A method for analyzing the long-term stability of soft rock slopes

Abstract

The present invention discloses a method for analyzing the long-term stability of a soft rock slope, including: S1: classifying soft rock creep damage and establishing various damage equations; S2: dividing the soft rock creep curve into a stable creep stage and an unstable creep stage; S3: establishing a creep equation; S4: establishing a three-dimensional creep damage mathematical model; S5: writing a custom constitutive model program; S6: establishing a slope model, and obtaining the distribution of the plastic zone of the slope, the potential sliding surface and the horizontal displacement change law under different dry-wet cycle times through the custom constitutive model program; S7: when the plastic zone of the slope is connected, the potential sliding surface is formed, and the horizontal displacement is accelerated under a certain dry-wet cycle number, it is determined that the soft rock slope is creep damaged under the dry-wet cycle number. The present invention takes into account the coupling effect of dry-wet cycles, axial pressure and time, and analyzes and predicts the long-term stability of the soft rock slope through simulation results.

Description

Technical Field

[0001] The invention belongs to the field of rock and soil technology, and specifically relates to an analysis method for the long-term stability of a soft rock slope. Background Art

[0002] After the excavation of soft rock slopes, the rock mass damage evolves from the surface to the inside due to the repeated dry-wet cycles of the atmosphere, and the long-term stability of the slope decreases accordingly, often causing geological disasters such as shallow slope instability, landslides and collapses; especially for some exposed soft rock slopes, the problem of creep damage is more serious. Accurate evaluation of the long-term stability of soft rock slopes is of great significance to my country's highway construction. In the past, the evaluation of the stability of soft rock slopes, but mostly only considered the damage and degradation of rock mass strength caused by dry-wet cycles, and rarely analyzed the long-term stability of soft rock slopes. Facts and practice have proved that the dry-wet cycles of the atmosphere have a significant impact on the chemical composition, microstructure and creep characteristics of soft rock, which is bound to have an adverse effect on the long-term stability of soft rock slopes. At present, there is still a lack of analysis methods that can accurately analyze the long-term stability of soft rock slopes. Summary of the invention

[0003] In view of the above-mentioned problems existing in the prior art, the purpose of the present invention is to provide an analysis method for the long-term stability of soft rock slopes, which takes into account the coupling effects of dry-wet cycles, axial pressure and time. The long-term stability of soft rock slopes can be analyzed and predicted by simulation software based on an established mathematical model, thereby reducing the analysis cost and improving the analysis and prediction efficiency.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] A method for analyzing the long-term stability of a soft rock slope comprises the following steps:

[0006] Step S1: According to the evolution law of the microstructure and macroscopic mechanical damage characteristics of the soft rock creep failure process under the action of dry-wet cycles, the soft rock creep damage is classified and various damage equations are established. The soft rock creep damage is divided into three categories: initial damage, time-dependent damage and crack extension damage, so as to quantitatively characterize the damage of the soft rock caused by dry-wet cycles, stress and time;

[0007] Step S2: According to the creep deformation law of soft rock under the action of dry-wet cycles, the creep curve of soft rock is divided into a stable creep stage and an unstable creep stage, and viscoelastic elements, viscoplastic elements and a creep model are constructed. The creep model is composed of viscoelastic elements and viscoplastic elements connected in series to characterize the viscoelastic strain and viscoplastic strain of soft rock under different stress states;

[0008] Step S3: Using the damage equation of step S1 and the creep model of step S2, the creep equations of the stable creep stage and the unstable creep stage are established. The coupled damage variables of initial damage and aging damage are used to correct the viscoelastic component parameters. The crack extension damage is introduced to correct the viscoplastic component parameters. A new soft rock creep damage model is constructed to characterize the time-varying law of strain of soft rock under different dry-wet cycles and stresses.

[0009] Step S4: Establish a three-dimensional creep damage mathematical model to analyze the stability of the time-dependent deformation characteristics of the soft rock slope under the action of dry-wet cycles;

[0010] Step S5: Select a simulation software, perform secondary development on the selected simulation software based on the mathematical model established in step S4, and write a custom constitutive model program;

[0011] Step S6: using modeling software to establish a slope model for stability analysis, and importing it into the simulation software of step S5, using the custom constitutive model program of step S5, to obtain the distribution of plastic zones, potential sliding surfaces and horizontal displacement variation of the slope under different dry-wet cycles;

[0012] Step S7: When the plastic zone of the slope is connected, the potential sliding surface is formed, and the horizontal displacement increases rapidly under a certain number of dry-wet cycles, it is determined that the soft rock slope is creep-damaged under the number of dry-wet cycles.

[0013] As a further improvement of the above technical solution:

[0014] In step S1, the initial damage Mesoscopic structural damage caused by the development of pores in soft rock due to dry-wet cycles; time-dependent damage Changes in rock mechanical properties caused by the directional flow of rock particles over time; crack extension damage It is the damage and deterioration of rock structure caused by the expansion and connection of rock cracks under load.

[0015] Preferably,

[0016] ;

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] in, is the total cross-sectional area, is the pore area, is the rock porosity, For the Wet-dry cycle under stage axial pressure The instantaneous elastic modulus, When time approaches infinity Wet-dry cycle under stage axial pressure The elastic modulus, is a function related to the number of dry-wet cycles and the axial pressure, It's time. is with , , Related functions, is with , , Related functions, yes The adaptation of the moment, and is the material parameter, , , They are the three principal stresses of soft rock in three mutually perpendicular directions in space, is the crack initiation angle, is the Poisson's ratio of the rock, is the crack radius, is the stress intensity factor of rock, According to the energy reciprocity theorem, is a parameter related to axial pressure. The least square method is used to calculate the soft rock under the action of dry-wet cycles. , , Fitting is performed to establish a functional relationship with the axial pressure.

[0026] In step S2, during the stable creep stage, < , soft rock only undergoes transient elastic and viscoelastic strains under load; in the unstable creep stage, ≥ , soft rock undergoes instantaneous elastic, viscoelastic and viscoplastic strains under load, among which, is the axial pressure, For long term strength.

