Slope stability analysis method, system, equipment and medium considering strain softening

Abstract

The present invention discloses a slope stability analysis method, system, equipment and medium considering strain softening. The method takes into account the strain softening effect of rock and soil, and reduces the peak cohesion, peak internal friction angle, residual cohesion and residual internal friction angle by using different reduction coefficients, thereby reflecting the different contribution degrees of these parameters in the slope instability process, and increasing the reduction ratio for the parameters with greater contribution. On the basis of the traditional double reduction coefficient and one reduction ratio, four reduction coefficients and two reduction ratios are introduced, and the proportional relationship between the four reduction coefficients is derived assuming that the cohesion parameters are reduced in equal proportion. The coordinate relationship of the initial points in the four-dimensional space coordinate system is used to derive the expression of the comprehensive safety factor. The comprehensive safety factor obtained thereby is smaller than the result of the traditional equal proportion reduction method, thereby improving the accuracy and reliability of the comprehensive safety factor and more realistically reflecting the stability of the rock and soil mass of the slope.

Description

Technical Field

[0001] The present invention belongs to the field of slope stability analysis, and in particular relates to a slope stability analysis method, system, equipment and medium considering strain softening. Background Art

[0002] The strength reduction method is one of the most commonly used slope stability analysis methods. Based on the principle of strength reserve, the safety factor is defined as the ratio of the slope's strength parameter in its current state to the strength parameter in its critical state. The strength reduction method is highly compatible with various geological conditions and is not restricted by the shape and location of the sliding surface. Furthermore, most rock and soil masses exhibit significant strain softening properties, making the traditional limit equilibrium method, based on the basic rigid body assumption, inadequate for calculating these special slopes. Consequently, the strength reduction method has become widely used in slope engineering.

[0003] To address the theoretical shortcoming of traditional strength reduction methods, which always reduce strength parameters proportionally, researchers at home and abroad have proposed a dual reduction coefficient method to account for the varying contributions of cohesion and internal friction angle as a slope reaches its critical state. However, current dual reduction coefficient methods are based on the Mohr-Coulomb constant model. Strain-softening strength reduction methods applicable to strain-softening materials still employ an equal reduction of peak cohesion, peak internal friction angle, residual cohesion, and residual internal friction angle. Currently, no method has been proposed to calculate the safety factor of a strain-softening slope that considers the varying contributions of these four parameters.

[0004] In summary, current slope stability analysis methods that consider strain softening have shortcomings. Slope stability calculations require consideration of both the strain softening properties of the rock mass itself and the varying contributions of peak cohesion, peak internal friction angle, residual cohesion, and residual internal friction angle to the safety factor. Existing strength reduction methods fail to fully account for these two factors, lack sufficient theoretical basis, and determine inaccurate safety factors. Summary of the Invention

[0005] The purpose of the present invention is to provide a slope stability analysis method, system, equipment and medium that take strain softening into account, so as to overcome the problem that the traditional method does not take into account the different contributions of peak cohesion, peak internal friction angle, residual cohesion and residual internal friction angle to the safety factor, resulting in inaccurate calculation of the safety factor.

[0006] The present invention solves the above technical problems through the following technical solutions: a slope stability analysis method considering strain softening, comprising the following steps:

[0007] Step 1: Establish a numerical calculation model for the slope, and determine the initial values ​​of calculation parameters related to the strain softening slope based on the numerical calculation model;

[0008] Step 2: reducing each of the calculation parameters individually until the slope numerical calculation model becomes unstable, obtaining a reduction coefficient corresponding to each of the calculation parameters, and obtaining a proportional relationship between the reduction coefficients corresponding to different calculation parameters;

[0009] Step 3: combining the initial values ​​of the calculation parameters, performing reduction iterations on different calculation parameters according to the proportional relationship until the slope numerical calculation model reaches a critical state, thereby obtaining the critical state calculation parameters under the proportional relationship;

[0010] Step 4: Determine a comprehensive safety factor based on the initial values ​​of the calculation parameters and the critical state calculation parameters under the proportional relationship.

[0011] Furthermore, in step 1, the calculated parameters include peak cohesion, peak internal friction angle, residual cohesion, and residual internal friction angle.

