Slope stability analysis method based on nonlinear strength criterion

Abstract

The invention discloses a slope stability analysis method based on a nonlinear strength criterion, and the method comprises the steps: obtaining a state parameter of a slope, building the nonlinear strength criterion and a nonlinear strength envelope according to the state parameter, and generating a potential sliding surface from a slope toe starting point; dividing the potential sliding body into a plurality of rigid body units, and calculating external work power and internal energy dissipation power of the rigid body units; confirming a critical sliding surface and a safety coefficient under a power balance condition, and taking the critical sliding surface and the safety coefficient as an initial critical state; gradually evolving and propelling to a target height by taking a critical height corresponding to the initial critical state as a starting point, constraining a search domain of a current height based on a critical state of a previous height, and performing consistency reduction under nonlinear intensity envelope constraint; and when the height evolution advances to the target height and the strength reduction iteration converges, outputting a stability evaluation index of the target slope. The method has the effect of improving the accuracy and efficiency of the slope stability analysis process.

Description

Technical Field

[0001] This application relates to the technical field of geotechnical engineering analysis and design, and in particular to a slope stability analysis method based on nonlinear strength criteria. Background Technology

[0002] Slope stability can be understood as a balance problem between external loads and internal resistance. Its implications include: firstly, the slope geometry and external force conditions determine the spatial extent of the potential failure surface; secondly, the constitutive model of the soil and rock mass determines the shear strength that the soil can provide under a given stress state. Therefore, the essence of slope stability is a mechanical equilibrium problem under the coupled effects of geometric conditions and constitutive relations. The key to slope stability analysis lies in accurately identifying the potential sliding surface and calculating the safety factor. Currently, the methods widely used in engineering practice are mainly divided into two categories: limit equilibrium methods (LEM) and numerical simulation methods (such as the finite element method (FEM) and the finite difference method (FDM).

[0003] Limit equilibrium methods typically require pre-assuming the geometry of the slip surface (such as circular arcs, logarithmic spirals, etc.) and then using a search algorithm to determine the most dangerous slip surface. While computationally simple, this method heavily relies on pre-defined geometric assumptions, making it difficult to reflect real, irregular failure modes under complex geological conditions. Furthermore, its global search strategy is computationally inefficient. Numerical simulation methods, through strength reduction techniques, infer stability by searching for plastic zones or abrupt displacement changes in the model, providing a relatively complete physical mechanism. However, this method is computationally expensive, heavily reliant on mesh generation and iterative convergence, and struggles to meet the demands of rapid analysis and multi-scheme comparison in engineering design.

[0004] In related technologies, slope stability analysis methods are generally based on linear strength criteria. However, numerous geotechnical tests show that the strength envelope of soil exhibits significant nonlinear characteristics, namely, a higher friction angle under low confining pressure and a gradual decrease in friction angle under high confining pressure. Ignoring this nonlinearity can lead to incorrect estimations of the strength of deep soil, resulting in a systematic overestimation of the safety factor (with deviations exceeding 20%) and misjudgments of the location and morphology of the critical slip surface. Summary of the Invention

[0005] The purpose of this application is to provide a slope stability analysis method based on nonlinear strength criteria, which can improve the efficiency and accuracy of slope stability analysis calculations.

[0006] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a slope stability analysis method based on a nonlinear strength criterion. The method includes: acquiring the state parameters of the slope; establishing a nonlinear strength criterion and a nonlinear strength envelope based on the state parameters; and generating a potential sliding surface from the toe of the slope based on the nonlinear strength criterion and related flow rules; identifying potential sliding bodies based on the potential sliding surfaces; dividing the potential sliding bodies into several rigid body elements; calculating the external work power and internal energy dissipation power of the rigid body elements to construct a power balance equation; identifying the critical sliding surface and safety factor under power balance conditions through an optimization algorithm based on the power balance equation, and using it as the initial critical state; gradually evolving towards the target height starting from the critical height corresponding to the initial critical state; constraining the search domain of the current height based on the critical state of the previous height; and performing consistency reduction under the constraint of the nonlinear strength envelope for iterative correction; and outputting the stability evaluation index of the target slope when the height evolution reaches the target height and the strength reduction iteration converges.

