Pile tip resistance prediction method and system based on mudstone damage constitutive model

Abstract

This invention provides a method and system for predicting pile end resistance based on a mudstone damage constitutive model, relating to the field of geotechnical engineering. Addressing the difficulty in quantitatively analyzing and calculating the bearing capacity of dynamically driven piles in mudstone foundations and the damage characteristics of the surrounding mudstone, this invention establishes a statistical damage constitutive model for mudstone based on the stress state-determined damage variable D and its association with rock failure criteria. Model parameters are determined according to triaxial test results, and the relationship between the critical damage variable and confining pressure is established. The damage characteristics of the mudstone surrounding the dynamically driven pile are analyzed, thereby calculating the pile end resistance and meeting the need for quantitative analysis of pile end damage characteristics.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a method and system for predicting pile end resistance based on a mudstone damage constitutive model. Background Technology

[0002] Rock is a heterogeneous, anisotropic geological material containing sensitive defects such as fissures and cavities, exhibiting complex constitutive relationships. Its constitutive model and engineering applications have always been a key research focus in geotechnical engineering. Soft rocks, especially mudstone, possess structure and are common geotechnical engineering materials. The stress process is essentially a process of internal defect propagation, thus inherently possessing initial damage. Furthermore, this gradual propagation of internal defects leading to the deterioration of mudstone's mechanical properties is irreversible, and this mechanical behavior does not fall within the strict elastoplastic deformation range. Therefore, descriptions based on elastoplastic theory cannot fully reflect the deformation characteristics of mudstone. Damage mechanics studies the damage evolution and failure process of materials under load; therefore, introducing damage theory to study the damage evolution and mechanical properties of mudstone has significant theoretical and practical implications.

[0003] Currently, research on mudstone damage models primarily relies on triaxial tests of mudstone samples taken from high-stress, deep mudstone deposits used in mining and tunnel engineering. There is a lack of research specifically addressing mudstone surrounding dynamically driven piles. Due to the unique engineering properties of mudstone, such as its susceptibility to disturbance and softening upon contact with water, abnormal bearing capacity of pile foundations in mudstone foundations is frequently observed. During dynamic pile driving, the surrounding soil exhibits a soil response. For mudstone foundations, the dynamic driving process of precast piles is accompanied by secondary damage. Initial damage coupled with dynamic pile driving damage affects the bearing characteristics of the mudstone foundation. This often results in abnormal phenomena where the vertical compressive bearing capacity of a single pile does not meet design requirements even after the engineering piles have passed acceptance testing. The main characteristic is a small pile tip force but significant pile tip settlement. Regarding this issue, the existing method for establishing a damage model containing cemented infill with initial damage, disclosed in CN202110681095.8, has limitations. After the mudstone surrounding the pile has undergone dynamic pile driving damage, the initial damage threshold becomes difficult to determine. Although CN202010825183.6 discloses a method for estimating the bearing capacity of a single threaded pile, calculating the end resistance requires not only soil parameters and pile body parameters such as pile diameter, pitch, pitch height, and pitch width, but also field construction parameters and static load test data. The calculation is complex and limited to threaded pile types. Therefore, it is difficult to meet the needs for quantitative analysis of the bearing capacity of dynamically driven piles in mudstone foundations and the characteristics of mudstone damage around the pile. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a method and system for predicting pile end resistance based on a mudstone damage constitutive model, and to establish damage variables determined by stress state.D A statistical damage constitutive model for mudstone, which is associated with rock failure criteria, is used to determine model parameters based on triaxial test results, establish the relationship between critical damage variables and confining pressure, analyze the damage characteristics of mudstone around dynamically driven piles, and calculate pile end resistance, thus meeting the needs for quantitative analysis of pile end damage characteristics.

[0005] The first objective of this invention is to provide a method for predicting pile end resistance based on a mudstone damage constitutive model, employing the following scheme:

[0006] Based on the triaxial compression test, the mechanical parameters of mudstone were obtained, and damage variables were defined.

[0007] Based on the principle of strain equivalence, the relationship between stress, strain and damage variables is established, and a damage evolution equation is established in combination with mudstone mechanical parameters. The relationship equation between damage variables, deviatoric stress and confining pressure is fitted.