[0027] In step S2, the viscoelastic element is composed of a spring and a damper, and the viscoplastic element is composed of a friction plate and a nonlinear damping element in parallel.

[0028] In step S3, during the stable creep stage, the damage of soft rock during the stable creep stage under the action of dry-wet cycles is Initial damage Time-related damage Coupling effect.

[0029] In step S3, during the stable creep stage, the damage equation of soft rock under the action of dry-wet cycles is:

[0030] .

[0031] In step S3, during the unstable creep stage, the time-dependent elastic modulus damage is the coupling effect of initial damage and time-dependent damage. , the viscoplastic viscosity coefficient damage is the crack extension damage .

[0032] In step S3, the creep equation in the unstable creep stage is:

[0033] ;

[0034] = ;

[0035] in, For strain, is the initial viscosity coefficient, is the initial elastic modulus.

[0036] when < When , the creep damage equation is:

[0037] ;

[0038] when ≥ When , the creep damage equation is:

[0039] ;

[0040] in, is the strain in the axial compression direction, , is the shear modulus, the bulk modulus .

[0041] During the secondary development in step S5, the mathematical model established in step S4 is converted into a function form recognizable by the selected simulation software, a new project is created based on the development environment and necessary plug-ins, all options are completed according to the requirements of the simulation software, and a custom constitutive model program is generated.

[0042] In step S5, the simulation software selected is FLAC3D, and a custom constitutive model is written in C++ language and embedded into the FLAC3D software for analysis.

[0043] In step S7, the accelerated increase of the horizontal displacement means that the horizontal displacement of the monitoring point presents a nonlinear change over time, and the slope of the horizontal displacement increasing over time increases.

[0044] The beneficial effects of the present invention are:

[0045] (1) The present invention constructs a creep damage constitutive equation for soft rock under the action of dry-wet cycles, i.e., a creep damage mathematical model. On this basis, an algorithm for the constitutive model is developed to simulate and analyze the mechanical properties and deformation laws of soft rock slopes under the action of atmospheric dry-wet cycles, and a method for accurately analyzing the long-term stability of soft rock slopes is proposed.

[0046] (2) The creep deformation mechanism of soft rock under the action of dry-wet cycles is analyzed from a microscopic perspective. The porosity, time-dependent elastic modulus and crack extension parameters are proposed as damage variables. The initial, time-dependent and crack extension damage equations of soft rock are established, which can accurately reflect the damage evolution law of soft rock under the action of dry-wet cycles, axial pressure and time factors.

[0047] (3) Based on fracture mechanics and the energy reciprocity theorem, it is proposed to use the viscoplastic creep rate to characterize the crack growth rate. A quantitative characterization relationship between rock microcrack growth parameters and damage is established, which provides a new idea for the quantitative study of rock crack growth damage evolution.

[0048] (4) It is proposed to use viscoelastic elements and elastoplastic elements to characterize the nonlinear characteristics of soft rock creep. Specifically, based on the element model theory, a soft rock creep model is established by constructing viscoelastic elements and viscoplastic elements in series. The coupled damage variables of initial damage and time-dependent damage are used to correct the parameters of the viscoelastic elements. Crack extension damage is introduced to correct the parameters of the viscoplastic elements. A new rock creep damage model is constructed. This model can better characterize the nonlinear creep characteristics of soft rock under the action of dry-wet cycles, and the physical meaning of the parameters is clear. It can be used for long-term stability analysis of carbonaceous mudstone slopes.

[0049] (5) Taking the three conditions of plastic zone penetration, potential slip surface formation and accelerated increase of horizontal displacement as the criteria for creep failure of carbonaceous mudstone slope is equivalent to establishing an evaluation standard for the long-term stability of carbonaceous mudstone slope. By comparing with the results of field investigation, it is shown that the analysis method of this scheme can better reveal the evolution law of slope rock damage with depth and reflect the characteristics of shallow slope sliding failure. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1(a)~1(d) These are the experimental results of triaxial creep curves of soft rock when the number of dry-wet cycles are 0, 3, 6, and 9.

[0051] Figure 2 This is a schematic diagram of the mesostructure evolution of soft rock.

[0052] Figure 3 Instantaneous elastic modulus of soft rock under dry-wet cycles.

[0053] Figures 4(a) to 4(d) They are the elastic modulus of soft rock when the number of dry-wet cycles is 0, 3, 6, and 9 respectively.

[0054] Figure 5(a) is a viscoelastic element model.

[0055] Figure 5(b) is the nonlinear damping element model.

[0056] Figure 5(c) is the friction plate model.

[0057] Figure 5(d) is the creep model.

[0058] Figure 6(a)~6(d) They are the soft rock creep experimental results and model calculation results when the number of dry-wet cycles is 0, 3, 6, and 9 respectively.

[0059] Figure 7 It is a comparison diagram of soft rock numerical simulation and test results when verifying a custom constitutive model program in an embodiment of the present invention.

[0060] Figure 8 It is a schematic diagram of a soft rock slope model according to an embodiment of the present invention.

[0061] Figures 9(a) to 9(f) It is a cloud map of the plastic zone of a charcoal mudstone slope when the number of dry-wet cycles of soft rock is 500, 1000, 1500, 2000, 3000 and 4000 times respectively, which is obtained by the custom constitutive model program of the present invention.

[0062] Figure 10(a) to 10(f) It is a cloud diagram of the maximum shear strain increment of a carbonaceous mudstone slope when the number of dry-wet cycles of soft rock is 500, 1000, 1500, 2000, 3000 and 4000 times respectively, obtained by the custom constitutive model program of the present invention.

[0063] Figures 11(a) to 11(f) It is a creep curve of each monitoring point of a carbonaceous mudstone slope when the number of dry-wet cycles of soft rock is 500, 1000, 1500, 2000, 3000 and 4000 respectively, which is obtained by the custom constitutive model program of the present invention. DETAILED DESCRIPTION

[0064] The specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the present invention, and is not used to limit the present invention.

