Geotechnical material creep practical constitutive model construction method based on space curved surface polynomial fitting

Abstract

The invention relates to a geotechnical material creep practical constitutive model construction method based on spatial curved surface polynomial fitting, and the method comprises the steps: carrying out the polynomial fitting of a change relation between final creep volume strain and final creep shear strain along with a stress state, and obtaining an expression equation of the final creep volume strain and the final creep shear strain about the stress state; the relationship between the final creep strain and the stress state of the geotechnical material can be more accurately captured by improving the order of the expression equations of the two; meanwhile, an index model is adopted to reflect the change of the creep strain along with time, the change rate of the creep strain along with time is controlled by adjusting index parameter values, high flexibility and adaptability are achieved, then the model prediction precision is improved, the engineering applicability is widened, and the method belongs to the technical field of geotechnical engineering constitutive model research.

Description

Technical Field

[0001] This invention belongs to the technical field of geotechnical engineering constitutive model research, specifically involving a practical constitutive model construction method for geotechnical materials creep based on spatial surface polynomial fitting, applicable to soft soil, soft rock and other geotechnical bodies with significant creep characteristics. Background Technology

[0002] In geotechnical engineering, the constitutive relationship of soil and rock materials is the core theory describing the complex stress-strain mechanical behavior of soil and rock. Among these, the stress-strain relationship of soil and rock materials is time-dependent in some cases; this property is collectively referred to as the creep characteristic of soil and rock materials. This characteristic is one of the main factors affecting deformation and failure in geotechnical engineering. Studying the creep law of soil and rock materials and constructing creep constitutive models of soil and rock materials are currently important theoretical foundations for predicting deformation and failure in geotechnical engineering.

[0003] Currently, commonly used constitutive models for creep in geotechnical materials include element creep models, empirical creep models, semi-empirical and semi-theoretical creep models, and yield surface creep models. Compared with other creep models, empirical creep models, although having problems such as unclear physical meaning of parameters and insufficient theoretical basis, also have advantages such as fewer parameters and ease of obtaining them. They can well describe the long-term creep characteristics of geotechnical materials and have certain guiding significance for engineering applications.

[0004] Well-known empirical creep models include the three-parameter rheological model proposed by Shen Zhujiang and the seven-parameter rheological model proposed by Li Guoying. Both have simple structures, clear parameter meanings, and simple determination methods. However, the limitations of the above-mentioned construction methods gradually become apparent when facing complex and ever-changing practical engineering problems. In particular, when dealing with the nonlinear creep characteristics of complex materials such as soft soil and soft rock, they lack sufficient flexibility and adaptability, and are difficult to accurately describe and predict the creep behavior of materials under different stress states. Summary of the Invention

[0005] To address the technical problems existing in the prior art, the purpose of this invention is to provide a practical constitutive model construction method for creep of soil and rock materials based on polynomial fitting of spatial surfaces.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A practical constitutive model construction method for creep of soil and rock materials based on polynomial fitting of spatial surfaces includes the following steps:

[0008] S1. Conduct indoor triaxial tests on soil and rock samples to obtain the cohesion of the samples. With internal friction angle ;

[0009] S2. Based on the confining pressures set in the triaxial compression creep test... , the cohesion obtained in step S1 and the internal friction angle , obtain the confining pressure of each level corresponding to the limit generalized shear stress , and divide the generalized shear stress into several levels , further determine the confining pressure of each level corresponding to the hierarchical axial load ;

[0010] S3, according to the confining pressure of each level obtained in step S2 and the corresponding hierarchical axial load , conduct a triaxial compression creep test on the rock-soil sample, and record the axial creep strain and the volumetric creep strain of the sample under different confining pressures and corresponding hierarchical axial loads over time , and draw a “time -volumetric creep strain ” curve graph;

[0011] S4, according to the axial creep strain and the volumetric creep strain over time obtained in step S3, pre-process the data to obtain the shear creep strain over time under the corresponding stress state, and further draw a “time -shear creep strain ” curve graph;

[0012] S5, according to the confining pressure of each level obtained in step S2 and the corresponding hierarchical axial load , pre-process the data to obtain a plurality of groups of average normal stress and generalized shear stress ;