[0007] For example, the state parameters include the slope height, slope angle, slope length, unit weight, cohesion, and internal friction angle of the slope; the nonlinear strength criterion is in power function form, as shown below: in, and These represent the normal stress and shear stress on the sliding surface, respectively. The initial cohesion, For axial tensile strength, This is a nonlinear parameter.

[0008] For example, generating a potential sliding surface from the toe of the slope based on the nonlinear strength criterion and the relevant flow law includes: taking the toe of the slope as the starting point, calculating the instantaneous internal friction angle of the starting point based on the nonlinear strength criterion and the nonlinear strength envelope; determining the position of the next node based on the instantaneous internal friction angle of the starting point and the relevant flow law through a discrete rotation-velocity discontinuity mechanism, thereby generating a sliding surface path; taking each new node as the current point, iteratively advancing the sliding surface path until it intersects with the top of the slope, forming a complete potential sliding surface; confirming the potential sliding body based on the potential sliding surface includes defining the closed area jointly enclosed by the potential sliding surface and the slope surface as the potential sliding body.

[0009] For example, after establishing the nonlinear strength criterion and nonlinear strength envelope based on the state parameters, the method further includes: constructing a tangent at any stress point on the nonlinear strength envelope based on the power function form of the nonlinear strength criterion; calculating the instantaneous cohesion and instantaneous internal friction angle based on the tangent to perform local linearization, thereby obtaining equivalent linear parameters that dynamically change with the stress state.

[0010] For example, calculating the external work power and internal energy dissipation power of the rigid body element to construct a power balance equation includes: identifying the motion parameters in the potential sliding body, wherein the motion parameters include the weight of the sub-blocks, displacement power, shear stress, and relative displacement rate of the sliding surface; calculating the external work power and internal energy dissipation power of the rigid body element based on the motion parameters; and constructing a power residual function based on the external work power and internal energy dissipation power, wherein the power residual function is as follows: Wherein, Wext represents the external power, Wdis represents the internal energy dissipation power, and R represents the residual. When the residual is less than the set tolerance, power balance is achieved. The optimization algorithm includes a sequential quadratic programming method or a bisection method, which are used to solve for the position of the rotation center and the critical height.

[0011] For example, the step of gradually evolving towards the target height starting from the critical height corresponding to the initial critical state includes: confirming the position of the rotation center and the critical height in the initial critical state; and confirming the height evolution path based on the target height, the position of the rotation center, and the critical height, as shown below: in, This is the path advancement coefficient. This indicates that it is in the initial state. ; This indicates that the target height has been reached, that is... ;when hour, and its corresponding center of rotation of the sliding surface This serves as the starting state for path advancement, and proceeds in small steps. Gradually increase.

[0012] For example, the search domain constraining the current height based on the critical state of the previous height includes: an initial safety factor constraining the current height and a rotation center contraction domain, wherein the initial safety factor is as follows: The rotation center contraction region is shown below: in, This represents the initial safety factor at the current altitude. This indicates the contraction zone of the rotation center at the current altitude. It is the convergent solution of the previous height safety factor and the center of rotation. The safety factor is relative to the disturbance amplitude. For Center, radius The rotation center trust region.

[0013] For example, the search domain constrained by the critical state of the previous altitude to the current altitude further includes: dynamically expanding the relative disturbance amplitude of the safety factor and the rotation center trust domain when a preset condition is met; if the evolution process cannot converge, triggering a global rotation center search for re-initialization; wherein the preset condition includes at least one of the following: no rotation center satisfying the power balance condition can be found in the contraction domain; the safety factor and the sliding surface morphology undergo abrupt changes; the energy residual decreases non-monotonically.

