A method for calculating the time-dependent deformation of slopes

Abstract

This invention discloses a method for calculating the time-dependent deformation of rock slopes under freeze-thaw cycles. This method considers the damaging effects of freeze-thaw cycles on slope rocks, the thermal expansion and contraction effects of rocks, and the influence of temperature changes on the creep properties of slope rocks. It is used to determine the time-dependent deformation characteristics of slopes under freeze-thaw cycles and ensure the long-term stability of slope engineering in cold regions of my country.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering technology, specifically relating to a method for calculating the time-dependent deformation of a freeze-thaw cycle slope. Background Technology

[0002] Geotechnical engineering projects, such as rock slopes in cold regions, are subjected to multiple impacts from the natural environment, including freeze-thaw cycles, water erosion, and human mining activities. The combined effect of these factors can easily trigger various geological disasters and engineering accidents. For example, on March 29, 2013, a landslide occurred at Zeri Mountain in the Jiama mining area of ​​Tibet, causing the collapse of over 2 million cubic meters of slope and resulting in the deaths of 83 workers. The accident investigation revealed that long-term freeze-thaw cycles were the main cause of the degradation of the rock mass's mechanical properties, and the frequent snowfall and melting that month further exacerbated the decrease in rock mass stability, ultimately triggering instability during mining activities. In fact, geotechnical engineering structures in cold regions not only experience mechanical property deterioration due to freeze-thaw cycles but also suffer from creep deformation caused by long-term loads. Therefore, in-depth research on the time-varying mechanical properties of rocks under freeze-thaw conditions is of extremely important scientific significance and practical application value for the stability assessment and safe operation of geotechnical engineering projects in cold regions.

[0003] Existing constitutive models cannot simultaneously account for the damage effects of freeze-thaw cycles on rocks, the thermal expansion and contraction effects of rocks, and the influence of temperature on the creep rate deformation of rocks. However, the time-dependent deformation of slope rocks is a superposition of these three effects. Calculating the time-dependent deformation of slopes under freeze-thaw cycles using existing methods yields insufficient accuracy, thus casting doubt on the reliability of slope stability analysis results. In long-term use, slopes designed using existing methods may pose potential safety hazards.

[0004] The accuracy of existing methods for calculating the time-dependent deformation of slopes under the influence of freeze-thaw cycles is questionable. Therefore, there is an urgent need for a constitutive model that simultaneously considers the damage effect of freeze-thaw cycles on rocks, the thermal expansion and contraction effect of rocks, and the influence of temperature on the creep rate of rocks. This model would enable more accurate calculation of the long-term time-dependent deformation of slopes and ensure the reliability of slope stability analysis. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for calculating the time-dependent deformation of rock slopes under freeze-thaw cycles. This method considers the damaging effects of freeze-thaw cycles on slope rocks, the thermal expansion and contraction effects of rocks, and the influence of temperature changes on the creep properties of slope rocks. It is used to determine the time-dependent deformation characteristics of slopes under freeze-thaw cycles and ensure the long-term stability of slope engineering in cold regions of my country.

[0006] This invention is achieved through the following technical solution:

[0007] A method for calculating the time-dependent deformation of a freeze-thaw cycle slope includes the following steps:

[0008] Step 1: Establish a three-dimensional creep constitutive model considering the effects of freeze-thaw cycles.

[0009]

[0010] In the formula, Let S be the total strain rate tensor of the slope rock. For elastic strain rate, For thermal expansion strain rate, It is a viscoplastic strain rate;

[0011] The elastic strain rate and thermal expansion strain rate They are represented as follows:

[0012]

[0013] In the formula, E is the elastic modulus, ν is Poisson's ratio; E and ν are elastic parameters; The stress rate tensor, in Cartesian coordinates, can be expressed as:

[0014]

[0015] δ ij The Kronecker notation is defined as follows:

[0016]

[0017] α th It is the linear thermal expansion coefficient. The rate of temperature change;

[0018] The viscoplastic strain rate Represented as:

[0019]

[0020] In the formula, For equivalent stress, S is the equivalent rate of change. ij It is the deviatoric stress tensor;

[0021] The equivalent rate of variation Represented as:

[0022]

[0023] Equivalent variability It can be divided into two parts: The main purpose is to describe the strain hardening characteristics of slope rocks during long-term creep. In the long-term creep process, the creep rate of slope rocks is not constant, but decreases continuously with the increase of time, exhibiting strain hardening characteristics. It can describe the behavior of slope rock during the transient creep stage, as well as the reverse creep characteristics during load unloading.

