Slope aging deformation calculation method

Abstract

The invention discloses an aging deformation calculation method for a freeze-thaw cycle rock slope, which considers the damage effect of the freeze-thaw cycle on the slope rock, the thermal expansion and cold contraction effect of the rock and the influence of the temperature change on the creep property of the slope rock, and is used for determining the aging deformation characteristics of the slope under the freeze-thaw cycle. And long-term stability of cold region slope engineering in China is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of civil engineering, and particularly relates to a method for calculating the time-dependent deformation of a slope under freeze-thaw cycles. Background Art

[0002] Geotechnical engineering such as rock slopes in cold regions has been under the multiple influences of the natural environment for a long time, including freeze-thaw action, water erosion, and human mining activities. The superimposed effects of these factors are extremely likely to induce various geological disasters and engineering accidents. For example, on March 29, 2013, a landslide occurred on Zeri Mountain in the Jiama mining area of Tibet. This incident caused a slope collapse of more than 2 million cubic meters, resulting in the death of 83 workers. The accident investigation results showed that the long-term freeze-thaw cycle effect was the main reason for the degradation of the mechanical properties of the rock mass, and the frequent snowfall and snowmelt processes that month further exacerbated the reduction of the rock mass stability, ultimately triggering the instability of the rock mass during the mining activities. In fact, the geotechnical engineering structures in cold regions not only experience the degradation of mechanical properties due to the freeze-thaw cycle effect, but also suffer from the problem of creep deformation caused by long-term load effects. Therefore, in-depth research on the time-dependent mechanical properties of rocks under freeze-thaw environments has extremely important scientific significance and practical application value for the stability assessment and safe operation of geotechnical engineering in cold regions.

[0003] In the existing constitutive models, it is impossible to simultaneously consider 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 deformation of rocks. However, the time-dependent deformation of slope rocks is the superposition of these three effects. Using the existing calculation methods to calculate the time-dependent deformation of slopes under freeze-thaw cycles, the accuracy of the results is insufficient, and thus the reliability of the slope stability analysis results is questionable. In long-term use, slopes designed using existing methods may have potential safety hazards.

[0004] The accuracy of the existing calculation methods for the time-dependent deformation of slopes under the influence of freeze-thaw cycles is in doubt. Therefore, there is an urgent need for a constitutive model that can simultaneously consider 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 deformation of rocks, in order to achieve 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 the present invention is to overcome the deficiencies of the prior art and provide a method for calculating the time-dependent deformation of a freeze-thaw cycle rock slope. This calculation method takes into account the damage effect of freeze-thaw cycles on slope rocks, the thermal expansion and contraction effect of rocks, and the influence of temperature changes on the creep properties of slope rocks, so as 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 our country.

[0006] The present invention is realized through the following technical solutions:

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

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

[0009]

[0010] In the formula, is the total strain rate tensor of the slope rock, is the elastic strain rate, is the thermal expansion strain rate, is the viscoplastic strain rate;

[0011] The elastic strain rate and the thermal expansion strain rate are respectively expressed as:

[0012]

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

[0014]

[0015] δ ij is the Kronecker symbol, and its definition is:

[0016]

[0017] α th is the linear thermal expansion coefficient, is the temperature change rate;

[0018] The viscoplastic strain rate is expressed as:

[0019]

[0020] In the formula, is the equivalent stress, is the equivalent strain rate, S ij is the deviatoric stress tensor;

[0021] The equivalent strain rate is expressed as:

[0022]

[0023] The equivalent strain rate can be divided into two parts: Mainly to describe the strain hardening characteristics of slope rock during long-term creep. During the long-term creep process, the creep rate of slope rock is not constant, but continuously decreases with the increase of time, showing strain hardening characteristics. It can describe the behavior of slope rock in the transient creep stage and the reverse creep characteristics during load unloading.