[0012] Furthermore, in step 3, the calculation formula for the reduction iteration is:

[0013]

[0014]

[0015] in, is the peak cohesion after the i-th reduction, is the peak internal friction angle after the i-th reduction, is the residual cohesion after the i-th reduction, is the residual internal friction angle after the i-th reduction, F cp is the reduction coefficient corresponding to the peak cohesion, is the reduction coefficient corresponding to the peak internal friction angle, F cr is the reduction coefficient corresponding to the residual cohesion, is the reduction coefficient corresponding to the residual internal friction angle. When i=1, is the initial value of peak cohesion, is the initial value of the peak internal friction angle, is the initial value of residual cohesion, is the initial value of the residual internal friction angle.

[0016] Furthermore, in step 4, the calculation formula of the comprehensive safety factor is:

[0017]

[0018] Among them, F is the comprehensive safety factor, is the initial value of peak cohesion, is the initial value of the peak internal friction angle, is the initial value of residual cohesion, is the initial value of the residual internal friction angle, c' p is the critical peak cohesion, is the critical peak internal friction angle, c' r is the residual cohesion at the critical state, is the residual internal friction angle in the critical state.

[0019] The present invention also provides a slope stability analysis system considering strain softening, comprising:

[0020] A model building unit is used to establish a numerical calculation model of the slope and determine the initial values ​​of calculation parameters related to the strain softening slope according to the numerical calculation model of the slope;

[0021] a reduction coefficient determination unit, configured to reduce each of the calculation parameters individually until the slope numerical calculation model becomes unstable, obtain a reduction coefficient corresponding to each of the calculation parameters, and obtain a proportional relationship between the reduction coefficients corresponding to different calculation parameters;

[0022] a critical parameter determination unit, configured to perform iterative reduction on different calculation parameters according to the proportional relationship in combination with the initial values ​​of the calculation parameters, until the slope numerical calculation model reaches a critical state, and obtain critical state calculation parameters under the proportional relationship;

[0023] The safety factor determination unit is used to determine the comprehensive safety factor according to the initial value of the calculation parameter and the critical state calculation parameter under the proportional relationship.

[0024] Furthermore, the critical parameter determination unit is specifically configured to perform iterative reduction on different calculation parameters according to the proportional relationship according to the following calculation formula:

[0025]

[0026]

[0027] in, is the peak cohesion after the i-th reduction, is the peak internal friction angle after the i-th reduction, is the residual cohesion after the i-th reduction, is the residual internal friction angle after the i-th reduction, F cp is the reduction coefficient corresponding to the peak cohesion, is the reduction coefficient corresponding to the peak internal friction angle, F cr is the reduction coefficient corresponding to the residual cohesion, is the reduction coefficient corresponding to the residual internal friction angle. When i=1, is the initial value of peak cohesion, is the initial value of the peak internal friction angle, is the initial value of residual cohesion, is the initial value of the residual internal friction angle.

[0028] Furthermore, the safety factor determination unit is specifically configured to calculate the comprehensive safety factor by calculating the parameters according to the following calculation formula:

[0029]

[0030] Among them, F is the comprehensive safety factor, is the initial value of peak cohesion, is the initial value of the peak internal friction angle, is the initial value of residual cohesion, is the initial value of the residual internal friction angle, c' p is the critical peak cohesion, is the critical peak internal friction angle, c' r is the residual cohesion at the critical state, is the residual internal friction angle in the critical state.

[0031] The present invention also provides a device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the slope stability analysis method considering strain softening as described above is implemented.

[0032] The present invention also provides a medium having a computer program stored thereon, which, when executed by a processor, implements the slope stability analysis method considering strain softening as described above.

[0033] Beneficial effects

[0034] Compared with the prior art, the advantages of the present invention are:

[0035] The present invention takes into account the strain softening effect of rock and soil, and reduces the peak cohesion, peak internal friction angle, residual cohesion, and residual internal friction angle using different reduction coefficients, thereby reflecting the different contributions of these parameters in the slope instability process, and increasing the reduction ratio for parameters with greater contributions; on the basis of the traditional double reduction coefficient and one reduction ratio, four reduction coefficients and two reduction ratios are introduced, and the proportional relationship between the four reduction coefficients is derived assuming that the cohesion parameters are reduced in equal proportion; the expression of the comprehensive safety factor is derived using the coordinate relationship of the initial points in the four-dimensional space coordinate system, and the comprehensive safety factor obtained in this way is smaller than the result of the traditional equal proportion reduction method, thereby improving the accuracy and reliability of the comprehensive safety factor and more realistically reflecting the stability of the slope rock and soil. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only one embodiment of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0037] Figure 1 is a flow chart of a slope stability analysis method considering strain softening in an embodiment of the present invention;

