void ratio in the critical state of the soil body on the basis of a critical state soil mechanics theory and a critical state line third law; the method comprises the following steps: establishing a relational expression between the excess pore water pressure in a soil body critical state and the average effective stress in the soil body critical state, calculating a correlation expression, establishing an excess pore water pressure function expression, and establishing an excess pore water pressure prediction equation by using the excess pore water pressure function expression, the soil body initial effective confining pressure and the void ratio in the soil body critical state. The problem that in the prior art, a soil body average effective stress, deviatoric stress and void ratio relation model established through a traditional critical state soil mechanics method is insufficient in precision is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of monitoring and prediction of water conservancy engineering and geotechnical engineering, and in particular 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 fail 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 to understanding the mechanical behavior of saturated sand.

[0003] At present, the traditional critical state soil mechanics method can be used to establish a relationship model between the average effective stress of soil, the deviatoric stress of soil and the porosity of soil under the critical state. Although this model has achieved certain results in describing the mechanical behavior of soil, it still has problems such as insufficient model accuracy and weak adaptability. In addition, in the undrained triaxial shear test, for soil samples with the same porosity level, the smaller the initial average effective stress of the sample, the greater the undrained shear dilatancy potential of the sample, but the occurrence of real liquefaction mainly depends on the initial porosity, but has nothing to do with the initial average effective stress. When the initial porosity is less than the intercept porosity, how to predict the excess pore water pressure under the critical state through the initial conditions of the sample is still a key problem to be solved. 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 the soil established by the traditional critical state soil mechanics method is insufficiently accurate and that in an undrained triaxial shear test, when the initial porosity of the soil sample is less than the intercept porosity ratio, 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: Step S1: Based on the critical state soil mechanics theory and the third law of critical state line, calculate the average effective stress of the soil under the critical state , the void 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 The functional relationship of The functional relationship of Step S3: Establish the excess pore water pressure of soil under critical state in undrained triaxial shear test Function expressions; Step S4: Using 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 , the void ratio of soil under critical state The prediction equation of excess pore water pressure of saturated soil under critical state is established.

[0006] Furthermore, the specific operations of step S1 are as follows: Step S101: Calculate the void ratio intercept of the soil under the critical state according to the undrained triaxial shear test data and the slope of the critical state line in the power law model ; Step S102: According to the porosity intercept of the soil under the 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: (1) Where: is the reference atmospheric pressure, is the void ratio intercept of soil under 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; (2) Step S103: Set the critical state 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 under 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 mechanical constants The function expression between them is as follows: (3).

[0007] Furthermore, in step S103, the critical state soil mechanics constant transition parameter The natural logarithm form of the function expression is as follows: (4).

[0008] Furthermore, the specific operations of step S2 are as follows: 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): (5) (6) 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 under the critical state of soil, is the total stress, is the effective stress, is the ultra-clean pore water pressure; Step S202: Establishing a standard triaxial shear test The gradient equation of the total stress path on the surface is expressed as follows: (7) 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 of the soil under critical state, is the initial confining pressure; 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 mass established in step S201 Function expression, the excess pore water pressure under the first critical state of soil is obtained The function expression is as follows: (8) in: is the initial effective confining pressure of soil; Step S204: The functional expression of the critical state line in the plane is shown in formula (9), Substitute the first excess pore water pressure into the functional expression of the critical state line in the plane Function expressions, eliminating variables , the excess pore water pressure under the second critical state of soil is obtained Function expressions, Functional expression of critical state line in plane and excess pore water pressure under the second critical state of soil The function expressions are as follows: (9) (10) in: is the slope of the traditional critical state line; Assume that the excess pore water pressure under the second soil critical state 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: (11) gradient k The function expression is: (12) The excess pore water pressure under the third soil critical state All variables in the function expression are divided by ,get Functional relationship; (13) in: is the initial effective confining pressure of soil under critical state.

[0009] Furthermore, the specific operations of step S3 are as follows: 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 functional relationship is used to obtain the excess pore water pressure of soil under critical state in undrained triaxial shear test Function expression: (14).

[0010] Furthermore, the specific operations of step S4 are as follows: 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 void ratio of the soil , whose function expression is shown in formula (15), the 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): (15) (16) in: is the initial void ratio parameter of soil under critical state; 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, get the excess pore water pressure under the critical state of soil Prediction Model: (17) in: are the state parameters under initial conditions.