[0014] For example, the step of performing consistent reduction under nonlinear strength envelope constraint for iterative correction includes: confirming the reduction coefficient, performing reduction based on the instantaneous cohesion and the instantaneous internal friction angle, and ensuring that the strength parameters after reduction are consistent with the original nonlinear envelope; The reduction process is as follows: in, This represents the instantaneous cohesion after reduction. This represents the instantaneous friction angle after reduction. The reduction factor is represented by a bisection method for iterative correction. A sliding path under the current reduction factor is constructed according to the sliding surface adaptive generation strategy. A reduction factor F that satisfies the power balance condition is searched. If it exists, then F is the upper limit solution of the safety factor. The interval is updated by the bisection method until the minimum upper limit solution within the tightening threshold is obtained, which is used as the final safety factor.

[0015] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the slope stability analysis method based on nonlinear strength criteria described above.

[0016] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a slope stability analysis method based on nonlinear strength criteria. By establishing a nonlinear strength criterion and a nonlinear strength envelope, it abandons the distorted linear strength assumption and can more realistically reflect the nonlinear law of soil strength changing with stress state. Based on the nonlinear strength criterion and related flow laws, a potential sliding surface is generated from the slope toe, eliminating the dependence on the preset sliding surface shape and significantly improving the prediction accuracy of the sliding surface position and shape. Starting from the initial critical state, it gradually evolves towards the target height. Based on the critical state of the previous height, the search domain of the current height is constrained. Consistency reduction is performed under the constraint of nonlinear strength envelope, transforming the solution of complex problems into an asymptotic and continuous convergence process, narrowing the scope of optimization search, avoiding the blindness of traditional global search, and thus significantly improving computational efficiency while effectively ensuring the stability and convergence of the iterative process. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of the slope stability analysis method based on nonlinear strength criteria in the embodiments of this application.

[0020] Figure 2 This is a diagram showing the relationship between the nonlinear intensity criterion and the instantaneous tangent in an embodiment of this application.

[0021] Figure 3 This is a schematic diagram of the discrete rotary type failure mechanism in the embodiments of this application.

[0022] Figure 4 This is a schematic diagram of the generation of the rotational-chord discontinuity in an embodiment of this application.

[0023] Figure 5 This is a schematic diagram of the sliding body unit division and energy calculation in an embodiment of this application.

[0024] Figure 6 This is a flowchart illustrating the safety factor calculation process in the embodiments of this application. Detailed Implementation

[0025] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0026] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] like Figure 1 As shown in the figure, this application provides a slope stability analysis method based on a nonlinear strength criterion, including the following steps: S110. Obtain the state parameters of the slope, establish the nonlinear strength criterion and nonlinear strength envelope based on the state parameters, and generate a potential sliding surface from the toe of the slope based on the nonlinear strength criterion and related flow rules.

[0028] S120. Identify potential sliding bodies based on potential sliding surfaces, divide potential sliding bodies into several rigid body elements, calculate the external work power and internal energy dissipation power of the rigid body elements, and construct power balance equations.

[0029] S130. Based on the power balance equation, the critical sliding surface and safety factor under power balance conditions are determined by optimization algorithm and used as the initial critical state.

[0030] S140. Starting from the critical height corresponding to the initial critical state, the evolution progresses step by step towards the target height. The search domain of the current height is constrained based on the critical state of the previous height, and consistency reduction is performed under the nonlinear strength envelope constraint for iterative correction.

[0031] S150. When the height evolution progresses to the target height and the strength reduction iteration converges, output the stability evaluation index of the target slope.

[0032] This application provides a slope stability analysis method based on a nonlinear strength criterion. By establishing a nonlinear strength criterion and a nonlinear strength envelope, it abandons the distorted linear strength assumption and can more realistically reflect the nonlinear law of soil strength changing with stress state. Based on the nonlinear strength criterion and related flow laws, a potential sliding surface is generated from the slope toe, eliminating the dependence on the preset sliding surface shape and significantly improving the prediction accuracy of the sliding surface position and shape. Starting from the initial critical state, it gradually evolves towards the target height. Based on the critical state of the previous height, the search domain of the current height is constrained. Consistency reduction is performed under the constraint of the nonlinear strength envelope, transforming the solution of complex problems into a gradual and continuous convergence process. This narrows the scope of the optimization search and avoids the blindness of traditional global search, thereby significantly improving computational efficiency while effectively ensuring the stability and convergence of the iterative process.