[0008] A constitutive model of mudstone damage was established, and the parameters of the constitutive model were calculated based on the results of triaxial tests to obtain the correspondence between confining pressure and peak stress.

[0009] Obtain the stress data of mudstone at the pile tip, convert it into confining pressure, and substitute it into the corresponding relationship to obtain the pile tip resistance.

[0010] Furthermore, the elastic modulus and shear strength indices are calculated to obtain the mechanical parameters of the mudstone.

[0011] Furthermore, the material is discretized into multiple basic units, and the damage variable is the ratio of the damaged cross-sectional area of ​​the material after damage to the initial cross-sectional area of ​​the mudstone. It is assumed that the strength of the basic units follows a Wechsler distribution.

[0012] Furthermore, damage variables were calculated based on conventional triaxial test data, and the relationship equations between damage variables, deviatoric stress, and confining pressure were fitted.

[0013] Furthermore, based on the principle of strain equivalence, the stress-strain relationship of mudstone damage based on the Wechsler distribution is obtained as a constitutive model, and the constitutive model of mudstone damage is optimized.

[0014] Furthermore, the determination of the constitutive model parameters includes the following steps:

[0015] After the stress-strain curve of mudstone under confining pressure reaches its ultimate strength, record the stress, strain, and confining pressure corresponding to the peak point.

[0016] Calculate the mudstone element strength corresponding to the peak point based on the triaxial test results, and calculate the constitutive model parameters.

[0017] Furthermore, the obtained constitutive model parameters are substituted into the constitutive model, and the damage variables and strains are calculated according to the loading levels of the triaxial test. The results of the triaxial test are then compared and verified.

[0018] Furthermore, through triaxial testing and damage analysis, the functional relationship between confining pressure and peak stress was fitted to obtain the correspondence between confining pressure and peak stress.

[0019] Furthermore, by obtaining the pile body parameters and the weight of the soil and rock, the horizontal earth pressure of mudstone at the pile tip is equivalent to the confining pressure. Substituting these into the corresponding relationship, the corresponding vertical destructive force is obtained, which is equivalent to a concentrated load as the pile tip resistance.

[0020] The second objective of this invention is to provide a pile end resistance prediction system based on a mudstone damage constitutive model, comprising:

[0021] The parameter acquisition module is configured to: acquire mudstone mechanical parameters based on triaxial compression tests and define damage variables;

[0022] The fitting module is configured to: establish the relationship between stress, strain and damage variables based on the principle of strain equivalence, and establish a damage evolution equation in combination with mudstone mechanical parameters, and fit the relationship equation between damage variables, deviatoric stress and confining pressure.

[0023] The modeling module is configured to: establish a constitutive model of mudstone damage, calculate the constitutive model parameters based on triaxial test results, and obtain the correspondence between confining pressure and peak stress.

[0024] The data output module is configured to: acquire the stress data of mudstone at the pile tip, convert it into confining pressure, and substitute it into the corresponding relationship to obtain the pile tip resistance.

[0025] Compared with the prior art, the advantages and positive effects of this invention are:

[0026] (1) To address the difficulty in quantitatively analyzing and calculating the bearing capacity of dynamic driven piles and the damage characteristics of mudstone around the piles in mudstone foundations, a damage variable based on stress state is established. D A statistical damage constitutive model for mudstone, which is associated with rock failure criteria, is used to determine model parameters based on triaxial test results, establish the relationship between critical damage variables and confining pressure, analyze the damage characteristics of mudstone around dynamically driven piles, and calculate pile end resistance, thus meeting the needs for quantitative analysis of pile end damage characteristics.

[0027] (2) The constitutive model was verified by combining triaxial tests, and the damage variables were calculated according to the loading levels of the triaxial tests. D Then, the strain was calculated from the stress, and the axial strain was plotted as the abscissa and the deviatoric stress as the ordinate. A comparison graph of the model calculation results and the triaxial test curves was plotted to verify the accuracy of the new damage constitutive model. Attached Figure Description

[0028] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0029] Figure 1 This is a flowchart of the damage constitutive model and pile end resistance prediction method in Embodiment 1 or 2 of the present invention.

[0030] Figure 2 This is a schematic diagram of the damage evolution curve in Embodiment 1 or 2 of the present invention.