[0024] In the formula and are respectively expressed as:

[0025]

[0026] In the formula, A L0 , A L1 , α, Q L / R, A M0 , A M1 , Q M / R are coefficients to be fitted, σ 0 is the unit stress, with a value of 1 MPa, used to unify the dimension; t is time, and T is temperature;

[0027] F is defined as:

[0028]

[0029] In the formula, B M0 and B M1 are coefficients to be fitted, is the integral with respect to time, which is the cumulative strain of this part, is the transient creep limit, expressed as:

[0030]

[0031] In the formula, C M0 and C M1 are coefficients to be fitted; σ 0 is the unit stress, with a value of 1 MPa, used to unify the dimension;

[0032] is the equivalent stress;

[0033] Preferably, when taking values, it should be the effective equivalent stress considering the freeze-thaw cycle damage Specifically:

[0034]

[0035] In the formula, σ 1 is the maximum principal stress, σ 2 is the intermediate principal stress, σ 3 is the minimum principal stress;

[0036] D is the damage variable of the stress-bearing unit of the slope rock material; it is expressed as:

[0037]

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

[0039] The calculation method is:

[0040]

[0041] In the formula, k is the number of freeze-thaw cycles; a and k 0 are Willbull distribution parameters;

[0042] Step 2: Conduct experiments on the slope rock and further perform fitting calculations to obtain the elastic modulus E, Poisson's ratio ν, and linear thermal expansion coefficient α in Step 1 th , Willbull distribution parameters a, k 0 and the coefficients to be fitted, so as 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 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 , B M0 , B M1 , C M0 and C M1 .

[0045] In the above technical solution, Step 2 is to respectively conduct multi-level loading triaxial creep experiments, rock thermal expansion experiments under hydrostatic pressure, and creep experiments during the rock freezing / thawing cycle process on the slope rock specimens, obtain the material parameters of the slope rock in Step 1, so as to obtain a three-dimensional creep constitutive model with slope rock parameters;

[0046] In the above technical solution, the multi-level loading triaxial creep experiment is specifically to apply confining pressure P and axial deviator stress F / A 0 ;

[0047] Monitor the deformation of the slope rock specimen to obtain the axial height change ΔL and the circumferential perimeter change ΔC;

[0048] Change the confining pressure P or the axial deviator stress F / A 0 , and repeat the above experimental steps.

[0049] In the above technical solution, the multi-stage loading triaxial creep test is specifically as follows: First, conduct freeze-thaw cycles on the slope rock specimen, and then apply the confining pressure P and the axial deviator stress F / A to the slope rock specimen after the freeze-thaw cycles are completed 0 ;

[0050] Monitor the deformation of the slope rock specimen to obtain the axial height change ΔL and the circumferential perimeter change ΔC;

[0051] Change the confining pressure P or the axial deviator stress F / A 0 , and repeat the above experimental steps.

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

[0053] In the above technical solution, the rock thermal expansion experiment under hydrostatic pressure is specifically as follows: Apply the confining pressure P to the slope rock specimen, maintain the confining pressure strength, and perform heating / cooling operations on the slope rock specimen;

[0054] Monitor the deformation of the slope rock specimen to obtain the axial height change ΔL and the circumferential perimeter change ΔC;

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

[0056] In the above technical solution, the creep experiment during the rock freezing / thawing cycle process is specifically as follows: Apply axial stress to the slope rock specimen, maintain the stress strength, and when the deformation of the slope rock specimen is stable or the strain change value is lower than 0.01 / h, cool down to conduct the creep experiment during the freezing process; When the temperature drops to the set value and the deformation of the slope rock specimen is stable, heat up to thaw and start the creep test during the thawing process. Preferably, the slope rock specimen thaws naturally under normal temperature conditions. After the deformation of the fully thawed rock sample is stable, obtain the axial height change ΔL and the circumferential perimeter change ΔC;

[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, the stress level initially applied to the slope rock specimen in the creep experiment during the rock freezing / thawing cycle process is set at 30±5% of the peak strength; The next stress level increases by 10 to 20%.

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

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

[0061] By defining the freeze-thaw damage variable, the damage effect of freeze-thaw cycles on slope rocks is quantified. The freeze-thaw damage variable is introduced into the three-dimensional creep constitutive model of slope rocks, considering the deterioration effect of freeze-thaw damage on the mechanical properties of rocks, and the influence of freeze-thaw damage on the creep rate is obtained. The temperature variable is introduced into the three-dimensional creep constitutive model, considering the influence of temperature change on the creep deformation rate. By introducing the thermal expansion strain component, the deformation caused by the thermal expansion and contraction of rocks is considered. The functionality and accuracy of the constitutive model are verified by a variety of laboratory tests, and the effect of the constitutive model is verified. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a schematic flow chart of the calculation method for the time-dependent deformation of a slope considering freeze-thaw cycles in Embodiment 1 of the present invention.