[0024] In the formula and They are represented as follows:

[0025]

[0026] In the formula, A L0 A L1 α, Q L / R、A M0 A M1 Q M / R represents the coefficients to be fitted, σ0 represents the unit stress, which is 1 MPa and is used to unify the dimensions; t represents time and T represents temperature.

[0027] F is defined as:

[0028]

[0029] In the formula B M0 and B M1 The coefficients to be fitted are... for The integral over time is the cumulative strain of that part. The transient creep limit is expressed as:

[0030]

[0031] In the formula, C M0 and C M1 σ0 represents the coefficients to be fitted; σ0 is the unit stress, with a value of 1 MPa, used to unify the dimensions.

[0032] Equivalent stress;

[0033] Preferred, The value should be taken into account the effective equivalent stress after freeze-thaw cycle damage. Specifically:

[0034]

[0035] In the formula, σ1 is the maximum principal stress, σ2 is the intermediate principal stress, and σ3 is the minimum principal stress;

[0036] D is the damage variable of the stress element of the slope rock material; expressed as:

[0037]

[0038] In the formula, n is the number of rock micro-elements that have been damaged after k freeze-thaw cycles, and N is the number of rock micro-elements before the freeze-thaw cycles.

[0039] The calculation method is as follows:

[0040]

[0041] In the formula, k is the number of freeze-thaw cycles; a and k0 are Willbull distribution parameters;

[0042] Step 2 involves conducting experiments on the slope rock and further fitting calculations to obtain the elastic modulus E, Poisson's ratio ν, and linear thermal expansion coefficient α obtained in Step 1. th Willbull distribution parameters a, k0 and the coefficients to be fitted are used to obtain a three-dimensional creep constitutive model with slope rock parameters;

[0043] Step 3: Embed the three-dimensional creep constitutive model with slope rock parameters into the finite element calculation software to calculate the time-dependent deformation of the freeze-thaw cycle slope.

[0044] In the above technical solution, in step 2, the coefficients to be fitted include: A L0 A L1 α, Q L / R、A M0 A M1 Q M / R、B M0 B M1 C M0 and C M1 .

[0045] In the above technical solution, step 2 is to conduct a multi-stage loading triaxial creep test, a rock thermal expansion test under hydrostatic pressure, and a rock freezing / thawing cycle creep test on the slope rock sample to obtain the material parameters of the slope rock in step 1, thereby obtaining a three-dimensional creep constitutive model with slope rock parameters.

[0046] In the above technical solution, the multi-stage loading triaxial creep test specifically involves applying confining pressure P and axial deviatoric stress F / A0 to the slope rock sample.

[0047] The deformation of the slope rock sample was monitored to obtain the axial height change ΔL and the circumferential circumference change ΔC.

[0048] Repeat the above experimental steps by changing the confining pressure P or the axial deviatoric stress F / A0.

[0049] In the above technical solution, the multi-stage loading triaxial creep test specifically involves first subjecting the slope rock sample to freeze-thaw cycles, and then applying confining pressure P and axial deviatoric stress F / A0 to the slope rock sample after the freeze-thaw cycles have been completed.

[0050] The deformation of the slope rock sample was monitored to obtain the axial height change ΔL and the circumferential circumference change ΔC.

[0051] Repeat the above experimental steps by changing the confining pressure P or the axial deviatoric stress F / A0.

[0052] In the above technical solution, the freezing temperature of the freeze-thaw cycle is set to -20 (±5)℃, the thawing temperature is set to 20 (±5)℃, and the number of cycles is 0 to 75.

[0053] In the above technical solution, the rock thermal expansion experiment under hydrostatic pressure specifically involves applying a confining pressure P to the slope rock sample, maintaining the confining pressure strength, and performing heating / cooling operations on the slope rock sample.

[0054] The deformation of the slope rock sample was monitored to obtain the axial height change ΔL and the circumferential circumference change ΔC.

[0055] Change the confining pressure and repeat the above experimental process, preferably repeating it 3 to 5 times.