[0065] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used here to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0066] A method for analyzing the long-term stability of a soft rock slope comprises the following steps:

[0067] Step S1: Classify the soft rock creep damage and establish the damage equations of each category;

[0068] Step S2: Divide the soft rock creep curve into a stable creep stage and an unstable creep stage, and construct viscoelastic elements, viscoplastic elements and a creep model;

[0069] Step S3: using the damage equation of step S1 and the creep model of step S2 to establish creep equations of the stable creep stage and the unstable creep stage;

[0070] Step S4: Establish a three-dimensional creep damage model.

[0071] Step S5: Select a simulation software, perform secondary development on the selected simulation software based on the mathematical model established in step S4, and write a custom constitutive model program;

[0072] Step S6: using modeling software to establish a slope model for stability analysis, and importing it into the simulation software of step S5, using the custom constitutive model program of step S5, to obtain the distribution of plastic zones, potential sliding surfaces and horizontal displacement variation of the slope under different dry-wet cycles;

[0073] Step S7: When the plastic zone of the slope is connected, the potential sliding surface is formed, and the horizontal displacement increases rapidly under a certain number of dry-wet cycles, it is determined that the soft rock slope is creep-damaged under the number of dry-wet cycles.

[0074] In this embodiment, the soft rock used is carbonaceous mudstone.

[0075] The following is a detailed analysis of this plan.

[0076] Firstly, the creep characteristics are analyzed and the triaxial creep test results of soft rock under dry-wet cycle are obtained by using the Boltzmann superposition principle. Figure 1(a)~1(d) In the figure, For axial compression, multiple or multi-level axial compression loading is performed under the same number of dry-wet cycles. The loading levels are 8 or 7, as follows: The triaxial rheological tester RLW-2000 is used to conduct triaxial compression rheological tests on the samples that have completed the dry-wet cycle. The confining pressure is set to 2MPa, and a graded incremental loading method is used. The first level of creep test loading is designed to be 40% of the uniaxial compressive strength, that is, 14.26MPa. The graded loading increment is 3MPa. Each level of axial compression loading lasts for 48 hours, and then the next level of loading is performed until the rock sample is destroyed. Figure 1(a)~1(d) It can be seen that the axial strain of soft rock increases with the increase of dry-wet cycles and axial pressure. Under the same axial pressure, the strain of soft rock increases with the increase of dry-wet cycles; the axial strain of soft rock samples with 0, 3, 6 and 9 dry-wet cycles under axial pressure of 17.26 MPa after creep for 20 hours is 0.606×10 -3 , 0.958×10 -3 , 1.168×10 -3 and 1.340×10 -3 The average axial strain increases by 9.75×10 -5 Under the same number of dry-wet cycles, the axial strain of soft rock increases with the increase of axial pressure; the axial strain of soft rock with 6 dry-wet cycles at level 1 to 7 creep for 20h is 1.168×10 -3 , 1.468×10 -3 , 1.786×10 -3 , 2.144×10 -3 , 2.538×10 -3 , 2.978×10 -3 and 3.364×10 -3The average axial strain increases by 3.34×10 -4 In addition, soft rock has a low axial pressure ( < , is the long-term strength of rock), only attenuation creep occurs, and the strain increases with time first and then remains stable; when the axial pressure is high ( ≥ ), first decay creep occurs, then the strain gradually increases with time, and finally creep failure occurs. When the dry-wet cycle is 0 and 3 times, the soft rock only undergoes decay creep in the first four levels of loading (23.26MPa), and accelerated creep failure occurs at the eighth level of loading (35.26MPa); when the dry-wet cycle is 6 and 9 times, the soft rock only undergoes decay creep in the first three levels of loading (20.26MPa), and accelerated creep failure occurs at the seventh level of loading (32.26MPa).

[0077] From the above, we can see that the number of dry-wet cycles, axial pressure and time are important factors affecting the creep of soft rock.

[0078] The creep damage mechanism is as follows: The schematic diagram of the microstructure evolution of the soft rock creep damage process under the action of dry-wet cycles is shown in Figure 2 Soft rock is affected by geological structures, resulting in tiny pores inside it. After the dry-wet cycle, the internal pores gradually develop and increase in number. Under the load, the pores in the soft rock are first compressed and elastically deformed. As time goes by, the soft rock particles flow in a directional manner, causing the development of internal microcracks, and the soft rock undergoes viscoelastic strain. ; When the axial pressure is greater than the long-term strength of the rock When the load continues, the crack gradually expands and the plastic strain of the soft rock Gradually develop; when the crack extension continues for a certain period of time, the cracks accelerate and connect, the plastic strain of the soft rock increases sharply, and finally deformation and failure occur. The value of can be 70-80% of the uniaxial compressive strength, or refer to other solutions in the prior art.

[0079] In step S1, according to Figure 2 The evolution law of the microstructure and macroscopic mechanical damage characteristics of soft rock creep damage process under the action of medium-wet-dry cycle. The creep damage of soft rock can be divided into initial damage , Time-dependent damage and crack extension damage Category 3. Initial damage Mesoscopic structural damage caused by the development of pores in soft rock due to dry-wet cycles; time-dependent damage Changes in rock mechanical properties caused by the directional flow of rock particles over time; crack extension damage It is the damage and deterioration of rock structure caused by the expansion and connection of rock cracks under load.

[0080] The following equations are established for the three types of damage.

[0081] 1. Initial damage equation

[0082] Under the action of dry-wet cycles, soft rock pores develop, resulting in a reduction in the stress-bearing area of ​​the rock mesostructure. According to the geometric damage theory, rock damage is defined by the stress-bearing area of ​​the rock:

[0083] (1)

[0084] in, For the initial damage, is the total cross-sectional area, is the pore area, is the rock porosity.