[0011] The beneficial effect of the present invention is that the present invention combines the porosity ratio under the critical state soil mechanics framework and mean effective stress Excess pore water pressure increment and mean effective stress By combining the relationship between the two, a prediction model for describing the excess pore water pressure under the critical state in the undrained triaxial shear test is derived, which solves the technical problems of insufficient model accuracy in the prior art and the inability to predict the excess pore water pressure under the critical state through the initial conditions of the sample when the initial porosity of the soil sample is less than the intercept porosity in the undrained triaxial shear test. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] 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.

[0013] Figure 1 is a flow chart of the present invention; Figure 2 The present invention Schematic diagram of three regions divided by different mechanical responses under undrained triaxial shear conditions in a plane; Figure 3are the predicted and measured excess pore water pressure diagrams of four clean sands during undrained triaxial shear at different initial states. DETAILED DESCRIPTION

[0014] 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 creative work are within the scope of protection of the present invention.

[0015] 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 comprises: step S1: based on critical state soil mechanics theory and the third law of critical state line, calculate the average effective stress of soil under critical state , the void 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 The functional relationship of Step S3: Establish the excess pore water pressure of soil under critical state in undrained triaxial shear test Function expression; Step S4: using 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 , the void 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.

[0016] The specific operations of step S1 are as follows: Step S101: Calculate the void ratio intercept of the soil under the critical state according to the undrained triaxial shear test data and the slope of the critical state line in the power law model ; Step S102: According to the porosity intercept of the soil under the 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: (1) Where: is the reference atmospheric pressure, is the void ratio intercept of soil under 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; (2) Step S103: Set the critical state 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 under critical state , establish the void ratio of soil under critical state The average effective stress of the soil at the critical state Transition parameters of critical soil mechanical constants The function expression between them is as follows: (3) The transition parameter of the critical state soil mechanics constant in step S103 The natural logarithm form of the function expression is as follows: (4) The specific operations of step S2 are as follows: 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): (5) (6) 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 under the critical state of soil, is the total stress, is the effective stress, is the ultra-clean pore water pressure; Step S202: Establishing a standard triaxial shear test The gradient equation of the total stress path on the surface is expressed as follows: (7) 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 of the soil under critical state, is the initial confining pressure.

[0017] 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 mass established in step S201 Function expression, the excess pore water pressure under the first critical state of soil is obtained The function expression is as follows: (8) in: is the initial effective confining pressure of soil, is the deviatoric stress at the critical state; Step S204: The functional expression of the critical state line in the plane is shown in formula (9), Substitute the first excess pore water pressure into the functional expression of the critical state line in the plane Function expressions, eliminating variables , the excess pore water pressure under the second critical state of soil is obtained Function expressions, Functional expression of critical state line in plane and excess pore water pressure under the second critical state of soil The function expressions are as follows: (9) (10) in: is the slope of the traditional critical state line; Assume that the excess pore water pressure under the second soil critical state 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: (11) 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.

[0018] gradient k The function expression is: (12) The excess pore water pressure under the third soil critical state All variables in the function expression are divided by get Functional relationship; (13) in: is the initial effective confining pressure of soil under critical state.

[0019] Formula (13) can also be written as shown in formula (19): (19) 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.

[0020] The specific operation of step S3 is as follows: 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 functional relationship is used to obtain the excess pore water pressure of soil under critical state in undrained triaxial shear test Function expression: (14) The specific operations of step S4 are as follows: 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 void ratio of the soil , whose function expression is shown in formula (15), the 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): (15) (16) in: is the initial void ratio parameter of soil under critical state; 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, get the excess pore water pressure under the critical state of soil Prediction Model: (17) in: are the state parameters under initial conditions.

[0021] More specific: Figure 2 It means that the present invention Schematic diagram of three regions divided by different mechanical responses under undrained triaxial shear conditions in a plane. The prediction model of excess pore water pressure under critical state (Eq. (17)) can also be obtained by Eq. (16) and Figure 2 Description composition.

[0022] Figure 2 In the undrained triaxial shear test, for specimens with initial conditions S1 and S2 or other states in region III, the undrained triaxial shear test will end the critical steady state at T1 and T2, respectively. For specimens with initial conditions S3 with lower mean effective stress and S4 with higher mean effective stress, the undrained triaxial shear test will end the critical steady state at the same state T3 of the critical state line. For specimens with initial state S3 or other states in region I, the undrained triaxial shear test will show an undrained stable response. For specimens with initial state S4 or other states in region II, the undrained triaxial shear test will show an undrained unstable response.