[0056] In the above technical solution, the creep test of the rock freezing / thawing cycle process specifically involves applying axial stress to the slope rock sample, maintaining the stress intensity, and then cooling down to conduct a freezing process creep test after the deformation of the slope rock sample stabilizes or the strain change value is less than 0.01 / h. After the temperature drops to a set value and the deformation of the slope rock sample stabilizes, the temperature is raised to thaw, and the creep test of the thawing process begins. Preferably, the slope rock sample is thawed naturally under normal temperature conditions. After the rock sample is completely thawed and the deformation stabilizes, the axial height change ΔL and the circumferential circumference change ΔC are obtained.

[0057] Increase the axial stress to the next stress level and repeat the above steps until the rock sample fails.

[0058] In the above technical solution, in the creep test of the rock freezing / thawing cycle, the initial stress level applied to the slope rock sample is set to 30±5% of the peak strength; the next stress level is increased by 10-20%.

[0059] In the above technical solution, the finite element software used in step 3 is FLA3D.

[0060] Compared with the prior art, the beneficial effects of the present invention are:

[0061] By defining freeze-thaw damage variables, the damage effect of freeze-thaw cycles on slope rocks was quantified. These variables were then incorporated into a three-dimensional creep constitutive model of the slope rocks, considering the deteriorating effect of freeze-thaw damage on the rock's mechanical properties and revealing the influence of freeze-thaw damage on the creep rate. A temperature variable was introduced into the three-dimensional creep constitutive model to account for the effect of temperature changes on the creep deformation rate. Furthermore, the deformation caused by thermal expansion and contraction of the rock was considered by introducing thermal expansion strain components. The functionality and accuracy of the constitutive model were validated using various laboratory tests, verifying its effectiveness. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the slope aging deformation calculation method considering freeze-thaw cycles in Embodiment 1 of the present invention.

[0063] Figure 2 This is a schematic diagram of axial compression loading in a triaxial creep test of rock under multi-stage loading in Embodiment 1 of the present invention.

[0064] Figure 3 This is a schematic diagram of the creep curve of the rock after the freeze-thaw cycle in Embodiment 1 of the present invention.

[0065] Figure 4 This is a flowchart of the creep test during the freezing / thawing process in Embodiment 1 of the present invention.

[0066] Figure 5 This is a schematic diagram of the creep curve of the creep test during the freezing / thawing process in Embodiment 1 of the present invention.

[0067] Figure 6 The diagram shows the stress and deformation of the cylindrical specimen in the triaxial creep test in Embodiment 1 of the present invention, where a is the specimen size; b is the stress condition; and c is the deformation condition.

[0068] Figure 7 This is a schematic diagram illustrating the fitting effect of the constitutive model of the present invention on experimental data in Embodiment 1 of the present invention.

[0069] Figure 8 This is a schematic diagram of the slope deformation under freeze-thaw cycle calculated by the present invention in Embodiment 1 of the present invention.

[0070] Figure 9 This is the creep curve obtained by multi-stage loading triaxial creep in Embodiment 2 of the present invention.

[0071] Figure 10 This is the creep curve obtained during the rock thawing / freezing process in Example 2 of the present invention.

[0072] Figure 11 This is the fitting curve of the experimental results in Embodiment 2 of the present invention.

[0073] Figure 12 This is a numerical model diagram of the slope established in Embodiment 2 of the present invention.

[0074] Figure 13 This is a cloud map of shear deformation of a rock slope under different freeze-thaw cycles in Example 2 of the present invention. Detailed Implementation

[0075] The present invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0076] Example 1

[0077] S1 defines the freeze-thaw damage variable.

[0078] Rock is a natural material containing numerous initial fissures and defects. When subjected to loads and environmental influences, new fissures form within it, and existing fissures connect to form larger fissures, causing damage to the rock. In cold regions, slope rocks are subjected to freeze-thaw cycles and undergo long-term creep deformation. This process leads to the accumulation of damage within the rock mass, resulting in the deterioration of the slope rock's mechanical properties, greater time-dependent deformation, and impact on slope stability, potentially leading to landslides and other phenomena.

[0079] According to damage mechanics, the damage variable D of a stress-bearing element of a slope rock material is defined as the ratio of the number of damaged rock elements n after k freeze-thaw cycles to the number of rock elements N before the freeze-thaw cycles, i.e.:

[0080]

[0081] The failure probability of rock micro-elements follows a Willbull distribution, and its probability density function is:

[0082]

[0083] In the formula, Q(k) is the rock freeze-thaw damage distribution function; k is the number of freeze-thaw cycles; and a and k0 are Willbull distribution parameters.