[0085] 2. Time-dependent damage equation

[0086] Under continuous load, soft rock particles flow in a directional manner over time, which causes changes in its macroscopic mechanical properties. According to the Lemaitre strain equivalence principle, the rock damage equation is expressed as:

[0087] (2-1)

[0088] in, and are the axial pressure and strain vectors, respectively, \left [ {C} \right ] is the material elastic matrix, is the rock damage variable. The deformation of rock under nominal axial pressure is equivalent to the deformation under effective axial pressure, then:

[0089] (2-2)

[0090] In the formula, , , and They are the nominal axial pressure, nominal elastic modulus, effective axial pressure and effective elastic modulus respectively.

[0091] According to formula (2-1) and formula (2-2), we can get:

[0092] (3)

[0093] In the formula, Time-dependent damage to rocks.

[0094] The instantaneous elastic modulus of soft rock under the action of dry-wet cycles can be calculated by the following formula:

[0095] (4)

[0096] In the formula, For the Wet-dry cycle under stage axial pressure The instantaneous elastic modulus, Creep time Approaching 0 Wet-dry cycle under stage axial pressure The axial pressure increment is For the Wet-dry cycle under stage axial pressure The instantaneous strain increment is calculated by formula (4) to obtain the instantaneous elastic modulus of soft rock. Figure 3 , in the figure is the elastic modulus value corresponding to the fitting curve obtained under fixed axial pressure, is the number of cycles, is the correlation coefficient.

[0097] The instantaneous elastic modulus of soft rock under the action of dry-wet cycles is fitted by the least squares method:

[0098] (5)

[0099] in, , is a parameter related to axial pressure. , The functional relationship with the axial pressure is:

[0100] (6)

[0101] (7)

[0102] Substituting equations (6) and (7) into equation (5), we can obtain the instantaneous elastic modulus equation of soft rock under the action of dry-wet cycles:

[0103] (8)

[0104] The elastic modulus of the soft rock under the first four loading levels of dry-wet cycles is shown in Figure 4 (a) to (d). The elastic modulus decreases rapidly with time, and then remains basically stable after 15 hours. The elastic modulus at stability decreases with the increase of the number of dry-wet cycles.

[0105] The relationship between the elastic modulus of soft rock under the action of dry-wet cycles is obtained by fitting the least square method:

[0106] (9)

[0107] For the Wet-dry cycle under stage axial pressure Second-rate The elastic modulus at the moment, parameter , and It is a function related to the number of dry-wet cycles and axial pressure. Through parameter fitting, we get:

[0108] (10)

[0109] (11)

[0110]

[0111] Analyzing formula (9), when =0:

[0112] (12)

[0113] when → hour:

[0114] (13)

[0115] Substituting equation (12) and equation (13) into equation (9), we get:

[0116] (14)

[0117] Substituting equation (14) into equation (3), we get the time-dependent damage equation of rock:

[0118] (15)

[0119]

[0120] 3. Crack propagation damage equation

[0121] Under load, cracks in rocks gradually expand and connect, which leads to the degradation of rock mechanical properties. According to the prior art, the axial pressure at the crack tip of an open crack in a rock that expands in an airfoil shape is:

[0122] (16)

[0123] In the formula, is the stress intensity factor of rock, is the crack initiation angle, is the radius of the crack. , , They are radial axial pressure, annular axial pressure, and tangential axial pressure.

[0124] The axial pressure at the crack tip converted from the coordinate system to the rectangular coordinate system:

[0125] (17)

[0126] In formula 17, , , They are Axial pressure, Axial pressure, Tangential pressure of the coordinate system.

[0127] Assuming that the rock material fracture obeys the Mohr-Coulomb yield criterion, the calculation formula for the principal axial pressure is:

[0128] (18)

[0129] In the formula, , , They are the three principal stresses of soft rock in three mutually perpendicular directions in space. is the Poisson's ratio of the rock. The principal axial pressure of the rock is obtained from equations (17) and (18):

[0130] (19)

[0131] (20)

[0132] The axial compressive strength factor of rock is obtained by formula (19):

[0133] (twenty one)

[0134] According to the law of energy reciprocity, the total elastic strain energy that can be released by the unit under the action of external force is , which is equal to the elastic strain energy stored in the material and the change in elastic strain energy sum.

[0135] (twenty two)

[0136] According to the existing technology, the total elastic strain energy that can be released by the unit is :

[0137] (twenty three)

[0138] In the formula, is the damage in the crack propagation stage, is the unit volume of rock.

[0139] Elastic strain energy stored in the material :

[0140] (twenty four)

[0141] In the false triaxial state = , then formula (24) is:

[0142] (25)

[0143] is the elastic modulus of rock, which can be taken as the elastic modulus in the linear elastic stage; For the initial damage, is the initial elastic modulus.

[0144] According to the prior art, the change in elastic strain energy caused by crack extension is :

[0145] (26)

[0146] In the formula, is the crack extension length. By integrating formula (26), we can get:

[0147] (27)

[0148] Assume that there is If there are cracks, the damage equation of the rock crack when it is not extended can be expressed as:

[0149] (28)

[0150] Substituting equations (24) to (28) into equation (22), we can obtain the rock crack propagation damage equation:

[0151] (29)

[0152] Where:

[0153] (30)

[0154] (31)

[0155] According to the existing technology, the functional relationship between the rock micro-crack extension length and the macro-strain is:

[0156] (32)

[0157] In the formula, and is the material parameter, It's strain. is the initial length of the crack. Generalize equation (32) to the time-dependent equation:

[0158] (33)

[0159] Substituting equation (33) into equation (29) yields the crack propagation damage equation for rock:

[0160] (34)

[0161] In step S2, according to FIG. 1 and Figure 2 The creep deformation law of soft rock under the action of medium-wet-dry cycle is used to divide the creep curve of soft rock into stable creep stage and unstable creep stage. < ): Soft rock only undergoes transient elastic and viscoelastic strains under load; unstable creep stage ( ≥ ): Soft rock undergoes instantaneous elastic, viscoelastic and viscoplastic strains under load. To this end, this scheme constructs viscoelastic elements and viscoplastic elements, as shown in Figure 5(a) to (d). The viscoelastic element (Figure 5(a)) consists of a spring and a damper. After being subjected to force, the spring undergoes instantaneous elastic deformation, and the elastic modulus of the element is As time goes by, the damper is gradually compressed, the elastic modulus of the element is gradually weakened, and the elastic strain is gradually increased. The viscoplastic element is composed of a friction plate (Figure 5 (c)) and a nonlinear damping element (Figure 5 (b)) in parallel. When the axial pressure is greater than the long-term strength (i.e. ≥ ), the friction plate starts to slide, the viscoplastic element starts to deform, and the rock plastic deformation increases with time. As the rock deformation increases, the viscosity coefficient of the nonlinear damping element The smaller the value, the faster the viscoplastic creep rate of the rock increases. Based on the above understanding, this scheme uses viscoelastic elements and viscoplastic elements in series to form a creep model (see Figure 5 (d)), which can characterize the nonlinear characteristics of the rock.