[0013] S6, according to the volumetric creep strain over time obtained in step S3 and the shear creep strain over time obtained in step S4, take the creep strain corresponding to the last data point of each test curve as the final creep strain, and combine the plurality of groups of average normal stress and generalized shear stress obtained in step S5 to obtain a plurality of groups of final creep volumetric strains corresponding to different stress state combinations With final creep shear strain ;

[0014] S7. According to the final creep volumetric strain described in step S6 With final creep shear strain The relationship between stress state and strain is fitted using a polynomial to obtain the final creep volumetric strain. With final creep shear strain The equation expressing the stress state is constructed as follows: "mean normal stress" -Generalized shear stress -Final creep volumetric strain "and mean normal stress" -Generalized shear stress -Final creep shear strain "Three-dimensional spatial surface diagram;"

[0015] S8. The final creep volumetric strain corresponding to each stress state described in step S6. With final creep shear strain Based on the volumetric creep strain described in steps S3 and S4 With shear creep strain Over time The change process data were analyzed using an exponential model to assess the volumetric creep strain. With shear creep strain Regarding time By fitting parameters to the expression equation, the control volume creep strain is obtained. With shear creep strain Exponential parameters of their respective rates of change and ;

[0016] S9, based on an arbitrary given stress tensor The mean normal stress was calculated. With generalized shear stress Substitute the final creep volumetric strain described in step S7 With final creep shear strain The final creep strain is obtained by applying the respective expression equations, and the volumetric creep strain is determined according to step S8. With shear creep strain The expression equation, and its time... Differentiation yields the volumetric creep strain rate. With shear creep strain rate By using their respective expression equations, their respective creep strain rates are calculated, and thus the creep strain rate tensor is obtained. Then, the given stress tensor is obtained by time integration. Lower creep strain tensor Over time The data predicts the changes in the process.

[0017] As a preferred option, in step S2, the ultimate generalized shear stress is determined according to the Mohr-Coulomb strength criterion. The calculation is as follows:

[0018] ,

[0019] In the formula: For the ultimate generalized shear stress; It is cohesive force; It is the internal friction angle; For confining pressure;

[0020] Set confining pressure Intermediate axial load The calculation is as follows:

[0021] ,

[0022] In the formula: For axial loads; It is the generalized shear stress.

[0023] As a preferred embodiment, in step S4, the shear creep strain The calculation is as follows:

[0024] ,

[0025] In the formula: For shear creep strain; For axial creep strain; This represents volumetric creep strain.

[0026] As a preferred embodiment, in step S5, the average normal stress With generalized shear stress The calculation is as follows:

[0027] ,

[0028] ,

[0029] In the formula: It is the average normal stress; It is the generalized shear stress.

[0030] As a preferred embodiment, in step S7, the final creep volumetric strain is determined based on a two-dimensional polynomial fitting equation. With final creep shear strain The equation expressing this is as follows:

[0031] ,

[0032] ,

[0033] In the formula: and These are the final creep volumetric strain and the final creep shear strain, respectively. and These are the orders of the two-dimensional polynomial fitting equations for the final creep volumetric strain and the final creep shear strain, respectively. and These are the coefficients of the two-dimensional polynomial fitting equations for the final creep volumetric strain and the final creep shear strain, respectively. In the two-dimensional polynomial fitting equation The index; In the two-dimensional polynomial fitting equation The index.

[0034] As a preferred option, in step S8, an exponential model is used to measure volumetric creep strain. With shear creep strain The equation expressing this is as follows:

[0035] ,

[0036] ,

[0037] In the formula: and The time is respectively Volumetric creep strain and shear creep strain at time; and These are exponential parameters that control the rate of change of volumetric creep strain and shear creep strain, respectively. For time.

[0038] As a preferred embodiment, in step S9, the average normal stress With generalized shear stress The calculation is as follows:

[0039] ,

[0040] ,

[0041] In the formula: It is the first invariant of the stress tensor; It is the second invariant of the stress deviatoric tensor.

[0042] As a preferred embodiment, in step S9, the volumetric creep strain rate With shear creep strain rate The equation expressing this is as follows:

[0043] ,

[0044] ,

[0045] In the formula: and The time is respectively The volumetric creep strain rate and shear creep strain rate at that time.