[0084] When the number of freeze-thaw cycles reaches a certain level k, the number of destroyed infinitesimal elements is:

[0085]

[0086] Substituting equation (3) into equation (2), we get

[0087]

[0088] Based on the assumption of equivalent variation, then we have

[0089]

[0090] In the formula, σ * Let σ be the effective stress, σ be the nominal stress, and D be the damage variable.

[0091] S2 establishes a three-dimensional creep constitutive model considering the effects of freeze-thaw cycles.

[0092] Total strain rate tensor of slope rock It can be decomposed into elastic strain rate Thermal expansion strain rate and viscoplastic strain rate

[0093]

[0094] Among them, elastic strain rate and thermal expansion strain rate They can be represented as:

[0095]

[0096] In the formula, E and ν are elastic parameters, namely the elastic modulus and Poisson's ratio, respectively. The stress rate tensor, in Cartesian coordinates, can be expressed as:

[0097]

[0098] δ ij The Kronecker notation is defined as follows:

[0099]

[0100] α th It is the linear thermal expansion coefficient. This represents the rate of temperature change.

[0101] viscoplastic strain rate Represented as:

[0102]

[0103] In the formula, For equivalent stress, S is the equivalent rate of change. ij This is the deviatoric stress tensor. The equivalent strain can be divided into two parts:

[0104]

[0105] The main purpose is to describe the strain hardening characteristics of slope rocks during long-term creep. In the long-term creep process, the creep rate of slope rocks is not constant, but decreases continuously with the increase of time, exhibiting strain hardening characteristics. It can describe the behavior of slope rock mass during the transient creep stage, as well as the reverse creep characteristics during load unloading. The two parts are represented as follows:

[0106]

[0107] In the formula, A L0 A L1 α, Q L / R、A M0 A M1 Q M / R represents the coefficients to be fitted, σ0 is the unit stress, with a value of 1 MPa, used for dimensionless measurement. F is defined as:

[0108]

[0109] In the formula B M0 and B M1 The coefficients to be fitted are... The transient creep limit is expressed as:

[0110]

[0111] In the formula, C M0 and C M1 The coefficients are to be fitted.

[0112] In the above calculations, equivalent stress The value should be determined by taking into account the effective equivalent stress after freeze-thaw cycle damage. Specifically:

[0113]

[0114] Where σ1 is the maximum principal stress, σ2 is the intermediate principal stress, and σ3 is the minimum principal stress.

[0115] S3 conducts slope rock freeze-thaw cycle mechanical test

[0116] Using slope rock as the test object, rock samples were drilled in-situ and prepared into cylindrical specimens with a diameter of 100 mm and a height of 200 mm (height-to-diameter ratio 2:1). Various rock mechanics experiments were conducted on the rock specimens, including triaxial creep tests under multi-stage loading after freeze-thaw cycles, thermal expansion tests under hydrostatic pressure, and creep tests during the freezing / thawing process. Based on the test results, the elastic modulus E, Poisson's ratio ν, and linear thermal expansion coefficient α in the constitutive model can be determined. thThe Willbull distribution parameters a, k0, and the coefficients to be fitted were determined, and the accuracy of the constitutive model was verified.

[0117] S31 Triaxial Creep Test of Rock under Multi-Stage Loading After Freeze-Thaw Cycle

[0118] First, the rock samples were subjected to freeze-thaw cycles, with different numbers of cycles set for different samples. For example, the number of cycles could be set to 0, 25, 50, and 75. The recommended freezing-thaw temperature was -20 to 20°C. Different confining pressures were set, such as 0 MPa, 10 MPa, and 20 MPa. Triaxial creep tests were then conducted on the samples after different number of cycles. The axial compression was applied in multiple stages. For example, the average uniaxial compressive strength of the rock could be used as the stress level for the staged loading test, representing 50%, 60%, 70%, 80%, 90%, 100%, and 110% of the peak value. A schematic diagram of the axial compression loading is shown below. Figure 2 The axial and circumferential deformation of the specimens were monitored, and partial creep curves were obtained as follows: Figure 3 As shown in Table 1.