[0162] In step S3, the process of establishing the creep equation in the stable creep stage is as follows:

[0163] When the axial pressure is less than the long-term strength ( < ), the elastic modulus deteriorates over time, and the rock undergoes viscoelastic creep. In this stage, the rock can remain stable for a long time, which is the stable creep stage. At this time, the friction plate in the model has not yet slipped, and the soft rock only undergoes instantaneous elastic and viscoelastic strains, which is equivalent to the creep model shown in Figure 5(d) at this time, where only the viscoelastic element works. According to Hooke's law, its creep equation can be expressed as:

[0164] (35)

[0165] In the stable creep stage, the time-dependent elastic modulus of rock Due to dry-wet cycles, axial pressure and gradual degradation over time, Figure 2 The cause of the damage in the middle stage can be considered that the damage in the stable creep stage of soft rock under the action of dry-wet cycles is the initial damage. Time-related damage Coupling effect. According to damage theory (35), it can be expressed as:

[0166] (36)

[0167] In the formula The damage is in the stable creep stage.

[0168] The initial damage As the first type of damage state, time-dependent damage It is the second type of damage state. According to the damage definition and Lemaitre strain equivalent equation, we have:

[0169] (37)

[0170] From equation (36) and equation (37), we get:

[0171] (38)

[0172] Substituting equations (1) and (15) into equation (38), the damage equation of the soft rock in the stable creep stage under the action of dry-wet cycles is obtained as follows:

[0173] (39)

[0174] The process of establishing the creep equation G in the unstable creep stage is as follows:

[0175] When the axial pressure is greater than the long-term strength ( ≥ ), rock cracks gradually initiate, its elastic modulus and viscosity coefficient weaken over time, and the rock undergoes viscoelastic-plastic deformation. This stage increases with time and the rock eventually creeps and fails, which is the unstable creep stage. At this time, the friction plate in the model begins to slide, and the soft rock undergoes instantaneous elastic, viscoelastic and viscoplastic strains. Its creep equation can be expressed as:

[0176] (40)

[0177] is the viscosity coefficient of the nonlinear damper.

[0178] Unstable creep stage, aging elastic modulus Under the influence of dry-wet cycles, axial pressure and time, the rock gradually deteriorates; under the influence of load, the rock yields locally, the internal cracks continue to expand and connect, and the viscoplastic viscosity coefficient gradually decreases due to the influence of crack expansion. Therefore, it can be considered that the damage of the time-dependent elastic modulus is the coupling effect of initial damage and time-dependent damage. , the viscoplastic viscosity coefficient damage is the crack extension damage According to the damage theory formula (40), it can be expressed as:

[0179] (41)

[0180] In the formula is the initial viscosity coefficient, = It can be obtained from (29).

[0181] In step S4, a three-dimensional creep damage model is established. Considering the actual stress state of the rock, the creep damage model of soft rock under the action of dry-wet cycles is extended to three dimensions, and then:

[0182] when < When , the creep model is:

[0183] (42)

[0184] when ≥ When , the creep model is:

[0185] (43)

[0186] in, 1~3, representing the three directions of three dimensions. 1~3, representing the three directions of three dimensions. ≠ . is the deviatoric stress, which is the total stress minus the confining pressure. is the strain corresponding to the deviatoric stress. is the shear modulus. is the Kronecker symbol, =1, =1; ≠1, =0.

[0187] (44)

[0188] is the stress tensor, is the Kronecker function.

[0189] Assuming that the sample is homogeneous and isotropic, a triaxial rheological test is performed at t=0. Under the pseudo triaxial condition, > = , its axial pressure state is:

[0190] (45)

[0191] In the Cartesian coordinate system, the coordinate axis 1 is along the axial direction, then:

[0192] (46)

[0193] From equation (44) to equation (46), we can get:

[0194] (47)

[0195] In the formula, .

[0196] Likewise for strain:

[0197] (48)

[0198] In the formula, . is the spherical stress tensor.

[0199] Then we have:

[0200] (49)

[0201] Because the confining pressure is applied first in the triaxial test loading process, the rock has already undergone compression deformation at this time, and the measured axial stress (i.e. axial pressure) is:

[0202] (50)

[0203] Substituting equations (46), (48) and (49) into equations (36) and (41), we can obtain the creep damage equation of soft rock under triaxial compression conditions: < When , the creep damage equation is:

[0204] (51)

[0205] when ≥ When , the creep damage equation is:

[0206] (52)

[0207] In the formula, is the principal stress or strain in the axial compression direction, and the bulk modulus , shear modulus .

[0208] Next, we will determine the parameters and verify the model.

[0209] Based on the creep damage model proposed in this paper, the model parameters can be determined according to the macro and micro experiments of soft rock. = , Poisson's ratio It can be determined by triaxial compression test. =0.12; According to the prior art, the crack initiation angle of the opening crack is =0; initial crack length It can be determined by electron microscopy experiments. =0.2mm; parameters , It can be determined by formula (12) and (13) respectively. It can also be determined by the above formula; Long-term strength can be determined using the isochronous curve method in the existing technology. It can be measured by low-field nuclear magnetic resonance method; and is a rock parameter, which can be determined according to existing methods in the prior art; The initial viscosity coefficient can be obtained from formula (53):

[0210] (53)

[0211] in is the rock viscoelastic strain, which can be obtained according to the method in the prior art. Other stable creep stage model parameters are shown in Table 1, and unstable creep stage model parameters are shown in Table 2.