[0063] Figure 2 It is a schematic diagram of the axial pressure loading in the multi-stage loading triaxial creep test of rocks in Embodiment 1 of the present invention.

[0064] Figure 3 It is a schematic diagram of the full-process creep curve of rocks after freeze-thaw cycles in Embodiment 1 of the present invention.

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

[0066] Figure 5 It 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 It shows the stress and deformation conditions 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; c is the deformation condition.

[0068] Figure 7 It is a schematic diagram of the fitting effect of the test data using the constitutive model of the present invention in Embodiment 1 of the present invention.

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

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

[0071] Figure 10It is the creep curve obtained from the creep of rock during thawing / freezing in Embodiment 2 of the present invention.

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

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

[0074] Figure 13 It is the shear deformation nephogram of the rock slope under different freeze-thaw cycles in Embodiment 2 of the present invention. Specific embodiments

[0075] The present invention will be further described in detail below in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0076] Embodiment 1

[0077] S1 Define the freeze-thaw damage variable

[0078] Rock is a natural material with many initial cracks and defects inside. When subjected to loads and environmental influences, new cracks will be generated inside, and the existing cracks will connect with each other to form larger cracks, which will cause damage to the rock. The rock on the slope in cold regions is subjected to freeze-thaw cycles and will produce long-term creep deformation. This process will lead to the accumulation of damage in the rock mass, resulting in the deterioration of the mechanical properties of the slope rock, generating greater time-dependent deformation, affecting the stability of the slope, and possibly causing landslides and other phenomena.

[0079] According to damage mechanics, the damage variable D of the stressed unit of the slope rock material is defined as the ratio of the number n of damaged rock micro-elements after k freeze-thaw cycles to the number N of rock micro-elements before freeze-thaw cycles, that is:

[0080]

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

[0082]

[0083] In the formula, Q(k) is the rock freeze-thaw failure distribution function; k is the number of freeze-thaw cycles; a and k 0 are the Willbull distribution parameters.

[0084] When the number of freeze-thaw cycles reaches a certain level k, the number of damaged micro-elements is

[0085]

[0086] Substitute Equation (3) into Equation (2), we get

[0087]

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

[0089]

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

[0091] S2 Establish a three-dimensional creep constitutive model considering the influence of freeze-thaw cycles

[0092] The total strain rate tensor of slope rock can be decomposed into the elastic strain rate the thermal expansion strain rate and the viscoplastic strain rate

[0093]

[0094] Among them, the elastic strain rate and the thermal expansion strain rate can be expressed as follows respectively:

[0095]

[0096] In the formula, E and ν are elastic parameters, which are the elastic modulus and Poisson's ratio respectively, is the stress rate tensor, and in the Cartesian coordinate system, it can be expressed as:

[0097]

[0098] δ ij is the Kronecker symbol, and its definition is:

[0099]

[0100] α th is the linear thermal expansion coefficient, is the temperature rate.

[0101] The viscoplastic strain rate is expressed as:

[0102]

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

[0104]

[0105] Mainly to describe the strain hardening characteristics of slope rock during long-term creep. During the long-term creep process, the creep rate of slope rock is not constant, but continuously decreases with the increase of time, showing strain hardening characteristics. It can describe the behavior of slope rock mass in the transient creep stage and the reverse creep characteristics during load unloading. The two parts are respectively expressed as:

[0106]

[0107] In the formula, A L0 , A L1 , α, Q L / R, A M0 , A M1 , Q M / R are coefficients to be fitted, and σ 0 is the unit stress, with a value of 1 MPa, used to unify the dimension. F is defined as:

[0108]

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

[0110]

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

[0112] In the above calculation, the value of the equivalent stress should be the effective equivalent stress after considering the freeze-thaw cycle damage. Specifically:

[0113]

[0114] Among them, σ 1 is the maximum principal stress, σ 2 is the intermediate principal stress, and σ 3 is the minimum principal stress.