[0046] As a preferred embodiment, in step S9, based on the Prandtl-Reuss assumption, the creep strain rate tensor The calculation is as follows:

[0047] ,

[0048] Among them, stress deviator tensor The calculation is as follows:

[0049] ,

[0050] In the formula: For time The creep strain rate tensor at time; For stress tensor; For the Kronecker tensor.

[0051] As a preferred embodiment, in step S9, the creep strain tensor From creep strain rate tensor The time integral is calculated using the following formula:

[0052] ,

[0053] In the formula: For time The creep strain tensor at time.

[0054] The principle of this invention is:

[0055] Based on the actual engineering conditions, different confining pressures were applied to the geotechnical materials. Axial load A triaxial compression creep test with graded loading was conducted, and the test data were recorded and preprocessed to construct a "time-weighted" model. -Volume creep strain "and time" -Shear creep strain "Curve graph; based on the final creep volumetric strain" With final creep shear strain By studying the relationship between stress state and stress state, polynomial fitting is performed to obtain the equations expressing both stress state, thus constructing the "mean normal stress". -Generalized shear stress -Final creep volumetric strain "and mean normal stress" -Generalized shear stress -Final creep shear strain "Three-dimensional spatial surface diagram; based on volumetric creep strain" With shear creep strain Over time The change process data were used to fit the expression equations of the two variables using an exponential model, thereby obtaining the exponential parameters that control the rate of change of both variables. and For any given stress state, substitute the final creep volumetric strain. With final creep shear strain The final creep strain is obtained by applying the respective expression equations to the volumetric creep strain. With shear creep strain Differentiating the expression equations yields the respective creep strain rates, which in turn yields the creep strain rate tensor. Then, the creep strain over time is obtained by integrating over time. The data predicts the changes in the process.

[0056] The present invention has the following advantages:

[0057] 1. This method involves measuring the final creep volumetric strain. With final creep shear strain By performing polynomial fitting on the relationship between stress state and stress state, we can obtain the expression equations of stress state for both. By increasing the order of the expression equations, we can more accurately capture the relationship between the final creep strain and stress state of soil and rock materials.

[0058] 2. This method uses an exponential model to reflect the relationship between creep strain and time. By adjusting the value of the exponential parameter, the relationship between creep strain and time can be controlled, thus allowing for a more flexible fitting of the relationship between creep strain and time in soil and rock materials.

[0059] 3. This framework organically combines polynomial fitting methods with exponential models, giving constitutive models high flexibility and adaptability, thereby improving model prediction accuracy and broadening engineering applicability, and providing more reliable theoretical support for long-term stability analysis and engineering design in geotechnical engineering. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating the method of the present invention.

[0061] Figure 2 For comparison, soft soil under confining pressure 100 kPa, generalized shear stress The time values ​​obtained from consolidated drained triaxial creep tests at 28 kPa, 56 kPa, 84 kPa, and 112 kPa are respectively. -Displacement "Graph".

[0062] Figure 3 For comparison, soft soil under confining pressure 100 kPa, generalized shear stress The time values ​​obtained from consolidated drained triaxial creep tests at 28 kPa, 56 kPa, 84 kPa, and 112 kPa are respectively. -Axial creep strain "Graph".

[0063] Figure 4 For comparison, soft soil under confining pressure 100 kPa, generalized shear stress The "time" is obtained by processing the consolidated drained triaxial creep test data at 28 kPa, 56 kPa, 84 kPa, and 112 kPa. -Volume creep strain "Graph".

[0064] Figure 5 For comparison, soft soil under confining pressure 100 kPa, generalized shear stress The "time" is obtained by processing the consolidated drained triaxial creep test data at 28 kPa, 56 kPa, 84 kPa, and 112 kPa. -Shear creep strain "Graph".

[0065] Figure 6 For comparison, soft soil under confining pressure 100 kPa, generalized shear stress The mean normal stress was obtained by processing the consolidated drained triaxial creep test data at 28 kPa, 56 kPa, 84 kPa, and 112 kPa. -Generalized shear stress -Final creep volumetric strain "Two-dimensional polynomial fitting equation and three-dimensional spatial surface plot."