[0212] Table 1 Stable creep stage model parameters:

[0213]

[0214] Table 2 Unstable creep stage model parameters:

[0215]

[0216] The model is verified below. The creep of soft rock under different dry-wet cycles at different loading levels is calculated by equations (51) and (52). Figure 6(a)~6(d). As can be seen from the figure: the creep damage model proposed in this scheme can better reflect the attenuation, steady and accelerated creep stages of rocks, and the creep model has a high degree of fit with the test data, which verifies the rationality of the soft rock creep damage model under the action of dry-wet cycles proposed in this scheme. From the creep model (Figure 5(d)), when the axial pressure is less than the long-term strength, the friction plate in the model does not slide, and the creep model degenerates into a viscoelastic model. By introducing damage variables that consider dry-wet cycles and time effects, the attenuation creep stage of rocks can be better reflected. This model is equivalent to the typical Maxwell model, but the model of this scheme is simple in form and can reflect the damage effects of dry-wet cycles and creep on rocks; when the axial pressure is greater than or equal to the long-term strength, rock cracks initiate, expand, and are locally damaged, the friction plate begins to slide, and the rock undergoes viscoelastic-plastic deformation. The model equation is relatively simple and can better reflect the accelerated creep stage of rocks. It also introduces crack extension damage, which can reveal the damage mechanism of rock accelerated creep stage.

[0217] In summary, the creep damage model proposed in this scheme, which combines the element model principle and damage theory, is highly consistent with the experimental results, has a simple structure, can better reveal the characteristics of the rock damage evolution mechanism, and has clear physical meanings of the parameters.

[0218] In step S5, the selected simulation software is FLAC3D, and FLAC3D can use C++ language to write a custom constitutive model and embed it into the software for analysis.

[0219] During the secondary development in step S5, the mathematical model established in step S4 is converted into a function form recognizable by FLAC3D, a new project is created based on the development environment and necessary plug-ins, all options are completed according to the requirements of the simulation software, and a custom constitutive model program is generated.

[0220] In this embodiment, in step S5, before writing the custom constitutive model, it is necessary to install Microsoft Visual Studio 2010 Community and FLAC3D500VS2010Addin.msi plug-in, create a new FLAC3D constitutive model project through Microsoft Visual Studio 2010 Community, specify all options, modify the model name, and generate a custom constitutive model solution. After obtaining the converted FLAC3D recognizable function, the process of the last secondary development is a technology well known to those skilled in the art, and will not be repeated here.

[0221] In step S5, the method of converting the mathematical model established in step S4 into a function form recognizable by FLAC3D is as follows:

[0222] According to the creep model established in step S2 and FIG. 5(d), we have:

[0223] (54)

[0224] in, for ~ The strain (creep) of the element, for ~ The viscoelastic strain of the element, i.e. the strain when the friction plate is not activated in the model; for ~ The viscoplastic strain of the element, that is, the strain of the viscoplastic bodies in the model.

[0225] Formula (54) can be expressed in the form of deviatoric strain rate:

[0226] (55)

[0227] According to formula (42), for viscoelastic bodies, it is obvious that:

[0228] (56)

[0229] in, for ~ The deviatoric stress of the element, is the shear modulus, Creep damage in the stable stage.

[0230] According to formula (43), the viscoplastic body of the model is:

[0231] (57)

[0232] The viscoplastic creep rate of the model can be obtained from formula (57):

[0233] (58)

[0234] is the viscosity coefficient, that is, the viscosity coefficient of the viscoplastic body, is the damage in the unstable creep stage, is the viscoplastic creep rate.

[0235] The total strain increment of the viscoplastic body is:

[0236] (59)

[0237] Assuming that the spherical stress does not produce plastic strain, the stress rate of the creep model is:

[0238] (60)

[0239] Formula (54) can be written in incremental form as:

[0240] (61)

[0241] The viscoelastic body is expressed in central difference form as:

[0242] (62)

[0243] Where:

[0244] (63)

[0245] (64)

[0246] , , , , are the new and old deviatoric stress and strain increments in a time step, respectively. Substituting equations (62), (63) and (64) into (61), we get:

[0247] (65)

[0248] The creep model ball stress is:

[0249] (66)

[0250] , , are the new and old stresses, is the bulk modulus, is the elastic volume strain increment.

[0251] As described above, the mathematical model established in step S4 (Formulas 51, 52 and 55) is converted into a function form recognizable by FLAC3D (Formula 65).

[0252] Step S5 obtains the custom constitutive model program and verifies its accuracy. Specifically, a certain soft rock is selected, and the data of its strain variation over time is obtained through experiments and numerical simulations. If the numerical simulation and the test results are similar, it is considered that the custom constitutive model can be used for the creep stability analysis of soft rock slopes. If it is determined that the numerical simulation and the test results are similar, it means that the model parameter values ​​are incorrect or the model is not established correctly, and remodeling and parameter selection are performed.

[0253] In this embodiment, for the first 7 levels of loading, the similarity between the numerical simulation and the test results is not less than 90%, and for the 8th level of loading, the similarity between the numerical simulation and the test results is not less than 80%, and it is determined that the similarity between the numerical simulation and the test results is high.

[0254] In this embodiment, the selected soft rock is a cylinder with a diameter of 50 mm and a height of 100 mm. A soft rock model of the same size as the cylinder is established in FLAC3D. The selected soft rock parameters are shown in Table 3.

[0255] Table 3 Parameters of carbonaceous mudstone triaxial compression creep model:

[0256]

[0257] In this embodiment, the comparison diagram between numerical simulation and experimental results is shown in Figure 7 . For the first 7 loading levels, the numerical simulation is very consistent with the test results, with a similarity of more than 90%. For the 8th loading level (axial pressure 35.26MPa), the similarity between the numerical simulation and the test results is 81.3%. The custom constitutive model of this scheme can be used for creep stability analysis of soft rock slopes.