[0031] Figure 3 As described in Embodiment 1 or 2 of the present invention Dq - s 3. Spatial scatter plot.

[0032] Figure 4 As described in Embodiment 1 or 2 of the present invention Dq-s 3. Relationship diagram of the space surface of the fitted equation.

[0033] Figure 5 As described in Embodiment 1 or 2 of the present invention Dq-s 3. Comparison of fitted data and experimental data.

[0034] Figure 6 This is a comparison chart of the calculation results of the model described in Embodiment 1 or 2 of the present invention and the triaxial test curve.

[0035] Figure 7 The confining pressure described in Embodiment 1 or 2 of the present invention s 3 and peak point s 1c Relationship diagram.

[0036] Figure 8 This is a schematic diagram of the stress state of mudstone at the pile end as described in Embodiment 1 or 2 of the present invention.

[0037] Figure 9 This is a force diagram of the pile end in the field test as described in Embodiment 1 or 2 of the present invention. Detailed Implementation

[0038] Example 1

[0039] In a typical embodiment of the present invention, such as Figure 1-Figure 9 As shown, a method for predicting pile end resistance based on a mudstone damage constitutive model is presented.

[0040] like Figure 1 As shown, the damage variables are determined based on the stress state. D A statistical damage constitutive model for mudstone, correlated with rock failure criteria, was developed. Model parameters were determined based on triaxial test results. The relationship between critical damage variables and confining pressure was established. The damage characteristics of mudstone surrounding dynamically driven piles were analyzed, and the confining pressure was fitted. s 3 and peak point s 1c The functional relationship between them equates the horizontal earth pressure on the mudstone at the pile tip to the confining pressure. s 3. Calculate the pile end resistance, especially the pile end resistance of precast piles in mudstone foundations, and verify the model by combining indoor and outdoor tests.

[0041] Combination Figure 1 The constitutive model for mudstone damage and the method for predicting pile end resistance include the following:

[0042] 1. Obtaining mechanical parameters through triaxial compression testing

[0043] Triaxial compression tests were conducted on mudstone to obtain its mechanical parameters and calculate its elastic modulus. E、m and shear strength index c、 f .

[0044] 2. Assuming the basic strength of the rock F Follows Weibull distribution

[0045] Discretizing the rock medium can be viewed as different elementary components, each of which exists in only two states: destroyed or undestroyed. Material defects and property differences are reflected in the order of destruction of these individual elementary components. The accumulation of destroyed components leads to changes in material properties, macroscopically manifested as a deterioration in mechanical properties.

[0046] Assuming rock elemental strength F It follows a Weibull distribution with the following probability density function:

[0047] (1)

[0048] In the formula, F For rock elemental strength, m At F 0 represents the Weibull distribution parameter, which is the parameter for subsequent models.

[0049] 3. Define damage variables D

[0050] Damage refers to the visual morphology of microcracks, microdefects, etc., within a material, possessing a certain geometric shape. Assume the initial cross-sectional area of ​​the stressed object is... A The damaged cross-sectional area is A "Then the net area of ​​the cross section is:

[0051] (2)

[0052] At this point, the damage variable is:

[0053] (3)

[0054] In the formula D When = 0, it corresponds to the lossless state, 0 < D <1 corresponds to a partial damage state; D When =1, it corresponds to a completely damaged state. Additionally, σ=F⁄A The nominal stress of the cross section, σ'=F⁄A' The effective stress of the cross section is the net stress.

[0055] 4. Based on the principle of strain equivalence, establish the relationship between stress, strain, and damage variables.

[0056] The principle of strain equivalence states that the strain caused by stress (nominal stress) acting on a damaged material is equivalent to the strain caused by effective stress (net stress) acting on an undamaged material with the same geometric dimensions.

[0057] (4)

[0058] In the formula, E、E' Let be the elastic modulus of the undamaged and damaged materials; according to this principle, the constitutive relation of the damaged material can be expressed by the nominal stress of the undamaged material.

[0059] 5. Establish the damage evolution equation

[0060] The evolution equation of the damage variable can be obtained by using the distribution density function:

[0061] (5)

[0062] Based on existing research, the general formula for the failure criterion of rocks is assumed to be:

[0063] (6)

[0064] In the formula, k 0 is a constant related to the material's cohesion and internal friction angle.