[0038] Figure 2 Schematic diagram of a numerical calculation model for slope according to an embodiment of the present invention;

[0039] Figure 3 4 is a simplified relationship diagram of strain softening in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The technical solutions of the present invention are described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. The technical solutions of this application are described in detail below with specific embodiments. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments.

[0041] like Figure 1 As shown, the present embodiment provides a slope stability analysis method considering strain softening, comprising the following steps:

[0042] Step 1: Establish a numerical calculation model for the slope and determine the initial values ​​of the calculation parameters related to the strain softening slope based on the numerical calculation model.

[0043] In this embodiment, the calculation parameters include peak cohesion, peak internal friction angle, residual cohesion, and residual internal friction angle.

[0044] like Figure 2 and 3 As shown, the slope is 10m high, the slope angle is 45°, and the load is 19.6kN / m 3 , considering the strain softening effect, the initial value of the peak cohesion Initial value of peak internal friction angle Initial value of residual cohesion Initial value of residual internal friction angle Plastic shear strain threshold k r =0.02.

[0045] Step 2: Reduce each calculation parameter individually until the slope numerical calculation model becomes unstable, obtain the reduction coefficient corresponding to each calculation parameter, and obtain the proportional relationship between the reduction coefficients corresponding to different calculation parameters.

[0046] Peak cohesion c p , peak internal friction angle Residual cohesion c r , residual internal friction angle The four strength parameters or calculation parameters are introduced into the corresponding reduction factor F cp 、 F cr 、 F cp is the reduction coefficient corresponding to the peak cohesion, is the reduction coefficient corresponding to the peak internal friction angle, F cr is the reduction coefficient corresponding to the residual cohesion, is the reduction coefficient corresponding to the residual internal friction angle. Then introduce two reduction ratios n p 、n r ,in,

[0047] Take the peak parameter to calculate, when the peak cohesion c p The reduction is carried out until the slope numerical calculation model becomes unstable, and the reduction coefficient F is obtained. cp =1.2726; when the peak internal friction angle is The reduction is carried out until the slope numerical calculation model becomes unstable, and the reduction coefficient is obtained. Discount ratio

[0048] Take the residual parameters for calculation. When the residual cohesion c is calculated separately r The reduction is carried out until the slope numerical calculation model becomes unstable, and the reduction coefficient F is obtained. cr =0.4864; when the residual internal friction angle is The reduction is carried out until the slope numerical calculation model becomes unstable, and the reduction coefficient is obtained. Discount ratio

[0049] Assuming that the cohesion parameters are reduced at the same ratio, that is, assuming that F cp :F cr =1:1, and the proportional relationship between the four reduction factors is obtained.

[0050] Step 3: Combined with the initial values ​​of the calculation parameters, different calculation parameters are iterated according to the proportional relationship until the slope numerical calculation model reaches the critical state and the critical state calculation parameters under the proportional relationship are obtained.

[0051] In this embodiment, the calculation formula for the reduction iteration is:

[0052]

[0053]

[0054] in, is the peak cohesion after the i-th reduction, is the peak internal friction angle after the i-th reduction, is the residual cohesion after the i-th reduction, is the residual internal friction angle after the i-th reduction. When i=1, is the initial value of peak cohesion, is the initial value of the peak internal friction angle, is the initial value of residual cohesion, is the initial value of the residual internal friction angle.

[0055] Through the reduction iteration, the slope numerical calculation model reaches the critical state and the proportional relationship is obtained. The critical state calculation parameter, namely the critical state peak cohesion c' p , critical state peak internal friction angle Critical residual cohesion c' r , critical state residual internal friction angle Specifically, c′ p =19.5532e 3 , c′ r =9.7766e 3 ,

[0056] When calculating the safety factor using the strength reduction method, an initial value for the reduction factor is given. Through iterative calculation, the reduction factor converges to a certain value at the time of slope failure. This value is the safety factor. This application considers four different reduction factors, which converge to four fixed values ​​during the iterative calculation. The final comprehensive safety factor is determined by these four fixed values. Step 4: Determine the comprehensive safety factor based on the initial values ​​of the calculation parameters and the critical state calculation parameters under the proportional relationship.