[0066] Figure 7 For comparison, soft soil under confining pressure 100 kPa, generalized shear stress The mean normal stress was obtained by processing the consolidated drained triaxial creep test data at 28 kPa, 56 kPa, 84 kPa, and 112 kPa. -Generalized shear stress -Final creep shear strain "Two-dimensional polynomial fitting equation and three-dimensional spatial surface plot."

[0067] Figure 8 To predict the confining pressure of soft soil in the example. 100 kPa, generalized shear stress The "time" at 28 kPa, 56 kPa, 84 kPa, and 112 kPa respectively -Volume creep strain "Graph".

[0068] Figure 9 To predict the confining pressure of soft soil in the example. 100 kPa, generalized shear stress The "time" at 28 kPa, 56 kPa, 84 kPa, and 112 kPa respectively -Shear creep strain "Graph". Detailed Implementation

[0069] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] The practical constitutive model constructed in this invention is applicable to soil and rock masses with significant creep characteristics, such as soft soil and soft rock. This embodiment uses a specific soft soil as the research object. In this embodiment, the soil and rock sample refers to a sample prepared from this soft soil.

[0071] The test equipment used was the LFTD1803-3 fully automatic triaxial apparatus, which can accurately control confining pressure and axial load, and collect data such as axial creep strain and water displacement in real time.

[0072] A practical constitutive model construction method for creep of soil and rock materials based on polynomial fitting of spatial surface is provided, which includes steps S1-S9.

[0073] (a) Step S1: Conduct an indoor triaxial test on the soil and rock sample to obtain the cohesion of the sample. With internal friction angle .

[0074] (ii) Step S2: According to the confining pressures set in the triaxial compression creep test, the confining pressures at each level are... Combined with the cohesion obtained in step S1 With internal friction angle To obtain confining pressure at various levels Corresponding ultimate generalized shear stress It is divided into several levels of generalized shear stress. Further determine each confining pressure Corresponding graded axial loads .

[0075] Furthermore, according to the Mohr-Coulomb strength criterion, the ultimate generalized shear stress The calculation is as follows:

[0076] ,

[0077] In the formula: For the ultimate generalized shear stress; It is cohesive force; It is the internal friction angle; For confining pressure.

[0078] Furthermore, the set confining pressure Intermediate axial load The calculation is as follows:

[0079] ,

[0080] In the formula: For axial loads; It is the generalized shear stress.

[0081] In this embodiment, the triaxial compression creep test is a consolidated drained triaxial creep test, and step S2 specifically includes:

[0082] (1) For the above-mentioned soft soil, the test confining pressure was used. For example, 100 kPa.

[0083] (2) Determine the ultimate generalized shear stress of the soft soil under a confining pressure of 100 kPa. The generalized shear stress is 112 kPa, and it is divided into 4 levels. The corresponding values ​​are 28 kPa, 56 kPa, 84 kPa, and 112 kPa.

[0084] (3) For each generalized shear stress According to the formula Calculate axial load 4 levels of axial load were obtained. The corresponding values ​​are 128 kPa, 156 kPa, 184 kPa, and 212 kPa.

[0085] (III) Step S3: Based on the confining pressures at each level in step S2 With the corresponding graded axial load A combination of methods was used to conduct triaxial compression creep tests on soil and rock samples, recording the data in real time under different confining pressures. With the corresponding graded axial load Axial creep strain Volumetric creep strain Over time The data on the process of change, and the depiction of "time" -Volume creep strain "A curve graph. Specifically:"

[0086] In this embodiment, the triaxial compression creep test is a consolidated drained triaxial creep test. It should be noted that this embodiment only demonstrates the test process under a specific confining pressure (100 kPa), but the invention is not limited thereto. The test process is as follows:

[0087] (1) Prepare a cylindrical sample with a diameter of 39.1 mm and a height of 78.2 mm.

[0088] (2) The sample is placed in the pressure chamber of the triaxial apparatus and subjected to reverse pressure saturation and consolidation in sequence (the consolidation pressure is 100 kPa, and the consolidation stability standard is ≤0.01% change in volumetric strain per hour).