[0065] For different destruction criteria F There are different forms of expression; considering the wide range of applications, the elementary strength based on the Mohr-Coulomb rock strength theory is adopted. F The Mohr-Coulomb rock strength criterion is in the following form:

[0066] (7)

[0067] In the formula: c , These are the rock cohesion and the angle of internal friction, respectively, from which the rock element strength is determined.

[0068] (8)

[0069] In the formula: α = (1- sin ) / (1+ sin ).

[0070] 6. Establishment of the constitutive model

[0071] Based on the assumption of strain equivalence, the constitutive relation of mudstone damage can be established as follows:

[0072] (9)

[0073] In the formula: [ C [ represents the elastic matrix of mudstone material,] s ′] is the effective stress matrix, [ s ] is the nominal stress matrix, [ e ] is the strain matrix, D Let be the variable representing mudstone damage. From the above formula, we can obtain...

[0074] (10)

[0075] or

[0076] (11)

[0077] In the formula s 1′= s 1′ / (1- D ); s 2′= s 2′ / (1- D ); s 3′= s 3′ / (1- D Therefore, we can obtain

[0078] (12)

[0079] Substituting equation (12) into equation (9), we can obtain the stress-strain relationship of mudstone damage based on the Weibull distribution, i.e., the constitutive relation.

[0080] (13a)

[0081] (13b)

[0082] (13c)

[0083] For conventional triaxial tests s 2= s 3, e 2= e3. The above formula simplifies to:

[0084] (14)

[0085] To better describe the damage evolution of mudstone around piles and apply it to the bearing capacity analysis of mudstone foundation piles, the modeling method can be optimized. Based on the concepts of damage theory, triaxial test data of mudstone can be fitted to directly establish the relationship between damage variables and stress-strain. The damage variables are directly determined by the stress state. D This simplifies the damage calculation process, thereby establishing a new damage constitutive model. The establishment of the optimized damage model still adopts the basic concepts and definitions of the aforementioned damage theory, and the specific process is as follows:

[0086] (1) Define the damage variable according to equation (3). D .

[0087] (2) Based on Lemaitre's principle of strain equivalence (4), the relationship between stress, strain, and damage variables is established, i.e.

[0088] (15)

[0089] (3) Establish the damage evolution equation. According to equation (13a), under conventional triaxial conditions, the following can be derived:

[0090] (16)

[0091] (4) Based on conventional triaxial test data, fit the relationship between the damage variable and the test results. D eccentric stress q Confining pressure s When performing nonlinear fitting on data, due to the uncertainty of the relationship between variables, it is necessary to conduct characteristic analysis on the experimental data and then select an equation with the corresponding trend for fitting. To find the optimal fitting function and fitting parameters, it is necessary to compare the goodness of fit of different models. Analysis of variance is performed using residuals, coefficient of determination, and weighted chi-square test coefficients. Combined with the AIC (Akaike Information Criterion) and other criteria, a quantitative assessment of the goodness of fit can be obtained. Finally, a Gaussian function (Gausscum equation) is chosen for fitting, and the equation is...

[0092] (17)

[0093] in a , b , c , d , e , f This is an experimental constant;

[0094] (5) Establish the constitutive relation equation. According to equation (13), under conventional triaxial test conditions, we can obtain:

[0095] (18-a)

[0096] (18-b)

[0097] This model is based on conventional triaxial tests and does not consider the intermediate principal stress. The intermediate principal stress has little effect on soil strength and can be ignored. s The impact of 2.

[0098] 7. Determination of Damage Model Parameters

[0099] Mudstone exhibits a downward segment (softening) in its stress-strain curve after reaching its ultimate strength under specific confining pressure, thus possessing extreme values. Let the stress and strain corresponding to the peak points be denoted as follows: s 1c and e 1c The mudstone element strength corresponding to the peak point was calculated based on the triaxial test results. F c

[0100] (19)

[0101] Calculate model parameters m and F 0

[0102] (19)

[0103] (20)

[0104] 8. Fitting confining pressure s 3 and peak point s 1c Functional relation

[0105] Through triaxial testing and damage analysis, the least squares method was used to fit the functional relationship between the two to obtain the confining pressure. s 3 and peak point s 1c The relational equation.

