Simulation method for stochastic fracture propagation in rock slopes considering freeze-thaw cycles

Abstract

This invention discloses a simulation method for the random propagation of cracks in rock slopes considering freeze-thaw cycles, comprising the following steps: defining the crack propagation area; calculating the frost heave force generated by the water-ice phase change in the crack; calculating the effective volume expansion coefficient; determining whether the crack can propagate; after determining that the crack has propagated, using the propagated crack as the initial crack, and based on the above steps, simulating the crack opening process in the next freeze-thaw cycle until one end of the crack reaches the boundary of the propagation area or the number of freeze-thaw cycles reaches its maximum value, at which point the simulation ends. The method provided by this invention simulates the crack propagation process of rock slopes under freeze-thaw cycles, yielding realistic crack morphologies, overcoming the limitations of existing methods that are restricted by sample size, and the generated crack model can be imported into numerical simulation software for mechanical analysis, with high computational efficiency.

Description

Technical Field

[0001] This invention belongs to the technical field of rock slope fissure propagation, specifically relating to a simulation method for the random propagation of rock slope fissures considering freeze-thaw cycles. Background Technology

[0002] The rock mass contains joints of varying scales, providing sites and channels for water storage and transport. Due to temperature differences caused by diurnal and seasonal changes, water-ice phase transitions and water migration frequently occur in high-altitude, cold-region rock slopes. Water freezing into ice causes approximately 9% volume expansion, generating frost heave force. When this force exceeds the threshold for crack propagation, it drives cracks in the rock slope to extend, ultimately leading to frost heave failure of the entire slope and geological hazards such as landslides and collapses. Establishing a multi-field coupled model (including seepage, temperature, chemical, and stress fields) to simulate the freeze-thaw cycle process of rock slopes, and using a strength reduction method to represent the deterioration process, allows for a preliminary analysis of the characteristics of freeze-thaw cycle failure in rock slopes. However, this method cannot simulate the extension and propagation of internal cracks in rock slopes under freeze-thaw cycles. Furthermore, it reduces the overall rock mass strength, neglecting the stress concentration caused by cracks in localized areas, which may underestimate the impact of cracks on the engineering safety of the rock mass. Fissures are a major factor affecting the frost heave characteristics of rock slopes, and simulating the expansion of fissures in real-world conditions under freeze-thaw cycles is a problem that urgently needs to be solved.

[0003] The discrete element method (DEM) simulates the propagation of cracks by breaking the bonds between rock particles. The extended finite element method (XFEM) and the real fracture process analysis (RFPA) represent crack propagation by the length of the crack extension. However, these numerical simulations struggle to accurately depict realistic crack morphology and do not consider the influence of water frost heave forces within the crack extension. While techniques like CT scans can capture realistic crack morphology, these methods are largely applicable to small sample sizes and are insufficient for capturing cracks within rock masses such as slopes. The foundation and key to overcoming these shortcomings lies in finding a method capable of simulating crack propagation in rock masses of different scales during freeze-thaw cycles, generating cracks that accurately represent realistic crack morphology, and establishing a model applicable to complex numerical calculations. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a simulation method for the random propagation of rock slope fissures that takes into account the effects of freeze-thaw cycles. This method is not limited by scale and can simulate the extension and propagation process of fissures in rock masses of different scales under freeze-thaw cycles and the actual fissure morphology.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A simulation method for the stochastic propagation of fractures in rock slopes considering freeze-thaw cycles includes the following steps:

[0007] Step 1: Determine the area of ​​crack propagation based on the actual situation of the simulated object;

[0008] Step 2: Determine the elastic modulus E of the rock mass based on the actual conditions of the simulated object. s Poisson's ratio v s and tensile strength f t ;

[0009] Step 3: Based on the actual situation of the simulated object, determine the initial crack length 'a', width 'b', and number. As the number of freeze-thaw cycles increases, calculate and update the shape factor 'η'. n ;

[0010] Step 4: Determine the elastic modulus E of ice based on the actual conditions of the simulated object. i Compared to Poisson's ratio v i The frost heave s and freezing rate q of fissure water were calculated, and the effective volumetric expansion coefficient β of the water-ice phase transition was also calculated. e ;

[0011] Step 5: Based on the parameters determined in Steps 2-4, calculate the frost heave force p generated by the water-ice phase transition in each fracture. n ;

[0012] Step 6: Using the maximum tensile stress as the fracture criterion, compare the tensile strength f of the rock mass in Step 2. t And the frost heave force p in step 5 n The size of p n ≥f t Then the crack has reached the propagation condition;

[0013] Step 7: Determine the fracture volume increment ΔV n Is it greater than 0?

[0014] Step 8: If p n ≥f t And ΔV n If the value is greater than 0, the crack is determined to propagate along the tip; otherwise, the crack is determined not to propagate.

[0015] Step 9: Using the expanded crack as the initial crack, simulate the cracking process in the next freeze-thaw cycle according to steps 1-8 until one end of the crack reaches the boundary of the expanded region or the number of freeze-thaw cycles reaches the maximum value, at which point the simulation ends.