[0089] (3) After consolidation is completed, the axial load is calculated. Discharge compression is performed when axial creep strain occurs. When the reading is stable or nearly stable, apply the next level of axial load. Loading and real-time recording of each stage of axial load. Axial creep strain Discharge Four sets of "time" were obtained. -Displacement ","time -Axial creep strain "Data, plotting curves, such as..." Figure 2 and Figure 3 As shown.

[0090] According to "time" -Displacement "Data, calculated volumetric creep strain" Four sets of "time" were obtained. -Volume creep strain "Data, plotting curves, such as..." Figure 4 As shown, the calculation formula is as follows:

[0091] ,

[0092] In the formula: For drainage volume; This represents the initial volume of the soil and rock sample.

[0093] (iv) Step S4: Based on the axial creep strain obtained in step S3 With volumetric creep strain Over time The change process data is obtained by preprocessing the data to obtain the shear creep strain under the corresponding stress state. Over time The data on the process of change further depicts the "time" -Shear creep strain "A curve graph. Specifically:"

[0094] (1) According to Figure 3 Each "time" in -Axial creep strain "Curve and Figure 4 Each "time" in -Volume creep strain "Curve, by time" Data points were collected at equal intervals, with a total of 100 data points for each curve, ensuring that the number of data points was consistent across curves and that the timing of each data point was consistent. They are synchronized with each other.

[0095] (2) According to "time" -Axial creep strain "Curve and Time" -Volume creep strain "The data points of each curve are calculated according to the formula." Calculate shear creep strain Four sets of "time" were obtained. -Shear creep strain "Data, plotting curves, such as..." Figure 5 As shown.

[0096] (v) Step S5: Based on the confining pressures obtained in step S2, With the corresponding graded axial load The data is preprocessed to obtain multiple sets of average normal stresses. Generalized shear stress The combination is as follows:

[0097] (1) Based on confining pressure With axial loads of all levels According to the formula Calculate the mean normal stress .

[0098] (2) Based on confining pressure With axial loads of all levels According to the formula Calculation of generalized shear stress .

[0099] The specific calculations yielded the average normal stress for each group. With generalized shear stress The combinations are as follows:

[0100]

[0101] (vi) Step S6: Based on the volumetric creep strain obtained in step S3 Over time The change process data and the shear creep strain obtained in step S4 Over time The creep strain corresponding to the last data point of each test curve is taken as the final creep strain, and combined with the multiple sets of average normal stresses obtained in step S5, the creep strain is analyzed. Generalized shear stress The combination yields multiple sets of different stress state combinations (mean normal stress). Generalized shear stress The final creep volumetric strain corresponding to ) With final creep shear strain .

[0102]

[0103] (vii) Step S7: According to the final creep volumetric strain described in step S6 With final creep shear strain The relationship between stress state and strain is fitted using a polynomial to obtain the final creep volumetric strain. With final creep shear strain The equation expressing the stress state is constructed as follows: "mean normal stress" -Generalized shear stress -Final creep volumetric strain "and mean normal stress" -Generalized shear stress -Final creep shear strain "Three-dimensional spatial surface diagram. Specifically:"

[0104] (1) Based on the two-dimensional polynomial fitting equation, the final creep volumetric strain The equation expressing this is as follows:

[0105] ,

[0106] In the formula: For the final creep volumetric strain; The order of the two-dimensional polynomial fitting equation for the final creep volumetric strain is given by . The coefficients of each term in the two-dimensional polynomial fitting equation for the final creep volumetric strain are given. In the two-dimensional polynomial fitting equation The index; In the two-dimensional polynomial fitting equation The index.

[0107] Select the order of the two-dimensional polynomial fitting equation for the final creep volumetric strain. The value is 2, and the specific calculation yields the "mean normal stress". -Generalized shear stress -Final creep volumetric strain "Two-dimensional polynomial fitting equation, three-dimensional spatial surface plot as follows" Figure 6 As shown, and the final creep volumetric strain The equation expressing the stress state is as follows:

[0108] ,

[0109] (2) Based on the two-dimensional polynomial fitting equation, the final creep shear strain The equation expressing this is as follows:

[0110] ,

[0111] In the formula: This represents the final creep shear strain; The order of the two-dimensional polynomial fitting equation for the final creep shear strain is given. The coefficients of each term in the two-dimensional polynomial fitting equation for the final creep shear strain are given. In the two-dimensional polynomial fitting equation The index; In the two-dimensional polynomial fitting equation The index.