[0115] S3 Conduct mechanical tests on slope rock under freeze-thaw cycles

[0116] Taking slope rocks as the test objects, rock samples are drilled on-site and made into cylindrical specimens with a diameter of 100 mm × a height of 200 mm (height-diameter ratio of 2:1). A variety of rock mechanics experiments are carried out on the rock specimens, namely the multi-level loading triaxial creep test of rocks after freeze-thaw cycles, the thermal expansion test of rocks under hydrostatic pressure, and the creep test of rocks during the freezing / thawing process. According to the test results, the elastic modulus E, Poisson's ratio ν, and linear thermal expansion coefficient α th , the Willbull distribution parameters a, k 0 and the coefficients to be fitted, and verify the accuracy of the constitutive model.

[0117] S31 Multi-level loading triaxial creep test of rocks after freeze-thaw cycles

[0118] First, conduct freeze-thaw cycles on the rock specimens. Different specimens are set with different numbers of cycles. For example, the number of cycles can be set to 0, 25, 50, and 75 times respectively. The freezing-thawing temperature is recommended to be set at -20~20°C. Set different confining pressures. For example, the confining pressures can be selected as 0 MPa, 10 MPa, and 20 MPa respectively. Conduct triaxial creep tests on the specimens after different numbers of cycles. The axial pressure is multi-level loading. For example, the average value of the uniaxial compressive strength of the rock can be used as 50%, 60%, 70%, 80%, 90%, 100%, and 110% of the peak value as the stress levels of the multi-level loading test. The schematic diagram of the axial pressure loading is shown in Figure 2 . Monitor the axial deformation and circumferential deformation of the specimens. Some of the obtained creep curves are as shown in Figure 3 . The test scheme example is shown in Table 1.

[0119] Table 1 Multi-level loading triaxial creep test scheme of rocks after freeze-thaw cycles

[0120]

[0121] S32 Thermal expansion test of rocks under hydrostatic pressure

[0122] Apply different confining pressures to the rock specimens, such as 0 MPa, 10 MPa, and 20 MPa. Conduct temperature rise and fall operations on the rocks, and monitor the axial deformation and circumferential deformation of the specimens during the temperature rise and fall process.

[0123] S33 Creep test of rocks during the freezing / thawing process

[0124] First, set the first-level stress level to be applied to 30% of the peak strength. When the deformation of the rock sample tends to be stable or the strain change value is lower than 0.01 / h, turn on the low-temperature cold bath circulation system to conduct the creep test during the freezing process. After the temperature drops to the set value, continue to observe until the deformation of the rock sample tends to be stable, then turn off the cold bath system (the rock sample thaws naturally under normal temperature conditions), and start the creep test during the thawing process. When the deformation of the rock sample tends to be stable after complete thawing, load it to the next-level stress level. After the deformation is stable, turn on the cold bath system again, and so on step by step until the rock sample fails. The creep test process during freezing / thawing is as Figure 4 shown. The obtained test curve is as Figure 5 shown.

[0125] S4 Calibrate the constitutive model parameters and verify the constitutive model

[0126] S41 Force and deformation analysis of indoor test specimens

[0127] The multi-level loading triaxial creep experiment, the rock thermal expansion experiment under hydrostatic pressure, and the creep experiment during the rock freezing / thawing cycle in S3 are all carried out in a conventional triaxial creep testing machine for rock; and the obtained data are analyzed and processed in this step. According to the results, the elastic modulus E, Poisson's ratio ν, and linear thermal expansion coefficient α th , Willbull distribution parameters a, k 0 and the coefficients to be fitted can be obtained, and the accuracy of the constitutive model is verified.

[0128] The conventional triaxial creep test carried out in the laboratory is a special stress state. Conventional triaxial creep testing machines usually adopt a triaxial chamber with self-balanced confining pressure, which can apply confining pressure P and axial deviator stress F / A 0 to the cylindrical specimen. For the deformation monitoring of the specimen, the change in the axial height ΔL of the specimen and the change in the circumferential perimeter ΔC of the specimen at the center height of the specimen are usually monitored. The force and deformation conditions of the cylindrical specimen in the triaxial creep test are as Figure 6 shown.