[0106] (twenty one)

[0107] in A , B , C This is an experimental constant.

[0108] 9. Calculate the pile end resistance

[0109] The stress condition of the mudstone at the pile tip was investigated. The stress state of the mudstone at the pile tip was similar to that of the mudstone in the triaxial test. The pile parameters (pile length, pile tip cross-sectional area) and the weight of the soil and rock were obtained. c The horizontal earth pressure of mudstone at the pile tip is equivalent to confining pressure. s Substituting 3 into equation (21), we obtain the corresponding vertical destructive force. s 1c This is equivalent to a concentrated load acting as pile end resistance.

[0110] Specifically, in this embodiment, combined with Figure 1-Figure 9 The above-mentioned method for predicting pile end resistance based on the mudstone damage constitutive model is described in detail.

[0111] 1. Obtaining mechanical parameters through triaxial compression testing

[0112] Moderately weathered mudstone from the pile tip affected by pile driving was obtained through drilling. The core tube diameter was 73 mm, and the mudstone sample diameter was 50 mm. The experimental apparatus used was a high-pressure, low-temperature hydrate static triaxial testing system, manufactured by GDS (UK), model ETAS, with a maximum confining pressure of 32 MPa and a maximum axial force of 100 kN. This system can perform standard triaxial tests, with confining pressures set at 0.5 MPa, 1.0 MPa, 1.5 MPa, and 2.0 MPa. The elastic modulus was calculated based on the mudstone triaxial test results. E , m and shear strength index c , f , E The calculation results are shown in Table 1. Poisson's ratio is taken as... m =0.3, the shear strength index is taken as the calculated average value. c =217.2 kPa f =21.6º.

[0113] Table 1. Parameters determined based on triaxial tests of mudstone. E

[0114]

[0115] 2. Assuming the basic strength of the rock F Follows Weibull distribution

[0116] Discretizing the rock medium can be viewed as different elementary components, each in one of two states: damaged or undamaged. Material defects and property differences are reflected in the order of failure of these individual elementary components. The accumulation of failed components leads to changes in material properties, macroscopically manifested as deterioration of mechanical properties. Assuming the rock's elementary component strength... F It follows a Weibull distribution, and its probability density function is:

[0117] (twenty two)

[0118] In the formula, F For rock elemental strength, m and F 0 represents the Weibull distribution parameter, which is also the model parameter mentioned below.

[0119] 3. Define damage variables D

[0120] Damage refers to the visual morphology of microcracks, microdefects, etc., within a material, possessing a certain geometric shape. Assume the initial cross-sectional area of ​​the stressed object is... A The damaged cross-sectional area is A "Then the net area of ​​the cross section is

[0121] (twenty three)

[0122] At this point, the damage variable is

[0123] (twenty four)

[0124] In the formula D When = 0, it corresponds to the lossless state, 0 < D <1 corresponds to a partial damage state; D When =1, it corresponds to a completely damaged state. Additionally, σ=F⁄A The nominal stress of the cross section, σ'=F⁄A' The effective stress of the cross section is the net stress.

[0125] 4. Based on the principle of strain equivalence, establish the relationship between stress, strain, and damage variables.

[0126] The principle of strain equivalence states that the strain caused by stress (nominal stress) acting on a damaged material is equivalent to the strain caused by effective stress (net stress) acting on an undamaged material with the same geometric dimensions.

[0127] (25)

[0128] In the formula, E、E' Let be the elastic modulus of the undamaged and damaged materials; according to this principle, the constitutive relation of the damaged material can be expressed by the nominal stress of the undamaged material.

[0129] 5. Establish the damage evolution equation

[0130] The evolution equation of the damage variable can be obtained by using the distribution density function.

[0131] (26)

[0132] Based on existing research, the general formula for the failure criterion of rocks is assumed to be:

[0133] (27)

[0134] In the formula, k 0 is a constant related to the material's cohesion and internal friction angle.

[0135] For different destruction criteria F There are different forms of expression; considering the wide range of applications, the elementary strength based on the Mohr-Coulomb rock strength theory is adopted. F The Mohr-Coulomb rock strength criterion is in the following form:

[0136] (28)

[0137] In the formula: c , These are the rock cohesion and the angle of internal friction, respectively, from which the rock element strength is determined.