[0258] In step S6, a slope mesh model is established by using Rhino 6 software, and is imported into FLAC3D to generate a finite model of the soft rock slope, and finally the soft rock slope analysis data is obtained.

[0259] In this embodiment, the schematic diagram of the soft rock slope model to be analyzed is shown in Figure 8 , the slope is a layer slope with a rock layer dip of 12°. 0~60m below the surface is carbonaceous mudstone, dark gray, low strength, soft texture, and poor rock structure; 60~150m is limestone, gray, moderately weathered, and microcracks are developed. The slope is naturally sloped, with two levels of slopes at the foot of the slope, each level is 10m, and the slope ratio is 1:0.75. A horse road is set in the middle with a width of 5m. The upper part of the slope is a natural slope with a slope height of 100m. The carbonaceous mudstone of the slope adopts the three-dimensional creep damage mathematical model, and the limestone adopts the Mohr-Coulomb elastoplastic model. The model parameters of carbonaceous mudstone and limestone are shown in Tables 4 and 5, respectively. It should be noted that the cohesion in Table 4 is the cohesion that is not affected by dry-wet cycles, in other words, it is the cohesion when the number of dry-wet cycles is 0.

[0260] Table 4 Carbonaceous mudstone model parameters:

[0261]

[0262] Table 5 Limestone model parameters:

[0263]

[0264] Existing research has found that the dry-wet cycle affects the depth of the slope rock mass to about 3m, and the range below 3m is basically unaffected by the dry-wet cycle. In this scheme, it is assumed that the dry-wet cycle affects the depth of the slope rock mass to 3m, and the cohesion of the slope rock mass It decreases linearly with depth. According to existing research results, cohesion The relationship with the number of dry-wet cycles is shown in formula (67). The cohesion parameters of the charcoal mudstone slope within the range of 0-1 m under different dry-wet cycles calculated by formula (67) are shown in Table 7.

[0265] (67)

[0266] The friction angle of charcoal mudstone under the action of dry-wet cycles is shown in Table 6, where the data in the table are obtained by experiments. Since the friction angle is greatly affected by dry-wet cycles, the influence of dry-wet cycles on the friction angle of charcoal mudstone is not considered. In this simulation, the average value of the friction angle of charcoal mudstone under different dry-wet cycles is 15.63° for analysis.

[0267] Table 6 Friction angle of carbonaceous mudstone under dry-wet cycle:

[0268]

[0269] Table 7 Cohesion of carbonaceous mudstone slope at different depths under dry-wet cycles (MPa):

[0270]

[0271] In Table 7, the cohesion at each number of dry-wet cycles for depths of 0-1 m is calculated according to formula (67). The cohesion at depths of 1-2 m and 2-3 m is obtained by linear interpolation at the corresponding number of dry-wet cycles. The slope below 3 m is not affected by dry-wet cycles, so the cohesion is the value of 6.6 MPa in Table 4, that is, 0 dry-wet cycles.

[0272] The custom constitutive model program obtained in step S5 was used, and the model parameters were selected from Tables 4, 5, and 7. Considering the creep effect of the charcoal mudstone slope for 60 years, the distribution of the plastic zone, the potential sliding surface, and the change law of the horizontal displacement of the charcoal mudstone slope under the action of dry-wet cycles (affected depth 3 m) were analyzed.

[0273] As can be seen from the above, in the above process, the time step of the custom constitutive model program calculation is equivalent to considering the influence of time on slope stability. Cohesion reflects the influence of the number of dry-wet cycles on slope stability. For axial pressure, in the slope, axial pressure is the gravity of the soil layer covering the upper part of the calculation unit, which is related to the height and is a constant value in the numerical analysis of the slope. Therefore, the modeled slope highly reflects the axial pressure.

[0274] The cloud diagrams of the plastic zone of the carbonaceous mudstone slope under the coupling effect of dry-wet cycle (affected depth 3m) and creep are shown in Figures 9(a) to 9(f).

[0275] From the analysis of the development law of the plastic zone: after 500 dry-wet cycles (see Figure 9 (a)), the creep plastic zone of the charcoal mudstone slope first appears at the foot of the first and second level slopes and near the 3 / 4 position of the slope; with the increase of the number of dry-wet cycles, the plastic zone expands along the surface of the first and second level slopes and develops deep into the rock mass; after 3000 dry-wet cycles, the plastic failure zone penetrates the surface of the first and second level slopes; therefore, it is judged that the charcoal mudstone slope will be instability-destroyed after 3000 dry-wet cycles (affected depth 3m).

[0276] From the evolution law of the potential sliding surface, after 500 dry-wet cycles (see Figure 10 (a)), the potential sliding surface of the charcoal mudstone slope first forms along the rock layer interface from the foot of the second-level slope; as the number of dry-wet cycles increases, the potential sliding surface gradually disappears at the rock layer interface, and gradually forms on the surface of the first and second-level slopes; after 4000 dry-wet cycles, the potential sliding surface forms on the surface of the first and second-level slopes. Therefore, it is judged that the charcoal mudstone slope is creep-instabilized and destroyed after 4000 dry-wet cycles (affected depth 3m).

[0277] From the analysis of the horizontal displacement change law: in the first 1000 dry-wet cycles, all monitoring points of the charcoal mudstone slope maintained stable creep; with the increase of the number of dry-wet cycles, the horizontal position of the top of the first and second level slopes gradually increased, and the top of the second level slope gradually decreased; after 4000 dry-wet cycles, the top of the first and second level slopes (monitoring point 4) appeared accelerated creep stage; therefore, it was judged that after 4000 dry-wet cycles (affected depth 3m), the charcoal mudstone slope was creep-instabilized and destroyed. Figure 11(a)~11(e) As shown in Figure 11(f), the horizontal displacement of each monitoring point shows a basically linear change with time, which is equivalent to a uniform change in the horizontal displacement of each monitoring point. However, after 4000 dry-wet cycles, as shown in Figure 11(f), the horizontal displacement of some monitoring points shows an obvious nonlinear change with time (monitoring points 4 and 2), and the change is accelerated, that is, the slope of the horizontal displacement increases with time. In other words, the creep curve has a concave trend.