[0129] The whole specimen is in an axisymmetric compression state, and the axis of symmetry is the geometric axis of symmetry of the cylindrical specimen. Take a microelement from the specimen, with the axial direction of the specimen as the z-axis, and any two mutually perpendicular directions in the specimen end face as the x-axis direction and the y-axis direction respectively. Then the x, y, and z-axis directions are the three principal stress directions (simultaneously the principal strain directions).

[0130] S411 Stress state of the microelement in the specimen

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

[0132]

[0133] wherein, σ zz = σ 1 , σ xx = σ yy = σ 3 , σ 1 and σ 3 are the maximum principal stress and the minimum principal stress respectively. The minimum principal stress σ 3 is equal to the hydrostatic pressure P applied in the creep test. The maximum principal stress is the sum of two parts, i.e., the hydrostatic pressure P and the axial deviator stress F / A 0 , where F is the axial deviator load and A 0 is the cross-sectional area of the specimen. Therefore, the stress state of the microelement can be further expressed as:

[0134]

[0135] The equivalent stress of the specimen microelement expressed in terms of principal stresses is:

[0136]

[0137] Considering the damage D of the rock specimen during creep and substituting the stress state of the microelement into the formula of the equivalent stress, i.e., substituting Eqs. (5) and (17) into Eq. (18), the effective equivalent stress can be obtained as:

[0138]

[0139] The strain state of the microelement in the S412 specimen

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

[0141]

[0142] wherein, ε xx = ε 1 , ε xx = ε yy = ε 3 , ε 1 and ε 3 are the maximum principal strain and the minimum principal strain respectively. The maximum principal strain ε 1 and the minimum principal strain ε 3 can be respectively expressed as:

[0143]

[0144] wherein, L 0 is the height of the specimen before the test, ΔL is the change in the height of the specimen during the test, D 0 is the diameter of the specimen before the test, and ΔC is the change in the circumferential perimeter of the specimen. Therefore, the stress state of the microelement can be further expressed as:

[0145]

[0146] The equivalent strain formula of the infinitesimal element is as follows:

[0147]

[0148] Substitute the strain state of the infinitesimal element into the equivalent strain formula, that is, substitute Equation (21) into Equation (22), and the equivalent strain can be obtained as follows:

[0149]

[0150] S42 Calibration of constitutive model parameters

[0151] Use the above test results to calibrate the parameters of the constitutive model. Specifically, use the test results of the thermal expansion of rock under hydrostatic pressure to calibrate the linear thermal expansion coefficient α th Perform calibration. Use the test results of the multi-level loading triaxial creep test of rock after freeze-thaw cycles and the creep test of rock during freezing / thawing process to calibrate a, n 0 , A L0 , A L1 , α, Q L / R, A M0 , A M1 , Q M / R and other parameters. E and ν are elastic parameters, and the parameters can be calibrated using the instantaneous deformation during loading in the multi-level loading creep test. Take the derivative of the equivalent strain obtained in Equation (25) with respect to time t to obtain the equivalent strain rate In each stress stage of the multi-level loading triaxial creep test, the stress and temperature remain unchanged, that is and are both 0, and and can be obtained as 0. Therefore, the equivalent strain rate in each stage is the viscoplastic strain rate, that is Substitute the obtained from the laboratory test and the effective equivalent stress in Equation (19) into in Equation (9) and the effective equivalent stress in Equation (15) respectively, and then the values of a, k 0 , A L0 , A L1 , α, Q L / R, A M0 , A M1 , Q M / R, B M0 , B M1, C M0 and C M1 parameter values. The schematic diagram of the fitting effect of the constitutive model on the test data is as Figure 7 shown.

[0152] S5 Embeds the constitutive model into the finite element calculation software to calculate the time-dependent deformation of the slope under freeze-thaw cycle load

[0153] S51 Secondary development of the constitutive model

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

[0155] S52 Calculation of the time-dependent deformation of the slope under freeze-thaw cycles

[0156] According to the actual situation of the project site, model the slope, determine the boundary conditions of the slope, and calibrate the parameters of the slope to calculate the time-dependent deformation of the slope under self-weight load and freeze-thaw cycles. The schematic diagram of the deformation of the slope is as Figure 8 shown.