[0112] Select the order of the two-dimensional polynomial fitting equation for the final creep shear strain. The value is 2, and the specific calculation yields the "mean normal stress". -Generalized shear stress -Final creep shear strain "Two-dimensional polynomial fitting equation, three-dimensional spatial surface plot as follows" Figure 7 As shown, and the final creep shear strain The equation expressing the stress state is as follows:

[0113] ,

[0114] (viii) Step S8: The final creep volumetric strain corresponding to each stress state described in step S6. With final creep shear strain Based on the volumetric creep strain described in steps S3 and S4 With shear creep strain Over time The change process data were analyzed using an exponential model to assess the volumetric creep strain. With shear creep strain Regarding time By fitting parameters to the expression equation, the control volume creep strain is obtained. With shear creep strain Exponential parameters of their respective rates of change and Specifically:

[0115] (1) Using an exponential model, the volumetric creep strain The equation expressing this is as follows:

[0116] ,

[0117] Specific parameters were obtained through fitting. .

[0118] (2) Using an exponential model, the shear creep strain The equation expressing this is as follows:

[0119] ,

[0120] Specific parameters were obtained through fitting. .

[0121] (ix) Step S9: Based on any given stress tensor The mean normal stress was calculated. With generalized shear stress Substitute the final creep volumetric strain described in step S7 With final creep shear strain The final creep strain is obtained by applying the respective expression equations, and the volumetric creep strain is determined according to step S8. With shear creep strain The expression equation, and its time... Differentiation yields the volumetric creep strain rate. With shear creep strain rate By using their respective expression equations, their respective creep strain rates are calculated, and thus the creep strain rate tensor is obtained. Then, the given stress tensor is obtained by time integration. Lower creep strain tensor Over time The data predicts the process of change. Specifically:

[0122] In this embodiment, stress tensor For example, the process of constructing an incremental time-strain relationship is illustrated below:

[0123] (1) Calculate the average normal stress under this stress state. With generalized shear stress :

[0124] ,

[0125] ,

[0126] Calculations show that the average normal stress is... Generalized shear stress .

[0127] (2) According to the final creep volumetric strain described in step S7 With final creep shear strain Each equation is used to calculate the final creep volumetric strain under this stress state. With final creep shear strain :

[0128]

[0129]

[0130] ,

[0131]

[0132]

[0133] ,

[0134] Calculations show that the average normal stress is... Generalized shear stress final creep volumetric strain Final creep shear strain .

[0135] (3) By time For example, according to the volumetric creep strain described in step S8 With shear creep strain The expression equation, and its time... Differentiation yields the volumetric creep strain rate. With shear creep strain rate Each equation is used to express the characteristics of the creep strain rate under that condition. With shear creep strain rate :

[0136] ,

[0137] ,

[0138] Calculations show that the time under this stress state is... Volumetric creep strain rate Shear creep strain rate .

[0139] (4) Based on the obtained volumetric creep strain rate With shear creep strain rate Based on the Prandtl-Reuss assumption, the creep strain rate tensor in this state is calculated. The formula is as follows:

[0140] ,

[0141] ,

[0142] Calculations show that the time under this stress state is... creep strain rate tensor as follows:

[0143] ,

[0144] (5) Based on the following formula, combined with the creep strain rate tensor obtained above, The creep strain tensor is calculated by time integration. Over time Predictive data on the process of change:

[0145] ,

[0146] Using the method described above, the incremental relationship under any stress state can be calculated.

[0147] Through creep strain tensor Over time Predicting data on changes in time processes to obtain "time" -Volume creep strain "and time" -Shear creep strain Prediction curve:

[0148] (1) Based on the creep strain tensor Over time The change process prediction data were used to calculate the volumetric creep strain. To obtain "time" -Volume creep strain "Predict the curve and plot the curve as follows..." Figure 8 As shown, the calculation formula is as follows:

[0149] ,

[0150] In the formula: It is the first invariant of the strain tensor.