[0033] The principle of analysis and calculation in this application embodiment is as follows: using the power function type nonlinear strength criterion as the basis of the constitutive relationship of the soil and rock mass, and incorporating the nonlinear strength characteristics into the slope stability analysis process, so that the stability evaluation results can be closer to the actual stress characteristics and failure trend of the soil.

[0034] For example, when this method begins execution, it first obtains state parameters, which include geometric parameters such as slope height. slope angle Slope length Physical and mechanical parameters: including specific weight Cohesion internal friction angle .

[0035] Then obtain the nonlinear coefficients For example, the nonlinear coefficients obtained through experimental fitting Indoor tests were conducted on soil and rock strength parameters according to the "Standard for Geotechnical Testing Methods" GB / T 50123-2019, and standard-sized soil specimens were prepared. During the tests, triaxial compression tests or direct shear tests were carried out under different confining pressure conditions to obtain the shear failure strength points at various stress levels. The cohesion of the soil was obtained by fitting the test data. internal friction angle Furthermore, by studying the nonlinear variation patterns of strength curves under multiple confining pressure conditions, the nonlinear coefficients were determined through regression analysis. .

[0036] The nonlinear intensity criterion is in power function form, and its expression is as follows: (1) In the above formula, and These represent the normal stress and shear stress on the sliding surface, respectively. The initial cohesion, For axial tensile strength, For nonlinear coefficients, when When the strength changes nonlinearly with confining pressure, it better reflects the true mechanical properties of soil and rock masses. When this happens, the formula degenerates into the linear (Mohr–Coulomb) criterion, with the corresponding expression being: (2) in, The initial internal friction angle has a tangent value equal to .

[0037] For example, in step S110, a potential sliding surface is generated from the toe of the slope based on the nonlinear strength criterion and related flow laws, specifically including: S111. Starting from the toe of the slope, calculate the instantaneous internal friction angle at the starting point based on the nonlinear strength criterion and the nonlinear strength envelope.

[0038] S112. Based on the instantaneous internal friction angle at the starting point and the relevant flow rules, the position of the next node is determined through a discrete rotation-velocity discontinuity mechanism, thereby generating a slip surface path.

[0039] S113. Take each new node as the current point and iteratively advance the sliding surface path until it intersects with the top of the slope to form a complete potential sliding surface.

[0040] S114. Identifying potential sliding bodies based on potential sliding surfaces includes defining a closed area enclosed by the potential sliding surface and the slope surface as a potential sliding body.

[0041] The relevant flow rule described in this embodiment refers to a fundamental rule in plasticity mechanics, which assumes that the plastic potential function of the material is the same as the yield function. In this method, the yield function can be the established power-law type nonlinear strength criterion. According to this rule, the direction of plastic shear displacement of any particle on the potential sliding surface is consistent with the normal direction of the yield surface at that point under the current stress state. This normal direction can be mathematically derived to be a specific angle with the tangent direction of the sliding surface at that point, which is the instantaneous internal friction angle determined by the nonlinear strength criterion. Therefore, the formation path of the sliding surface is directly controlled by the instantaneous internal friction angle, ensuring that the evolution process of the sliding surface strictly follows the nonlinear constitutive relation of the material.

[0042] In some embodiments, the discrete rotation-velocity discontinuity mechanism employs a "rotation-chord" discrete iterative mechanism, where the position of each new node is determined based on the instantaneous friction angle of the previous node, until a closure is achieved between the sliding surface and the crest of the slope. The sliding surface path is an adaptive path, formed by a velocity discontinuity configuration. According to relevant flow laws, the sliding surface advance direction is consistent with the direction controlled by the instantaneous friction angle, and the sliding surface morphology is dynamically adjusted according to the local stress state.