[0016] Furthermore, in step 3, the location and tilt angle of the crack can be fixed or random, and the formula for calculating the crack shape factor is as follows:

[0017]

[0018] Furthermore, in step 4, the effective volumetric expansion coefficient of the water-ice phase transition determines the volumetric expansion ΔV of the crack. n β e and ΔV n The calculation formulas are as follows:

[0019] β e =s(1-e -qt );

[0020] ΔV n =β e V n-1 ;

[0021] In the formula: V n-1 Let t be the volume of the crack after n-1 freeze-thaw cycles, and t be the freezing time.

[0022] Furthermore, in step 5, the frost heave force p is calculated. n Assuming the water in the fissures is saturated and its compressibility is neglected, as well as the rock strain caused by the ambient temperature gradient during freezing, and that the frost heave force is uniformly distributed in the fissures, the rock mass is treated as an isotropic elastic medium. The frost heave force, p, is calculated within the scope of a plane strain problem. n The calculation formula is as follows:

[0023]

[0024] In addition, in step 8, due to the stress concentration effect at the crack tip, the crack will extend and expand along the crack tip. The shape of the crack after expansion remains unchanged, and the crack is always filled with water.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0026] (1) This invention simulates the damage and deterioration process of rock slopes under freeze-thaw cycles based on MATLAB code, and can simulate the real crack morphology.

[0027] (2) The method of the present invention is not limited by scale and can simulate the extension and expansion process of cracks in rock masses of different scales under the action of freeze-thaw cycles;

[0028] (3) After n freeze-thaw cycles, the crack extends along the tip and the extended crack is still in a water-saturated state. The influence of the freeze-thaw force generated by the water-ice phase change of the initial crack and the extended crack section is considered in the n+1 freeze-thaw cycles, which is consistent with the actual working conditions.

[0029] (4) The present invention can efficiently simulate the extension and propagation process of cracks, and the generated model can be applied to complex numerical calculations with high computational efficiency. Attached Figure Description

[0030] Figure 1 This is a flowchart simulating the crack propagation process during freeze-thaw cycles in an embodiment of the present invention;

[0031] Figure 2 The shape and dimensions of the slopes in embodiments 1 and 2 of this invention;

[0032] Figure 3 This is a schematic diagram of the basic morphology and propagation mode of the crack in Embodiments 1 and 2 of the present invention, wherein P1, P2, and P3 represent the probability of the crack propagating in different directions, and the angle between adjacent propagation directions is 60°.

[0033] Figure 4 This is a schematic diagram of the model for calculating frost heave force in Embodiments 1 and 2 of the present invention;

[0034] Figure 5 This is the expansion process of a single crack in a rock slope under freeze-thaw cycles in Embodiment 1 of the present invention. a, b, and c represent the random single crack models after 25, 60, and 120 freeze-thaw cycles of the slope, respectively.

[0035] Figure 6 This is the expansion process of multiple cracks in the rock slope under the action of freeze-thaw cycles in Example 2. a and b represent the random multi-crack model after 50 and 60 freeze-thaw cycles, respectively. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. 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 of ordinary skill in the art without creative effort are within the scope of protection of the present invention. It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0037] The present invention will be further described below with reference to specific embodiments, but these are not intended to limit the scope of the invention.

[0038] Example 1:

[0039] See Figure 1 The simulation of the extension and propagation process of a single crack in a rock slope under freeze-thaw cycles includes the following steps:

[0040] Step 1: The dimensions of the slope are as follows Figure 2 As shown, the size of this slope is the area where the cracks propagate;

[0041] Step 2: Elastic modulus E of the rock mass s= 4.78 GPa, Poisson's ratio v s =0.26, tensile strength f t =7MPa;

[0042] Step 3: Create a surface fissure in the rock slope, with a size of 40×20cm. 2 The location is randomly generated; the initial crack shape coefficient η1 = 0.5, and the initial crack shape generated based on the MATLAB algorithm is as follows: Figure 3 As shown;

[0043] Step 4: Elastic modulus E of ice i =0.80 GPa, Poisson's ratio v i =0.30, the frost heave s and freezing rate q of fissure water are 1.128% and 0.2371 respectively; then the effective volumetric expansion coefficient β e The expression is as follows:

[0044] β e =0.01128×(1-e -0.2371t );

[0045] In the formula, t is the freezing time;

[0046] Step 5: Based on the parameters determined in Steps 2-4, calculate the frost heave force p generated by the water-ice phase change. n ,See Figure 4 In calculating the frost heave force p n Assuming the water in the fissures is saturated and its compressibility is neglected, as well as the rock strain caused by the ambient temperature gradient during freezing, and that the frost heave force is uniformly distributed in the fissures, the rock mass is treated as an isotropic elastic medium. The frost heave force, p, is calculated within the scope of a plane strain problem. n The calculation formula is as follows:

[0047]

[0048] Step 6: Compare the tensile strength f of the rock mass in Step 2. t And the frost heave force p in step 5 n The size of p n ≥f t Then the crack has reached the propagation condition;

[0049] Step 7: Determine the fracture volume increment ΔV n Is it greater than 0, ΔV n The calculation formula is: ΔV n =β e V n-1 In the formula: V n-1 Let t be the volume of the crack after n-1 freeze-thaw cycles, and t be the freezing time.