[0119] Table 1. Triaxial creep test scheme for rocks after freeze-thaw cycles under multi-stage loading

[0120]

[0121] Rock thermal expansion test under hydrostatic pressure S32

[0122] Different confining pressures, such as 0 MPa, 10 MPa and 20 MPa, were applied to the rock samples to perform heating and cooling operations, and the axial and circumferential deformation of the samples was monitored during the heating and cooling process.

[0123] S33 Creep Test of Rock Freezing / Thawing Process

[0124] First, the first-level stress level to be applied is set to 30% of the peak strength. Once the rock sample deformation stabilizes or the strain change value is below 0.01 / h, the low-temperature cooling bath circulation system is activated to conduct a creep test during the freezing process. After the temperature drops to the set value, the rock sample deformation is observed to stabilize. Then, the cooling bath system is turned off (the rock sample thaws naturally at room temperature), and the creep test during the thawing process begins. Once the rock sample deformation stabilizes after complete thawing, the next stress level is applied. After the deformation stabilizes, the cooling bath system is activated again, and this process is repeated step by step until the rock sample fails. The creep test procedure during freezing / thawing is as follows: Figure 4 As shown. The obtained experimental curve is as follows. Figure 5 As shown.

[0125] S4 calibrates constitutive model parameters and verifies the constitutive model.

[0126] Stress and Deformation Analysis of S41 Indoor Test Specimens

[0127] The multi-stage loading triaxial creep test, the rock thermal expansion test under hydrostatic pressure, and the rock freezing / thawing cycle creep test in S3 were all conducted in a conventional triaxial creep testing machine for rocks; and the obtained data were analyzed and processed in this step. Based on the results, the elastic modulus E, Poisson's ratio ν, and linear thermal expansion coefficient α in the constitutive model can be determined. th The Willbull distribution parameters a, k0, and the coefficients to be fitted were determined, and the accuracy of the constitutive model was verified.

[0128] Conventional triaxial creep testing conducted in the laboratory represents a special stress state. Conventional triaxial creep testing machines typically employ a self-balancing triaxial chamber to apply confining pressure P and axial deviatoric stress F / A0 to a cylindrical specimen. Specimen deformation is typically monitored by tracking the axial height change ΔL and the circumferential circumference change ΔC at the specimen's center height. The stress and deformation of a cylindrical specimen during triaxial creep testing are as follows: Figure 6 As shown.

[0129] The specimen is under axisymmetric compression, with the axis of symmetry being the geometric axis of symmetry of the cylindrical specimen. Consider a small element within the specimen, with the specimen's axis as the z-axis. Any two mutually perpendicular directions within the specimen's end face are the x-axis and y-axis directions. Then, the x, y, and z-axis directions represent the three principal stress directions (which are also the principal strain directions).

[0130] Stress state of the micro-elements within the S411 specimen

[0131] In the above coordinate system, the tensor of the stress state of the infinitesimal element can be expressed as:

[0132]

[0133] In the formula, σ zz =σ1,σ xx =σ yy =σ3, σ1, and σ3 are the maximum and minimum principal stresses, respectively. The minimum principal stress σ3 is equal to the hydrostatic pressure P applied during the creep test. The maximum principal stress is the sum of the hydrostatic pressure P and the axial deviatoric stress F / A0, where F is the axial deviatoric load and A0 is the cross-sectional area of ​​the specimen. Therefore, the stress state of the micro-element can be further expressed as:

[0134]

[0135] The equivalent stress of the sample element is expressed by the principal stresses as follows:

[0136]

[0137] Considering the damage D of the rock sample during creep, the stress state of the micro-element is substituted into the formula for equivalent stress, that is, equations (5) and (17) are substituted into equation (18), and the effective equivalent stress is obtained as follows:

[0138]

[0139] Strain state of the micro-elements within the S412 specimen

[0140] In the above coordinate system, the strain tensor of the infinitesimal element can be expressed as:

[0141]

[0142] In the formula, ε xx =ε1,ε xx =ε yy =ε3, where ε1 and ε3 are the maximum and minimum principal strains, respectively. The maximum principal strain ε1 and the minimum principal strain ε3 can be expressed as:

[0143]