[0057] In this embodiment, Expressed in four-dimensional space, we get the initial point P 0 (20e 3 ,0.2679,10e3 ,0.1763 and critical point P19.5532e 3 ,0.2301,9.7766e 3 The comprehensive safety factor of the slope is expressed as the ratio of the volumes of two hypercubes in four-dimensional space, and the final comprehensive safety factor is 1.0193.

[0058]

[0059] For the initial value The comprehensive safety factor was calculated using the traditional strain softening strength reduction method, and the comprehensive safety factor was 1.0686. The method of the present invention was compared with the traditional strain softening strength reduction method, as shown in Table 1.

[0060] Specific methods Traditional strain softening strength reduction method Method of the present invention Proportional relationship of reduction coefficient 1:1:1:1 1:1.1382:1:0.8669 Comprehensive safety factor 1.0686 1.0193

[0061] As can be seen from Table 1, the stability calculation results obtained by the present invention are highly consistent with those of the traditional method, proving the rationality and accuracy of the present method, and effectively solving the problems and shortcomings of the traditional strain softening slope safety factor calculation method. The safety factor of the slope based on strength reserve is defined as: the ratio of the strength parameter of the slope in the initial state to the strength parameter of the slope in the critical state. The traditional proportional reduction method has only one reduction coefficient. When the application reduction ratio is 1:1:1:1, Using the volume ratio of the hypercube to determine the comprehensive safety factor is an extension of the traditional method. It can consider the different contributions of peak cohesion, peak internal friction angle, residual cohesion, and residual internal friction angle, and determine the comprehensive safety factor under unequal proportions. In addition, the comprehensive safety factor is a dimensionless quantity that can eliminate the cross-influence between parameters.

[0062] Table 2 shows the comparison of the results of the method of the present invention and the traditional strain softening strength reduction method (referred to as the traditional method) under different rock and soil parameters and slope models with different slope angles (30°, 45°, and 60°).

[0063] The first set of rock and soil parameters are: The second set of rock and soil parameters are: The third set of rock and soil parameters are:

[0064] Table 2 Comparison between the method of the present invention and the traditional method under different rock and soil parameters and different slope angles

[0065]

[0066]

[0067] It can be seen from Table 2 that the results of the method of the present invention are similar to those of the traditional strain softening strength reduction method, and are both smaller than the results of the traditional proportional reduction method. The conventional proportional reduction method does not consider the contribution of each parameter. The method of the present invention considers both the strain softening effect and the contribution of different parameters to the comprehensive safety factor, increasing the reduction ratio for parameters with large contributions. The result is smaller than that of the traditional proportional reduction method. Therefore, the comprehensive safety factor obtained by the method of the present invention is more accurate and reliable.

[0068] The present invention provides a slope stability analysis method and system considering strain softening, taking into account the strain softening effect of rock and soil, and by using different reduction coefficients to reduce the peak cohesion, peak internal friction angle, residual cohesion, and residual internal friction angle, the different contributions of these parameters in the slope instability process are reflected, and the reduction ratio of the parameters with greater contribution is increased; on the basis of the traditional double reduction coefficient and one reduction ratio, the present invention introduces four reduction coefficients and two reduction ratios, assumes that the cohesion parameters are reduced in equal proportion, and derives the proportional relationship between the four reduction coefficients; uses the coordinate relationship of the initial points in a four-dimensional space coordinate system to derive the expression of the comprehensive safety factor, and the comprehensive safety factor obtained thereby is smaller than the result of the traditional equal proportion reduction method, thereby improving the accuracy and reliability of the comprehensive safety factor.

[0069] The above disclosure is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of changes or modifications within the technical scope disclosed in the present invention, and they should all be covered by the scope of protection of the present invention.