[0138] (29)

[0139] In the formula: α = (1- sin ) / (1+ sin ).

[0140] 6. Establishment of the constitutive model

[0141] Based on the assumption of strain equivalence, the constitutive relation of mudstone damage can be established as follows:

[0142] (30)

[0143] In the formula: [ C [ represents the elastic matrix of mudstone material,] s ′] is the effective stress matrix, [ s ] is the nominal stress matrix, [ e ] is the strain matrix, D Let be the variable representing mudstone damage. From the above formula, we can obtain...

[0144] (31)

[0145] or

[0146] (32)

[0147] In the formula s 1′= s 1′ / (1- D ); s 2′= s 2′ / (1-D ); s 3′= s 3′ / (1- D Therefore, we can obtain

[0148] (33)

[0149] Substituting equation (33) into equation (30), we can obtain the stress-strain relationship of mudstone damage based on the Weibull distribution, i.e., the constitutive relation.

[0150] (34a)

[0151] (34b)

[0152] (34c)

[0153] For conventional triaxial tests s 2= s 3, e 2= e 3. The above formula simplifies to:

[0154] (35)

[0155] To better describe the damage evolution of mudstone around piles and apply it to the bearing capacity analysis of mudstone foundation piles, the modeling method can be optimized. Based on the concept of damage theory, the triaxial test data of mudstone can be fitted to directly establish the relationship between damage variables and stress-strain. The damage variables are directly determined by the stress state, simplifying the calculation process of damage degree, thereby establishing a new damage constitutive model.

[0156] The establishment of the optimized damage model still adopts the basic concepts and definitions of the aforementioned damage theory, and the specific process is as follows:

[0157] (1) Define the damage variable according to equation (24). D .

[0158] (2) Based on Lemaitre's principle of strain equivalence (25), the relationship between stress, strain, and damage variables is established, i.e.

[0159] (36)

[0160] (3) Establish the damage evolution equation. According to equation (34a), under conventional triaxial conditions, the following can be derived:

[0161] (37)

[0162] Based on the results of the triaxial test of mudstone, the mudstone damage variable is calculated using equation (37). Dand axial strain e 1. With axial strain e 1 represents the horizontal axis, indicating the damage variable. D Plot the mudstone damage evolution curve on the ordinate, see... Figure 2 .

[0163] (4) Fitting damage variables D eccentric stress q Confining pressure s The relationship equation of 3.

[0164] like Figure 3 As shown, the data depicted from conventional triaxial test data... Dq - s 3. Spatial scatter plot: Nonlinear fitting of data based on spatial scatter plot characteristics. When performing nonlinear fitting, due to the uncertainty of the relationships between variables, it is necessary to perform feature analysis on the experimental data and then select an equation representing the corresponding trend for fitting. To find the optimal fitting function and fitting parameters, it is necessary to compare the goodness of fit of different models. The goodness of fit is mainly judged by comparing the degree of agreement between the fitted model and the actual data, but this is not a quantitative judgment. A variance analysis is performed using residuals, coefficient of determination, and weighted chi-square test coefficients, combined with the AIC (Akaike Information Criterion) and other criteria, to obtain a quantitative assessment of the goodness of fit, as shown in Table 2. The AIC criterion, when applied to variance analysis, can be expressed as...

[0165] (38)

[0166] In the formula: n —Sample size, which in this paper refers to the number of data points; —Sum of squared residuals; p —The independent parameter dimension in the model, i.e., the degree of freedom.

[0167] Table 2. Goodness-of-fit rating

[0168]

[0169] In Table 2, RCS—the weighted chi-square test coefficient—represents the sum of squares of the differences between the corresponding data points and the fitted function. Origin uses an iterative method to minimize this value; the closer this value is to 0, the better. 2 —Corrected coefficient of determination, the closer the value is to 1, the better the fit; RSS—Residual sum of squares, the smaller the value, the better the fit; AIC—Akaike information criterion based on the maximum entropy principle, the smaller the value, the better the fit.