[0144] Where L0 is the height of the specimen before the test, ΔL is the change in the specimen height during the test, D0 is the diameter of the specimen before the test, and ΔC is the change in the circumferential circumference of the specimen. Therefore, the stress state of the micro-element can be further expressed as:

[0145]

[0146] The equivalent strain formula for a infinitesimal element is:

[0147]

[0148] Substituting the strain state of the infinitesimal element into the formula for equivalent strain, that is, substituting equation (21) into equation (22), we can obtain the equivalent strain as follows:

[0149]

[0150] S42 constitutive model parameter calibration

[0151] The parameters of the constitutive model were calibrated using the above experimental results. Specifically, the linear thermal expansion coefficient α was calibrated using the experimental results of rock thermal expansion under hydrostatic pressure. th Calibration is performed. The results of triaxial creep tests with multi-stage loading after freeze-thaw cycles and creep tests during the freezing / thawing process of rocks can be used to calibrate a, n0, and A. L0 A L1 α, Q L / R、A M0 A M1 Q M / R and other parameters are used for calibration. E and ν are elastic parameters, which can be calibrated using the instantaneous deformation under loading in multi-stage loading creep tests. The equivalent strain obtained in equation (25) is... The equivalent rate of variation can be obtained by taking the derivative with respect to time t. In each stress stage of the multi-stage loading triaxial creep test, the stress and temperature remained constant, i.e. and If all are 0, then we can get and The value of is 0, therefore the equivalent strain rate at each stage is the viscoplastic strain rate, i.e. The results obtained from indoor tests Effective equivalent stress in equation (19) Substitute the data into equation (9) Effective equivalent stress in equation (15) In this way, numerical fitting software can be used to invert a, k0, A in the constitutive model. L0 A L1 α, Q L / R、A M0 A M1 Q M / R、B M0 B M1 C M0 and C M1 The parameter values ​​are shown in the diagram below. The diagram illustrates the fitting effect of the constitutive model on the experimental data. Figure 7 As shown.

[0152] S5 embeds the constitutive model into the finite element method software to calculate the age-dependent deformation of the slope under freeze-thaw cycles.

[0153] S51 performs secondary development on the constitutive model.

[0154] Based on the secondary development platform of the finite element software FLAC3D, the constitutive model established in this invention can be further developed using the Visual Studio development environment. Numerical simulations of rock multi-level loading triaxial creep test after freeze-thaw cycle, rock thermal expansion test under hydrostatic pressure, and rock freezing / thawing process creep test can be carried out using FLAC3D software. The correctness and applicability of the constitutive model can be verified by comparing the numerical simulation results with the laboratory test results.

[0155] S52 Slope Deformation Calculation under Freeze-Thaw Cycles

[0156] Based on the site conditions, a slope model was created, its boundary conditions were determined, and its parameters were calibrated. The time-dependent deformation of the slope under self-weight load and freeze-thaw cycles was calculated. A schematic diagram of the slope deformation is shown below. Figure 8 As shown.

[0157] Example 2

[0158] The calculation method of this invention is used to perform time-dependent deformation analysis of a rock slope in a cold region under freeze-thaw cycles. According to meteorological data, the ten-year average minimum temperature and maximum temperature in this region are -23℃ and 19℃, respectively. Therefore, it is assumed that the freeze-thaw temperature of the slope in this region is -20℃ to 20℃, and that the entire rock slope is affected by freeze-thaw action.

[0159] Step 1: Drill rock samples from the slope and prepare them into cylindrical specimens with a diameter of 100 mm and a height of 200 mm (height-to-diameter ratio 2:1). Conduct triaxial creep tests on the rock specimens after freeze-thaw cycles, thermal expansion tests under hydrostatic pressure, and creep tests during freeze / thaw cycles. The loading scheme for the triaxial creep tests is shown in Table 2, and the obtained creep curves are shown in Table 2. Figure 9 As shown in Table 3, the creep test scheme for the rock thawing / freezing cycle process is shown in Table 3, and the obtained curves are shown in [the table]. Figure 10 The test protocol for the rock thermal expansion test is shown in Table 4.