[0151] (2) Based on the creep strain tensor Over time The change process prediction data is used to calculate the shear creep strain. To obtain "time" -Shear creep strain "Predict the curve and plot the curve as follows..." Figure 9 As shown, the calculation formula is as follows:

[0152] ,

[0153] In the formula: It is the second invariant of the strain partial tensor.

[0154] (x) The experimental results of this invention are as follows:

[0155] Figure 8 , Figure 9 By comparing the predicted curves of the method of this invention with the experimental data, it can be seen that:

[0156] The predicted curves and experimental data show a high degree of agreement, accurately capturing the relationship between the final creep strain and stress state of soil and rock materials. The predicted curves and experimental data are basically consistent in terms of the change in the creep strain growth rate.

[0157] This method can increase the order in the polynomial fitting equations of final creep volumetric strain and final creep shear strain to accurately capture the relationship between the final creep strain and stress state of soil and rock materials. Furthermore, by adjusting the exponential parameter values ​​of the creep strain exponential model, the rate of change of creep strain over time can be controlled, making the constitutive model highly flexible and adaptable, with clearly defined parameter meanings.

[0158] In summary, this embodiment verifies the effectiveness of the practical constitutive model construction method for creep of geotechnical materials based on spatial surface polynomial fitting. It can accurately describe the creep behavior of geotechnical materials and improve the accuracy of numerical simulation in geotechnical engineering.

[0159] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for constructing a practical constitutive model of creep in soil and rock materials based on polynomial fitting of spatial surfaces, characterized in that, Includes the following steps, S1. Conduct indoor triaxial tests on soil and rock samples to obtain the cohesion of the samples. With internal friction angle ; S2. Based on the confining pressures set in the triaxial compression creep test... Combined with the cohesion obtained in step S1 With internal friction angle To obtain confining pressure at various levels Corresponding ultimate generalized shear stress It is divided into several levels of generalized shear stress. Further determine each confining pressure Corresponding graded axial loads ; S3. Based on the confining pressures at each level in step S2... With the corresponding graded axial load A combination of methods was used to conduct triaxial compression creep tests on soil and rock samples, recording the data in real time under different confining pressures. With the corresponding graded axial load Axial creep strain Volumetric creep strain Over time The data on the process of change, and the depiction of "time" -Volume creep strain "Curve graph;" S4. Axial creep strain obtained from step S3 With volumetric creep strain Over time The change process data is obtained by preprocessing the data to obtain the shear creep strain under the corresponding stress state. Over time The data on the process of change further depicts the "time" -Shear creep strain "Curve graph;" S5. Based on the confining pressures obtained in step S2, With the corresponding graded axial load The data is preprocessed to obtain multiple sets of average normal stresses. Generalized shear stress The combination; S6. Based on the volumetric creep strain obtained in step S3 Over time The change process data and the shear creep strain obtained in step S4 Over time The creep strain corresponding to the last data point of each test curve is taken as the final creep strain, and combined with the multiple sets of average normal stresses obtained in step S5, the creep strain is analyzed. Generalized shear stress By combining these factors, we can obtain the final creep volumetric strain corresponding to multiple combinations of different stress states. With final creep shear strain ; S7. According to the final creep volumetric strain described in step S6 With final creep shear strain The relationship between stress state and strain is fitted using a polynomial to obtain the final creep volumetric strain. With final creep shear strain The equation expressing the stress state is constructed to establish the "mean normal stress". -Generalized shear stress -Final creep volumetric strain "and mean normal stress" -Generalized shear stress -Final creep shear strain "Three-dimensional spatial surface diagram;" S8. The final creep volumetric strain corresponding to each stress state described in step S6. With final creep shear strain Based on the volumetric creep strain described in steps S3 and S4 With shear creep strain Over time The change process data were analyzed using an exponential model to assess the volumetric creep strain. With shear creep strain Regarding time By fitting parameters to the expression equation, the control volume creep strain is obtained. With shear creep strain Exponential parameters of their respective rates of change and ; S9, based on an arbitrary given stress tensor The mean normal stress was calculated. With generalized shear stress Substitute the final creep volumetric strain described in step S7 With final creep shear strain The final creep strain is obtained by applying the respective expression equations, and the volumetric creep strain is determined according to step S8. With shear creep strain The expression equation, and its time... Differentiation yields the volumetric creep strain rate. With shear creep strain rate By using their respective expression equations, their respective creep strain rates are calculated, and thus the creep strain rate tensor is obtained. Then, the given stress tensor is obtained by time integration. Lower creep strain tensor Over time The data predicts the changes in the process.