[0170] The comparison shows that the Gaussian function (Gausscum equation) is used to establish the damage model, resulting in the best fit. Origin software is used to fit the damage variables. D eccentric stressq Confining pressure s The equation relating 3 is as follows:

[0171] (39)

[0172] Dq - s 3. The relationship between the fitted equation and the spatial surface is shown in the figure. Figure 4 As shown, Figure 5 for Dq - s 3. Comparison of fitted data and experimental data shows that the two have a high degree of agreement.

[0173] (5) Establish the constitutive relation equation. According to equation (34), under conventional triaxial test conditions, we can obtain:

[0174] (40-a)

[0175] (40-b)

[0176] This model is based on conventional triaxial tests and does not consider the intermediate principal stress. The intermediate principal stress has little effect on soil strength and can be ignored. s The impact of 2.

[0177] 7. Determination of Damage Model Parameters

[0178] Mudstone exhibits a downward segment (softening) in its stress-strain curve after reaching its ultimate strength under specific confining pressure, thus possessing extreme values. Let the stress and strain corresponding to the peak points be denoted as follows: s 1c and e 1c The mudstone element strength corresponding to the peak point was calculated based on the triaxial test results. F c

[0179] (41)

[0180] Calculate model parameters m and F 0

[0181] (42)

[0182] (43)

[0183] The calculation results are shown in Table 3.

[0184] Table 3 Parameters of mudstone damage model

[0185]

[0186] 8. Compare and verify with triaxial test results.

[0187] The damage variable is calculated using equation (39) according to the loading level of the triaxial test. D Then, according to equation (40), the strain is calculated from the stress, and the axial strain is used as the strain. e 1 is the horizontal axis, representing the deviatoric stress ( s 1- s 3) Using the vertical axis, plot a comparison graph of the model calculation results and the triaxial test curves, see... Figure 6 .

[0188] like Figure 6 As shown, under different confining pressure levels, the curves calculated by the model in this paper agree well with the experimental curves, verifying the accuracy of the novel damage constitutive model.

[0189] 9. Fitting confining pressure s 3 and peak point s 1c Functional relation

[0190] Through triaxial testing and damage analysis, the least squares method was used to fit the functional relationship between the two to obtain the confining pressure. s 3 and peak point s 1c relational equations

[0191] (44)

[0192] Fit determination coefficient R 2 A correlation coefficient of 0.9999 indicates a good correlation. The relationship curve is shown below. Figure 7 As shown.

[0193] 10. Calculate the pile end resistance

[0194] The stress condition of mudstone at the pile tip of the triaxial test sampling pile in this paper is examined. Figure 8 As shown, the stress state of the mudstone at the pile tip is similar to that of the mudstone in the triaxial test. The field test pile is a precast pipe pile with a diameter of 500 mm and a length (depth of penetration) of 15 m. At this time, the horizontal earth pressure of the mudstone at the pile tip is approximately 280 kPa. This stress is equivalent to the confining pressure. s Substituting 3 into equation (44), we obtain the corresponding vertical destructive force. s 1c =972.1 kPa, equivalent to a concentrated load of 190.9 kN, compared with the pile end force results measured by the pile end sensor in the field test ( Figure 9 ), Figure 9The two piles that failed under static load tests had end forces of 253 kN and 221 kN, respectively, which are close to the results calculated by the model, further verifying the applicability of the model in analyzing pile end resistance.

[0195] Example 2

[0196] In another typical embodiment of the present invention, such as Figure 1-Figure 9 As shown, a pile end resistance prediction system based on a mudstone damage constitutive model is presented.

[0197] include:

[0198] The parameter acquisition module is configured to: acquire mudstone mechanical parameters based on triaxial compression tests and define damage variables;

[0199] The fitting module is configured to: establish the relationship between stress, strain and damage variables based on the principle of strain equivalence, and establish a damage evolution equation in combination with mudstone mechanical parameters, and fit the relationship equation between damage variables, deviatoric stress and confining pressure.

[0200] The modeling module is configured to: establish a constitutive model of mudstone damage, calculate the constitutive model parameters based on triaxial test results, and obtain the correspondence between confining pressure and peak stress.

[0201] The data output module is configured to: acquire the stress data of mudstone at the pile tip, calculate the confining pressure and input the corresponding relationship to obtain the pile tip resistance.