[0157] Example 2

[0158] Taking a certain rock slope in the cold region as an example, the time-dependent deformation analysis under freeze-thaw cycles is carried out using the calculation method of the present invention. According to the meteorological data, the average minimum and maximum temperatures in winter in this area are -23°C and 19°C respectively. Therefore, it is assumed that the freeze-thaw temperature of the slope in this area is -20°C - 20°C, and it is assumed that the entire rock slope is affected by freeze-thaw action.

[0159] Step 1: Drill rock samples from the slope site and make them into cylindrical specimens with a diameter of 100 mm × height of 200 mm (height-diameter ratio 2:1). Conduct the multi-stage loading triaxial creep test of rocks after freeze-thaw cycles, the thermal expansion test of rocks under hydrostatic pressure, and the creep test of rocks during the freezing / thawing cycle process on the rock specimens respectively. The loading scheme of the multi-stage loading triaxial creep test is shown in Table 2, and the obtained creep curve is as Figure 9 shown. The creep test scheme of the rock during the freezing / thawing cycle process is shown in Table 3, and the obtained curve is shown in Figure 10 . The test scheme of the rock thermal expansion test is shown in Table 4.

[0160] Table 2 Test scheme of the multi-stage loading triaxial creep test of rocks after freeze-thaw cycles

[0161]

[0162] Table 3 Creep test scheme for rock thawing / freezing process

[0163]

[0164] Table 4 Rock thermal expansion test plan

[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: According to the indoor test results, the constitutive model parameters are inverted. The linear thermal expansion coefficient α can be calculated by using the rock thermal expansion test results under hydrostatic pressure. th The results of the triaxial creep test of rock under multi-stage loading after freeze-thaw cycles and the creep test of rock during freezing / thawing can be used to calibrate a and n. 0 , A L0 , A L1 , α, Q L / R、A M0 , A M1 , Q M / R and other parameters are calibrated. E and ν are elastic parameters, which can be calibrated using the loading instantaneous deformation of the multi-stage loading creep test. The obtained parameters are shown in Table 5.

[0167] Table 5 Constitutive model parameters

[0168]

[0169] Step 3: Analysis of constitutive model fitting effect. Taking the triaxial creep test of rock multi-stage loading after 75 freeze-thaw cycles as an example, in order to compare the simulation effect of the new model, the damage module is removed from the model in this patent, and its fitting effect is compared with the new model. The fitting curve of the test results is shown in Figure 11 It can be seen that the model established in this patent has a good fitting effect on the test data, R 2 The model without considering damage has a good fitting effect on the creep behavior of the first two loading stages. 2 It reaches 0.9624, but the fitting effect of the creep behavior in the later stage is poor and there is a large error.

[0170] Step 4: Calculate the time-dependent deformation of the slope based on finite element calculation software. First, model the slope. The entire slope is a layered rock slope with a cut height of 40-60m. The established numerical model is as follows: Figure 12 As shown in the figure. The model is 60m wide, 55m long and 23m high. The total number of units is 15640, the number of nodes is 32630, the bottom of the model is fixedly constrained, the sides are horizontally constrained in one direction, and the upper surface is freely constrained. Self-weight stress is considered, but the effect of structural stress is not considered.

[0171] The time considering creep is taken as 2 years, and the time-dependent deformation analysis of the slope under different freeze-thaw cycles is carried out. Figure 13 It is the shear deformation nephogram of the rock slope under different freeze-thaw cycles. It can be seen from the figure that the maximum shear deformation of the rock slope with 0 freeze-thaw cycles appears on the upper slope surface of the slope toe, and no potential slip surface has been formed yet. After 10 freeze-thaw cycles, the maximum shear deformation of the slope increases, indicating that the stability of the rock slope decreases under the influence of freeze-thaw. After 20 freeze-thaw cycles, the maximum shear strain area of the slope continues to increase, and a potential slope slip surface is formed. From the shear strain diagram after 40 freeze-thaw cycles, the potential slip surface of the slope develops into an arc and extends towards the top of the slope. After 80 freeze-thaw cycles, the potential slip surface of the slope continues to expand, and the slip surface almost reaches the top of the slope. With the increase of the freeze-thaw cycles, the potential slip surface of the rock slope continuously expands to the top of the slope. Freeze-thaw cycles will increase the risk of slope sliding failure.