[0160] Table 2. Test scheme for triaxial creep of rock after freeze-thaw cycles under multi-stage loading

[0161]

[0162] Table 3 Creep Test Scheme for Rock Thawing / Freezing Process

[0163]

[0164] Table 4 Test Scheme for Thermal Expansion of Rocks

[0165] Serial Number Confining pressure / MPa Temperature / °C 1 0 0—10—20—30 2 5 0—10—20—30 3 10 0—10—20—30 4 20 0—10—20—30

[0166] Step 2: Based on the indoor test results, the constitutive model parameters are inverted. Using the test results of rock thermal expansion under hydrostatic pressure, the linear thermal expansion coefficient α can be determined. th Calibration is performed. The results of triaxial creep tests with multi-stage loading after freeze-thaw cycles and creep tests during the freezing / thawing process of rocks can be used to calibrate a, n0, and A. L0 A L1 α, Q L / R、A M0 A M1 Q M Other parameters such as / R are used for calibration. E and ν are elastic parameters, which can be calibrated using the instantaneous deformation under loading in multi-stage loading creep tests. The obtained parameters are shown in Table 5.

[0167] Table 5 Constitutive Model Parameters

[0168]

[0169] Step 3: Constitutive Model Fitting Effect Analysis. Taking the triaxial creep test of rock after 75 freeze-thaw cycles with multi-stage loading as an example, in order to compare the simulation effect of the newly built model, the damage module of the model in this patent was removed, and its fitting effect was compared with that of the newly built model. The fitting curve of the test results is shown in [reference needed]. Figure 11 It can be seen that the model established in this patent fits the experimental data well, with R... 2 The R value reached 0.9976, while the model that did not consider damage showed a decent fit to the creep behavior in the first two loading stages. 2 It reached 0.9624, but its fitting effect on the creep behavior in the later stages was poor, with a large error.

[0170] Step 4: Calculate the time-dependent deformation of the slope using finite element method (FEM) software. First, model the slope. The entire slope is a layered rock slope with a cut height between 40-60m. The established numerical model is as follows: Figure 12 As shown. The model is 60m wide, 55m long, and 23m high. It contains 15,640 elements and 32,630 nodes. The bottom of the model is fixed, the sides are horizontally unidirectionally constrained, and the top surface is freely constrained. Self-weight stress is considered, but structural stress is not.

[0171] Considering a creep time of 2 years, slope deformation analysis was conducted for different freeze-thaw cycles. Figure 13 The figures show shear deformation contour maps of rock slopes under different freeze-thaw cycles. As can be seen, the maximum shear deformation of the rock slope at 0 freeze-thaw cycles occurs on the upper slope surface at the toe, and no potential sliding surface has yet formed. After 10 freeze-thaw cycles, the maximum shear deformation of the slope increases, indicating that the stability of the rock slope has decreased under the influence of freeze-thaw cycles. After 20 freeze-thaw cycles, the area of ​​maximum shear strain of the slope continues to increase, forming a potential slope slip surface. After 40 freeze-thaw cycles, the potential sliding surface of the slope develops into an arc and extends towards the top of the slope. After 80 freeze-thaw cycles, the potential sliding surface of the slope continues to expand, and the sliding surface almost reaches the top of the slope. With the increase of the number of freeze-thaw cycles, the potential sliding surface of the rock slope continuously expands to the top of the slope. Freeze-thaw cycles increase the risk of slope sliding failure.

[0172] The above description is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the time-dependent deformation of a freeze-thaw cycle slope, characterized in that, Includes the following steps: Step 1: Establish a three-dimensional creep constitutive model considering the effects of freeze-thaw cycles. In the formula, Let S be the total strain rate tensor of the slope rock. For elastic strain rate, For thermal expansion strain rate, It is a viscoplastic strain rate; The elastic strain rate and thermal expansion strain rate They are represented as follows: In the formula, E is the elastic modulus and ν is Poisson's ratio; The stress rate tensor, in Cartesian coordinates, can be expressed as: The Kronecker notation is defined as follows: It is the linear thermal expansion coefficient. The rate of temperature change; The viscoplastic strain rate Represented as: In the formula, For equivalent stress, S is the equivalent rate of change. ij It is the deviatoric stress tensor; The equivalent rate of variation Represented as: In the formula and They are represented as follows: In the formula, A L0 A L1 α, Q L / R、A M0 A M1 Q M / R represents the coefficients to be fitted, σ0 represents the unit stress, which is 1 MPa and is used to unify the dimensions; t represents time and T represents temperature. F is defined as: In the formula B M0 and B M1 The coefficients to be fitted are... for Integral over time, i.e. The cumulative strain for this portion is denoted as , and the transient creep limit is denoted as: In the formula, C M0 and C M1 σ0 represents the coefficients to be fitted; σ0 is the unit stress, with a value of 1 MPa, used to unify the dimensions. Equivalent stress; Preferred, The value should be taken into account the effective equivalent stress after freeze-thaw cycle damage. Specifically: In the formula, σ1 is the maximum principal stress, σ2 is the intermediate principal stress, and σ3 is the minimum principal stress; D represents the damage variable of the stress element of the slope rock material; the calculation method is as follows: In the formula, k is the number of freeze-thaw cycles; a and k0 are Willbull distribution parameters; Step 2 involves conducting experiments on the slope rock and further fitting calculations to obtain the elastic modulus E, Poisson's ratio ν, and linear thermal expansion coefficient α obtained in Step 1. th Willbull distribution parameters a, k0 and the coefficients to be fitted are used to obtain a three-dimensional creep constitutive model with slope rock parameters; Step 3: Embed the three-dimensional creep constitutive model with slope rock parameters into the finite element calculation software to calculate the time-dependent deformation of the freeze-thaw cycle slope.

2. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 1, characterized in that, In step 2, the coefficients to be fitted include: A L0 A L1 α, Q L / R、A M0 A M1 Q M / R、B M0 B M1 C M0 and C M1 .

3. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 1, characterized in that, Step 2 involves conducting multi-stage triaxial creep tests, hydrostatic pressure-based thermal expansion tests, and rock freezing / thawing cycle creep tests on the slope rock samples to obtain the elastic modulus E, Poisson's ratio ν, and linear thermal expansion coefficient α obtained in Step 1. th Willbull distribution parameters a, k0 and the coefficients to be fitted are used to calibrate the three-dimensional creep constitutive model.

4. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 3, characterized in that, The multi-stage loading triaxial creep test specifically involves applying confining pressure P and axial deviatoric stress F / A0 to the slope rock sample. The deformation of the slope rock sample was monitored to obtain the axial height change ΔL and the circumferential circumference change ΔC. Repeat the above experimental steps by changing the confining pressure P or the axial deviatoric stress F / A0.

5. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 3, characterized in that, The multi-stage loading triaxial creep test specifically involves first subjecting the slope rock sample to freeze-thaw cycles, and then applying confining pressure P and axial deviatoric stress F / A0 to the slope rock sample after the freeze-thaw cycles have been completed. The deformation of the slope rock sample was monitored to obtain the axial height change ΔL and the circumferential circumference change ΔC. Repeat the above experimental steps by changing the confining pressure P or the axial deviatoric stress F / A0.

6. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 5, characterized in that, The freezing temperature of the freeze-thaw cycle is set to -20 (±5)℃, the thawing temperature is set to 20 (±5)℃, and the number of cycles is 0 to 75.

7. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 3, characterized in that, The rock thermal expansion experiment under hydrostatic pressure specifically involves applying a confining pressure P to a slope rock sample, maintaining the confining pressure strength, and then performing heating / cooling operations on the slope rock sample. The deformation of the slope rock sample was monitored to obtain the axial height change ΔL and the circumferential circumference change ΔC. Change the confining pressure and repeat the above experimental process, preferably repeating it 3 to 5 times.

8. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 3, characterized in that, The creep test of the rock freezing / thawing cycle process is specifically as follows: axial stress is applied to the slope rock sample, and the stress intensity is maintained. When the deformation of the slope rock sample stabilizes or the strain change value is less than 0.01 / h, the temperature is lowered to carry out the freezing process creep test; after the temperature drops to the set value and the deformation of the slope rock sample stabilizes, the temperature is raised to thaw and the thawing process creep test begins. Preferably, the slope rock sample is thawed naturally under normal temperature conditions. After the rock sample is completely thawed and the deformation stabilizes, the axial height change ΔL and the circumferential circumference change ΔC are obtained. Increase the axial stress to the next stress level and repeat the above steps until the rock sample fails.

9. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 8, characterized in that, In the creep test of the rock freezing / thawing cycle, the initial stress level applied to the slope rock sample was set to 30 ± 5% of the peak strength; the next stress level was increased by 10–20%.

10. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 1, characterized in that, In step 3, the finite element software used is FLA3D.

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