[0202] It is understood that the working method of the pile end resistance prediction system based on the mudstone damage constitutive model described above is the same as the pile end resistance prediction method based on the mudstone damage constitutive model provided in Example 1. Please refer to the detailed description in Example 1 above, which will not be repeated here.

[0203] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting pile tip resistance based on a shale damage constitutive model, characterized in that, The method comprises the steps of: Obtaining the mechanical parameters of mudstone according to triaxial compression test, and defining a damage variable; According to the strain equivalence principle, the relationship among stress, strain and damage variable is established, and the damage evolution equation is established combined with the mechanical parameters of mudstone, and the relationship equation among damage variable, deviatoric stress and confining pressure is fitted; A constitutive model of mudstone damage is established, the constitutive model parameters are calculated combined with the triaxial test results, and the corresponding relationship between confining pressure and stress peak value is obtained; Obtaining the stress data of mudstone at the pile end, equivalent to the confining pressure and brought into the corresponding relationship, the pile end resistance is obtained; Defining a damage variable D, the specific process is as follows: Assuming that the initial cross-sectional area of the stressed object is A, and the damaged cross-sectional area after damage is A'', then the net cross-sectional area is: At this time, the damage variable is: When D=0, it corresponds to the undamaged state, 0 The specific process of establishing the constitutive model is as follows: Based on the strain equivalence assumption, the following constitutive relationship of mudstone damage is established: In the formula: [C] is the elastic matrix of mudstone material, [σ'] is the effective stress matrix, [σ] is the nominal stress matrix, [ε] is the strain matrix, and D is the damage variable of mudstone.

2. The method for predicting pile tip resistance based on a shale damage constitutive model according to claim 1, wherein, The elastic modulus and shear strength index are calculated, and the mechanical parameters of mudstone are obtained.

3. The method of claim 1, wherein the method is characterized by: The material is discretized into multiple element bodies, the damage variable is the ratio of the damaged cross-sectional area of the material after damage to the initial cross-sectional area of the mudstone, and it is assumed that the strength of the element body obeys the Weibull distribution.

4. The method of claim 3, wherein the pile tip resistance is predicted based on a shale damage constitutive model. According to the triaxial test data, the damage variable is calculated, and the relationship equation among damage variable, deviatoric stress and confining pressure is fitted.

5. The method of claim 1, wherein the method further comprises: The determination of the constitutive model parameters comprises the following steps: After the stress-strain curve of mudstone under confining pressure reaches the ultimate strength, the stress, strain and confining pressure corresponding to the peak point are recorded; According to the triaxial test results, the mudstone element strength corresponding to the peak point is calculated, and the constitutive model parameters are calculated.

6. The method of claim 5, wherein the method is characterized by, The obtained constitutive model parameters are substituted into the constitutive model, the damage variable and strain are calculated according to the loading level of the triaxial test, and the triaxial test results are compared for verification.

7. The method of claim 5, wherein the method further comprises: Through triaxial test and damage analysis calculation, the functional relationship between confining pressure and peak point is fitted, and the corresponding relationship between confining pressure and stress peak value is obtained.

8. The method of claim 1, wherein the method is characterized by: Obtaining the parameters of the pile body and the specific gravity of the rock-soil body, equivalent the horizontal earth pressure of mudstone at the pile end to the confining pressure, substituting into the corresponding relationship, obtaining the corresponding vertical destructive force, and equivalent to the concentrated load as the pile end resistance.

9. A system for predicting pile tip resistance based on a clayey soil damage constitutive model, adopting the method for predicting pile tip resistance based on a clayey soil damage constitutive model according to any one of claims 1 to 8, characterized in that, The method comprises the steps of: The parameter acquisition module is configured to obtain the mechanical parameters of mudstone according to triaxial compression test, and define a damage variable; The fitting module is configured to establish the relationship among stress, strain and damage variable according to the strain equivalence principle, and establish the damage evolution equation combined with the mechanical parameters of mudstone, and fit the relationship equation among damage variable, deviatoric stress and confining pressure; The modeling module is configured to establish a constitutive model of mudstone damage, calculate the constitutive model parameters combined with the triaxial test results, and obtain the corresponding relationship between confining pressure and stress peak value; The data output module is configured to obtain the stress data of mudstone at the pile end, equivalent to the confining pressure and brought into the corresponding relationship, and obtain the pile end resistance.

Images