[0172] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for calculating the time-dependent deformation of a freeze-thaw cycle slope, characterized in that: The following steps are involved: Step 1 Establish a three-dimensional creep constitutive model considering the influence of freeze-thaw cycles In the formula, is the total strain rate tensor of the slope rock, is the elastic strain rate, is the thermal expansion strain rate, is the viscoplastic strain rate; The elastic strain rate and thermal expansion strain rate Respectively expressed as: Where E is the elastic modulus and ν is the Poisson's ratio; is the stress change rate tensor, which can be expressed in the Cartesian coordinate system as: δ ij is the Kronecker symbol, which is defined as: α th is the linear thermal expansion coefficient, is the temperature change rate; The viscoplastic strain rate It is expressed as: In the formula, is the equivalent stress, is the equivalent strain rate, S ij is the deviatoric stress tensor; The equivalent strain rate It is expressed as: In the formula and Respectively expressed as: In the formula, A L0 , A L1 ,α,Q L / R、A M0 , A M1 , Q M / R is the coefficient to be fitted, σ0 is the unit stress, which is 1MPa and is used to unify the dimensions; t is time, and T is temperature; F is defined as: Where B M0 and B M1 are the coefficients to be fitted, for The integral over time is the accumulated strain of this part, is the transient creep limit, expressed as: In the formula, C M0 and C M1 is the coefficient to be fitted; σ0 is the unit stress, which is 1MPa and is used to unify the dimensions; is the equivalent stress; Preferably, 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 is the damage variable of the slope rock material stress unit; the calculation method is: Where k is the number of freeze-thaw cycles; a and k0 are Willbull distribution parameters; Step 2: Conduct experiments on the slope rock, and further fit and calculate to obtain the elastic modulus E, Poisson's ratio ν, and linear thermal expansion coefficient α in step 1. th , Willbull distribution parameters a, k0 and coefficients to be fitted, thus obtaining a three-dimensional creep constitutive model with slope rock parameters; Step 3: embed the three-dimensional creep constitutive model with slope rock parameters into 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 is 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 is characterized in that: The step 2 is to respectively 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 elastic modulus E, Poisson's ratio ν, and linear thermal expansion coefficient α described in step 1. th , Willbull distribution parameters a, k0 and coefficients to be fitted, thus calibrating 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 is characterized in that: The multi-stage loading triaxial creep test specifically applies confining pressure P and axial deviator stress F / A0 to the slope rock sample; Monitoring the deformation of the slope rock sample to obtain an axial height change ΔL and an annular circumference change ΔC; Change the confining pressure P or the axial deviator stress F / A0 and repeat the above experimental steps.

5. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 3 is characterized in that: The multi-stage loading triaxial creep test specifically includes firstly subjecting the slope rock sample to a freeze-thaw cycle, and then applying a confining pressure P and an axial deviator stress F / A0 to the slope rock sample after the freeze-thaw cycle. Monitoring the deformation of the slope rock sample to obtain an axial height change ΔL and an annular circumference change ΔC; Change the confining pressure P or the axial deviator stress F / A0 and repeat the above experimental steps.

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

7. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 3 is characterized in that: The rock thermal expansion experiment under hydrostatic pressure specifically includes applying a confining pressure P to the slope rock sample, maintaining the confining pressure strength, and performing a heating / cooling operation on the slope rock sample; Monitoring the deformation of the slope rock sample to obtain an axial height change ΔL and an annular circumference change ΔC; Change the confining pressure and repeat the above experimental process, preferably 3 to 5 times.

8. The method for calculating the time-dependent deformation of a freeze-thaw cycle slope according to claim 3 is characterized in that: The rock freeze / thaw cycle creep experiment specifically includes applying axial stress to the slope rock sample, maintaining the stress intensity, and cooling down to perform a freezing process creep experiment after the deformation of the slope rock sample is stable 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 is stable, heating up and thawing to start a thawing process creep test, preferably the slope rock sample is naturally thawed at room temperature, and after the deformation of the completely thawed rock sample is stable, 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 is characterized in that: In the rock freeze / thaw cycle creep experiment, the stress level initially applied to the slope rock sample is set to 30±5% of the peak strength; the next level of stress level is 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 is FLA3D.

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