Claims

1. A slope stability analysis method considering strain softening, characterized in that: The following steps are involved: Step 1: Establish a numerical calculation model for the slope, and determine initial values ​​of calculation parameters related to the strain softening slope based on the numerical calculation model; the calculation parameters include peak cohesion, peak internal friction angle, residual cohesion, and residual internal friction angle; Step 2: reducing each of the calculation parameters individually until the slope numerical calculation model becomes unstable, obtaining a reduction coefficient corresponding to each of the calculation parameters, and obtaining a proportional relationship between the reduction coefficients corresponding to different calculation parameters; Step 3: combining the initial values ​​of the calculation parameters, performing reduction iterations on different calculation parameters according to the proportional relationship until the slope numerical calculation model reaches a critical state, thereby obtaining the critical state calculation parameters under the proportional relationship; Step 4: determining a comprehensive safety factor based on the initial values ​​of the calculation parameters and the critical state calculation parameters under the proportional relationship; The calculation formula of the comprehensive safety factor is: Among them, F is the comprehensive safety factor, is the initial value of peak cohesion, is the initial value of the peak internal friction angle, is the initial value of residual cohesion, is the initial value of the residual internal friction angle, c' p is the critical peak cohesion, is the critical peak internal friction angle, c' r is the residual cohesion at the critical state, is the residual internal friction angle in the critical state.

2. The slope stability analysis method considering strain softening according to claim 1, characterized in that: In step 3, the calculation formula for the reduction iteration is: in, is the peak cohesion after the i-th reduction, is the peak internal friction angle after the i-th reduction, is the residual cohesion after the i-th reduction, is the residual internal friction angle after the i-th reduction, F cp is the reduction coefficient corresponding to the peak cohesion, is the reduction coefficient corresponding to the peak internal friction angle, F cr is the reduction coefficient corresponding to the residual cohesion, is the reduction coefficient corresponding to the residual internal friction angle. When i=1, is the initial value of peak cohesion, is the initial value of the peak internal friction angle, is the initial value of residual cohesion, is the initial value of the residual internal friction angle.

3. A slope stability analysis system considering strain softening, characterized in that: include: A model building unit is used to establish a numerical calculation model of the slope and determine the initial values ​​of calculation parameters related to the strain softening slope according to the numerical calculation model of the slope; The calculation parameters include peak cohesion, peak internal friction angle, residual cohesion, and residual internal friction angle; a reduction coefficient determination unit, configured to reduce each of the calculation parameters individually until the slope numerical calculation model becomes unstable, obtain a reduction coefficient corresponding to each of the calculation parameters, and obtain a proportional relationship between the reduction coefficients corresponding to different calculation parameters; a critical parameter determination unit, configured to perform iterative reduction on different calculation parameters according to the proportional relationship in combination with the initial values ​​of the calculation parameters, until the slope numerical calculation model reaches a critical state, and obtain critical state calculation parameters under the proportional relationship; A safety factor determination unit is used to determine a comprehensive safety factor according to the initial value of the calculation parameter and the critical state calculation parameter under the proportional relationship, wherein the calculation formula of the comprehensive safety factor is: Among them, F is the comprehensive safety factor, is the initial value of peak cohesion, is the initial value of the peak internal friction angle, is the initial value of residual cohesion, is the initial value of the residual internal friction angle, c' p is the critical peak cohesion, is the critical peak internal friction angle, c' r is the residual cohesion at the critical state, is the residual internal friction angle in the critical state.

4. The slope stability analysis system considering strain softening according to claim 3, characterized in that: The critical parameter determination unit is specifically configured to perform iterative reduction on different calculation parameters according to the proportional relationship according to the following calculation formula: in, is the peak cohesion after the i-th reduction, is the peak internal friction angle after the i-th reduction, is the residual cohesion after the i-th reduction, is the residual internal friction angle after the i-th reduction, F cp is the reduction coefficient corresponding to the peak cohesion, is the reduction coefficient corresponding to the peak internal friction angle, F cr is the reduction coefficient corresponding to the residual cohesion, is the reduction coefficient corresponding to the residual internal friction angle. When i=1, is the initial value of peak cohesion, is the initial value of the peak internal friction angle, is the initial value of residual cohesion, is the initial value of the residual internal friction angle.

5. A device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the slope stability analysis method considering strain softening as claimed in claim 1 or 2 is implemented.

6. A medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the slope stability analysis method considering strain softening as claimed in claim 1 or 2 is implemented.

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