[0278] In summary, after 4000 dry-wet cycles (affected depth 3m), the plastic zones at the first and second slopes of the charcoal mudstone slope are connected, potential sliding surfaces are formed, and horizontal displacement increases rapidly, which can be determined as creep failure of the charcoal mudstone slope.

[0279] Finally, it is necessary to explain here that the above embodiments are only used to further illustrate the technical solution of the present invention in detail and cannot be understood as limiting the scope of protection of the present invention. Some non-essential improvements and adjustments made by technicians in this field based on the above content of the present invention all fall within the scope of protection of the present invention.

Claims

1. A method for analyzing the long-term stability of soft rock slopes, characterized in that: The steps include: Step S1: According to the evolution law of the microstructure and macroscopic mechanical damage characteristics of the soft rock creep failure process under the action of dry-wet cycles, the soft rock creep damage is classified and various damage equations are established. The soft rock creep damage is divided into three categories: initial damage, time-dependent damage and crack extension damage, so as to quantitatively characterize the damage of the soft rock caused by dry-wet cycles, stress and time; Step S2: According to the creep deformation law of soft rock under the action of dry-wet cycles, the creep curve of soft rock is divided into a stable creep stage and an unstable creep stage, and viscoelastic elements, viscoplastic elements and a creep model are constructed. The creep model is composed of viscoelastic elements and viscoplastic elements connected in series to characterize the viscoelastic strain and viscoplastic strain of soft rock under different stress states; Step S3: Using the damage equation of step S1 and the creep model of step S2, the creep equations of the stable creep stage and the unstable creep stage are established. The coupled damage variables of initial damage and aging damage are used to correct the viscoelastic component parameters. The crack extension damage is introduced to correct the viscoplastic component parameters. A new soft rock creep damage model is constructed to characterize the time-varying law of strain of soft rock under different dry-wet cycles and stresses. Step S4: Establish a three-dimensional creep damage mathematical model to analyze the stability of the time-dependent deformation characteristics of the soft rock slope under the action of dry-wet cycles; Step S5: Select a simulation software, perform secondary development on the selected simulation software based on the mathematical model established in step S4, and write a custom constitutive model program; Step S6: using modeling software to establish a slope model for stability analysis, and importing it into the simulation software of step S5, using the custom constitutive model program of step S5, to obtain the distribution of plastic zones, potential sliding surfaces and horizontal displacement variation of the slope under different dry-wet cycles; Step S7: when the plastic zone of the slope is connected, the potential sliding surface is formed, and the horizontal displacement increases at a certain number of dry-wet cycles, it is determined that the soft rock slope is creep-damaged at the number of dry-wet cycles; In step S1, the initial damage The mesostructure damage is caused by the development of pores in soft rock due to the dry-wet cycle. Time-related damage Changes in rock mechanical properties caused by the directional flow of rock particles over time; crack extension damage It is the damage and deterioration of rock structure caused by the expansion and connection of rock cracks under load: ， ， ， ， ， ， ， ， ， in, is the total cross-sectional area, is the pore area, is the rock porosity, For the Wet-dry cycle under stage axial pressure The instantaneous elastic modulus, When time approaches infinity x Wet-dry cycle under stage axial pressure n The elastic modulus, is a function related to the number of dry-wet cycles and the axial pressure, t is the time, is with , , v Related functions, is with v、 , Related functions, is the strain at time t, and is the material parameter, , , They are the three principal stresses of soft rock in three mutually perpendicular directions in space, is the crack initiation angle, is the Poisson's ratio of the rock, is the crack radius, is the stress intensity factor of rock, According to the energy reciprocity theorem, is a parameter related to axial pressure. The least square method is used to calculate the soft rock under the action of dry-wet cycles. , , Fitting is performed to establish a functional relationship with the axial pressure.

2. The analysis method according to claim 1, characterized in that: In step S2, during the stable creep stage, , soft rock only undergoes transient elastic and viscoelastic strains under load; in the unstable creep stage, , soft rock undergoes instantaneous elastic, viscoelastic and viscoplastic strains under load, among which, is the axial pressure, For long-term strength, the viscoelastic element consists of a spring and a damper, and the viscoplastic element consists of a friction plate and a nonlinear damping element in parallel.

3. The analysis method according to claim 2, characterized in that: In step S3, during the stable creep stage, the damage of soft rock during the stable creep stage under the action of dry-wet cycles is Initial damage Time-related damage The damage equation of soft rock under the action of dry-wet cycles is: .

4. The analysis method according to claim 2, characterized in that: In step S3, during the unstable creep stage, the time-dependent elastic modulus damage is the coupling effect of initial damage and time-dependent damage. , the viscoplastic viscosity coefficient damage is the crack extension damage , the creep equation in the unstable creep stage is: ， ， in, For strain, is the initial viscosity coefficient, is the initial elastic modulus.

5. The analysis method according to claim 4, characterized in that: when When , the creep damage equation is: ; when When , the creep damage equation is: , in, is the strain in the axial compression direction, , is the shear modulus, the bulk modulus .

6. The analysis method according to claim 5, characterized in that: During the secondary development in step S5, the mathematical model established in step S4 is converted into a function form recognizable by the selected simulation software, a new project is created based on the development environment and necessary plug-ins, all options are completed according to the requirements of the simulation software, and a custom constitutive model program is generated.

7. The analysis method according to claim 6, characterized in that: In step S5, the simulation software selected is FLAC3D, and a custom constitutive model is written in C++ language and embedded into the FLAC3D software for analysis.

8. The analysis method according to claim 6, characterized in that: In step S7, the accelerated increase of the horizontal displacement means that the horizontal displacement of the monitoring point presents a nonlinear change over time, and the slope of the horizontal displacement increasing over time increases.

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