[0050] Step 8: When p n ≥f t And ΔV n If the value is greater than 0, the crack is determined to propagate along its tip; otherwise, the crack does not propagate.

[0051] Step 9: Using the expanded crack as the initial crack, simulate the crack opening process in the next freeze-thaw cycle according to steps 1-8; the simulation ends when one end of the crack reaches the boundary of the expanded region or the number of freeze-thaw cycles reaches its maximum value. The model obtained from the random simulation is as follows: Figure 5 As shown.

[0052] Example 2:

[0053] The simulation of the extension and propagation process of multiple fissures in a rock slope under freeze-thaw cycles includes the following steps:

[0054] Step 1: The dimensions of the slope are as follows Figure 3 As shown.

[0055] Step 2: Elastic modulus E of the rock mass s = 4.78 GPa, Poisson's ratio v s =0.26, tensile strength f t =7MPa.

[0056] Step 3: Generate multiple surface cracks in the rock slope, each crack measuring 40×20cm. 2 The location is randomly generated. The initial crack shape coefficient η1 = 0.5, and the initial crack shape generated based on the MATLAB algorithm is as follows: Figure 3 As shown;

[0057] Step 4: Elastic modulus E of ice i =0.80 GPa, Poisson's ratio v i =0.30, the frost heave s and freezing rate q of fissure water are 1.128% and 0.2371 respectively; then the expression for the effective volumetric expansion coefficient is as follows:

[0058] β e =0.01128×(1-e -0.2371t )

[0059] Step 5: Based on the parameters determined in Steps 2-4, calculate the frost heave force p generated by the water-ice phase transition in each fracture. n .

[0060] Step 6: When p n ≥f t At that time, the crack reached the conditions for propagation;

[0061] Step 7: Determine the fracture volume increment ΔV n Is it greater than 0?

[0062] Step 8: When p n ≥f t And ΔV n When the value is greater than 0, the crack extends along the tip.

[0063] Step 9: Using the expanded crack as the initial crack, simulate the crack opening process in the next freeze-thaw cycle according to steps 1-8 until one end of the crack reaches the boundary of the expanded region or the number of freeze-thaw cycles reaches the maximum value, at which point the simulation ends; the model obtained from the random simulation is as follows. Figure 6 As shown.

[0064] The above are merely preferred embodiments of the present invention and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should recognize that any equivalent substitutions and obvious changes made based on the content of this specification should be included within the protection scope of the present invention.

Claims

1. A simulation method for the stochastic propagation of cracks in rock slopes considering freeze-thaw cycles, characterized in that, Includes the following steps: Step 1: Determine the area of ​​crack propagation based on the actual situation of the simulated object; Step 2: Determine the elastic modulus of the rock mass based on the actual conditions of the simulated object. E s Poisson's ratio v s and tensile strength f t ; Step 3: Determine the length of the initial crack based on the actual situation of the simulated object. a ,width b And quantity, as the number of freeze-thaw cycles increases, the shape factor is calculated and updated. ; Step 4: Determine the elastic modulus of ice based on the actual conditions of the simulated object. E i Compared to Poisson v i and the frost heave of fissure water s and freezing rate q And calculate the effective volume expansion coefficient of water-ice phase transition. ; Step 5: Based on the parameters determined in Steps 2-4, calculate the frost heave force generated by the water-ice phase transition in each fracture. ; Step 6: Using the maximum tensile stress as the fracture criterion, compare the tensile strength of the rock mass in Step 2. f t And the frost heave force in step 5 The size, if Then the crack has reached the propagation condition; Step 7: Determine the increase in fracture volume Is it greater than 0? Step 8: If and If the crack extends along its tip, it is determined that the crack does not extend; otherwise, it is determined that the crack does not extend. Step 9: Using the expanded crack as the initial crack, simulate the cracking process in the next freeze-thaw cycle according to steps 1-8 until one end of the crack reaches the boundary of the expanded region or the number of freeze-thaw cycles reaches the maximum value, at which point the simulation ends.

2. The simulation method for the random propagation of cracks in rock slopes considering freeze-thaw cycles according to claim 1, characterized in that, In step 3, the formula for calculating the crack shape factor is as follows: 。 3. The simulation method for the random propagation of cracks in rock slopes considering freeze-thaw cycles according to claim 1, characterized in that, In step 4, the effective volumetric expansion coefficient of the water-ice phase transition determines the volume of crack propagation. and The calculation formulas are as follows: ； ； In the formula: for n The volume of the crack after one freeze-thaw cycle. t This is the freeze time.

4. The simulation method for the random propagation of cracks in rock slopes considering freeze-thaw cycles according to claim 1, characterized in that, In step 5, the formula for calculating frost heave force is as follows: 。

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