[0023] Figure 2 Among them, 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.

[0024] When the initial porosity is greater than the trigger porosity of true liquefaction, true liquefaction of undrained triaxial shear should occur. 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.

[0025] Transition parameters of critical soil mechanical constants The exponential form of the function expression is as follows: (18) 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 tamping method and under-compaction technology. During the monotonic triaxial shear process, the shear strain rate parameter of each specimen was controlled to be 0.5% height / minute.

[0026] 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 prediction equation of excess pore water pressure under the critical state of soil shown in formula (17) into the predicted value of excess pore water pressure under the critical state of soil of each remolded specimen, the excess pore water pressure of each remolded specimen under the critical state is then measured. The results are shown in Table 1-4.

[0027] Table 1 Prediction value of excess pore water pressure Δ of QSA sand under critical state u cs Compared with the measured value of excess pore water pressure ;

[0028] Table 2 Prediction value of excess pore water pressure of QSB sand under critical state Δ u cs Compared with the measured value of excess pore water pressure ;

[0029] Table 3 Prediction value of excess pore water pressure of ZRS sand under critical state Δ u cs Compared with the measured value of excess pore water pressure ;

[0030] 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 .

[0031] 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.

[0032] like Figure 3 As shown in the figure, the predicted value of excess pore water pressure of each specimen of each sand and the test results can basically fit into a straight line, which proves that the value predicted by the model is highly consistent with the measured data.

[0033] like Figure 3 As shown in the figure, when the excess pore water pressure value is less than -300 kPa, the model-predicted value of the excess pore water pressure is less than the corresponding measured value. This is because: it is known that the gas solubility of carbon dioxide and air will decrease with the real-time decrease of the applied back pressure. During the undrained shear process, when the excess pore water pressure is less than the saturated back pressure applied value of the prepared sample, the physical pore pressure of the current sample is negative, the saturation will be severely reduced, and the saturation state of the specimen will change from saturated state to unsaturated state.

[0034] 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 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 of the soil under the critical state , the void 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 The functional relationship of The functional relationship of Step S3: Establish the excess pore water pressure of soil under critical state in undrained triaxial shear test Function expressions; Step S4: Using 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 , the void ratio of soil under critical state 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 as follows: Step S101: Calculate the void ratio intercept of the soil under the critical state according to the undrained triaxial shear test data and the slope of the critical state line in the power law model ; Step S102: According to the porosity intercept of the soil under the 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: （1） Where: is the reference atmospheric pressure, is the porosity intercept of soil under 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; （2） Step S103: Set the critical state 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 under 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 mechanical constants The function expression between them is as follows: （3）。 3. The method for predicting excess pore water pressure of saturated soil under critical state according to claim 2, characterized in that: Critical state soil mechanics constant transition parameter in step S103 The natural logarithm form of the function expression is as follows: （4）。 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 as follows: 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): （5） （6） 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 under the critical state of soil, is the total stress, is the effective stress, is the ultra-clean pore water pressure; Step S202: Establishing a standard triaxial shear test The gradient equation of the total stress path on the surface is expressed as follows: （7） 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 of the soil under critical state, is the initial confining pressure; 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 mass established in step S201 Function expression, the excess pore water pressure under the first critical state of soil is obtained The function expression is as follows: （8） in: is the initial effective confining pressure of soil; Step S204: The functional expression of the critical state line in the plane is shown in formula (9), Substitute the first excess pore water pressure into the functional expression of the critical state line in the plane Function expressions, eliminating variables , the excess pore water pressure under the second critical state of soil is obtained Function expressions, Functional expression of critical state line in plane and excess pore water pressure under the second critical state of soil The function expressions are as follows: （9） （10） in: is the slope of the traditional critical state line; Assume that the excess pore water pressure under the second soil critical state 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: （11） gradient k The function expression is: （12） The excess pore water pressure under the third soil critical state All variables in the function expression are divided by ,get Functional relationship; （13） in: 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 2 or 4, characterized in that: The specific operation of step S3 is as follows: 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 mechanical constants The function expression between The functional relationship is used to obtain the excess pore water pressure of soil under critical state in undrained triaxial shear test Function expression: （14）。 6. 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 as follows: 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 void ratio of the soil , whose function expression is shown in formula (15), the 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): （15） （16） in: is the initial void ratio parameter of soil under critical state; 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, get the excess pore water pressure under the critical state of soil Prediction Model: （17） in: are the state parameters under initial conditions.

Images