2. The method for constructing a practical constitutive model of creep in soil and rock materials based on polynomial fitting of spatial surfaces according to claim 1, characterized in that, In step S2, according to the Mohr-Coulomb strength criterion, the ultimate generalized shear stress is... The calculation is as follows: ， In the formula: For the ultimate generalized shear stress; It is cohesive force; It is the internal friction angle; For confining pressure; Set confining pressure Intermediate axial load The calculation is as follows: ， In the formula: For axial loads; It is the generalized shear stress.

3. The method for constructing a practical constitutive model of creep in soil and rock materials based on polynomial fitting of spatial surfaces according to claim 2, characterized in that, In step S4, shear creep strain The calculation is as follows: ， In the formula: For shear creep strain; For axial creep strain; This represents volumetric creep strain.

4. The method for constructing a practical constitutive model of creep in soil and rock materials based on polynomial fitting of spatial surfaces according to claim 3, characterized in that, In step S5, the average normal stress With generalized shear stress The calculation is as follows: ， ， In the formula: It is the average normal stress; It is the generalized shear stress.

5. A method for constructing a practical constitutive model of creep in soil and rock materials based on polynomial fitting of spatial surfaces, as described in claim 4, is characterized in that... In step S7, based on the two-dimensional polynomial fitting equation, the final creep volumetric strain is calculated. With final creep shear strain The equation expressing this is as follows: ， ， In the formula: and These are the final creep volumetric strain and the final creep shear strain, respectively. and These are the orders of the two-dimensional polynomial fitting equations for the final creep volumetric strain and the final creep shear strain, respectively. and These are the coefficients of the two-dimensional polynomial fitting equations for the final creep volumetric strain and the final creep shear strain, respectively. In the two-dimensional polynomial fitting equation The index; In the two-dimensional polynomial fitting equation The index.

6. A method for constructing a practical constitutive model of creep in soil and rock materials based on polynomial fitting of spatial surfaces, as described in claim 5, is characterized in that... In step S8, an exponential model is used to measure volumetric creep strain. With shear creep strain The equation expressing this is as follows: ， ， In the formula: and The time is respectively Volumetric creep strain and shear creep strain at time; and These are exponential parameters that control the rate of change of volumetric creep strain and shear creep strain, respectively. For time.

7. A method for constructing a practical constitutive model of creep in soil and rock materials based on polynomial fitting of spatial surfaces, as described in claim 6, is characterized in that... In step S9, the average normal stress With generalized shear stress The calculation is as follows: ， ， In the formula: It is the first invariant of the stress tensor; It is the second invariant of the stress deviatoric tensor.

8. A method for constructing a practical constitutive model of creep in soil and rock materials based on polynomial fitting of spatial surfaces, as described in claim 7, characterized in that: In step S9, the volumetric creep strain rate With shear creep strain rate The equation expressing this is as follows: ， ， In the formula: and The time is respectively The volumetric creep strain rate and shear creep strain rate at that time.

9. A method for constructing a practical constitutive model of creep in soil and rock materials based on polynomial fitting of spatial surfaces, as described in claim 8, characterized in that: In step S9, based on the Prandtl-Reuss assumption, the creep strain rate tensor The calculation is as follows: ， Among them, stress deviator tensor The calculation is as follows: ， In the formula: For time The creep strain rate tensor at time; For stress tensor; For the Kronecker tensor.

10. A method for constructing a practical constitutive model of creep in soil and rock materials based on polynomial fitting of spatial surfaces, as described in claim 9, characterized in that... In step S9, the creep strain tensor From creep strain rate tensor The time integral is calculated using the following formula: ， In the formula: For time The creep strain tensor at time.

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