[0043] like Figure 2 The figure shown is a graph illustrating the relationship between the nonlinear strength criterion and the instantaneous tangent in an embodiment of this application. It demonstrates the power-function type nonlinear strength criterion and its linearization method. In the figure, the horizontal axis represents the normal stress σ, and the vertical axis represents the shear stress τ. Figure 2 The curve in the figure represents the nonlinear strength envelope. In engineering applications, to facilitate the calculation of slip surface generation, the nonlinear criterion needs to be locally linearized. A tangent is drawn at any stress point on the envelope. The slope of this tangent represents the instantaneous internal friction angle under that stress state, and the intercept of the tangent on the vertical axis is the instantaneous cohesion.

[0044] For example, in step S110 above, after establishing the nonlinear intensity criterion and nonlinear intensity envelope based on the state parameters, this method further includes: Based on the power function form of the nonlinear strength criterion, a tangent is constructed at any stress point on the nonlinear strength envelope; the instantaneous cohesion and instantaneous internal friction angle are calculated according to the tangent for local linearization, and equivalent linear parameters that dynamically change with stress state are obtained.

[0045] After constructing the tangent, instantaneous cohesion is introduced. and instantaneous internal friction angle The calculation methods are as follows: (3) (4) in, and These represent the normal stress and shear stress on the sliding surface, respectively. The initial cohesion, For axial tensile strength, These are nonlinear coefficients. Indicates instantaneous cohesion. This represents the instantaneous internal friction angle. Through local linearization, the nonlinear strength criterion is transformed into an equivalent linear parameter that dynamically changes with the stress state, facilitating subsequent path advancement and power calculation.

[0046] In this application's embodiments, the potential sliding surface refers to the boundary of the slope most likely to undergo shear failure, derived from mechanical principles under given slope geometry, soil parameters, and strength criteria. It is a theoretically existing curved surface (represented as a curve in a two-dimensional profile) that separates the unstable soil mass (i.e., the sliding body) from the stable soil mass below it.

[0047] The following describes the adaptive generation process of the slip surface. Starting with the slope angle as the initial point, it rotates around the center of rotation, setting the rotational angular velocity to... rad / s, the mechanism rotation control angle is set to According to relevant flow rules, the instantaneous friction angle is used. Control the path direction; form a velocity discontinuity curve through iterative advancement to obtain the geometry of the potential sliding surface.

[0048] like Figure 3 The diagram illustrates a discrete rotational failure mechanism. The toe point A of the slope cross-section serves as the starting point for slip surface generation, and the entire sliding system rotates around the rotation center O with an angular velocity ω. The velocity discontinuity AC divides the soil into two parts: the upper sliding body ABC (considered a rigid body) and the lower stable soil. Discontinuity AC is composed of a series of discrete line segments, each with a different distance (radius) and angle from the rotation center O. This discrete rotational mechanism provides a kinematic framework for the gradual generation of the slip surface. Starting from the slope toe, AC represents the velocity discontinuity of the failure mechanism. and These represent the angles and radii at various points on the discontinuity. This mechanism adopts the rigid body assumption, with both the upper and lower parts of the velocity discontinuity being rigid bodies. The sliding block ABC revolves around the center of rotation. Rotation, angular velocity is .

[0049] like Figure 4 The diagram shown illustrates the generation of a rotation-chord discontinuity, demonstrating the iterative generation process of a sliding surface node based on the rotation-chord mechanism, starting from a known node P. i Starting from this point, the instantaneous internal friction angle is calculated based on the stress state. According to relevant flow laws, the direction of the sliding surface's propulsion is determined, and a circle with radius OP is drawn with the rotation center O as the center. i Rotate by a small angular increment to obtain a new radius direction. The intersection of the advancing direction and the new radius direction is the next node P. i+1 Repeat this iterative process to generate a sequence of nodes in sequence. Connecting these nodes forms a complete potential sliding surface.

[0050] Specifically, node coordinates are generated through a "rotation-chord" iterative mechanism, and the position of each node is... Determined by the stress state of the previous node. Combining geometric relationships and relevant flow rules, the calculation formula is as follows: (5) in, To control the rotation angle of the mechanism, Center of rotation coordinates Let the coordinates of the previous point be... The instantaneous internal friction angle at the previous point.

[0051] For example, the center of rotation The coordinates are from the initial point of the discontinuity. With initial radius The decision is made, and the calculation formula is as follows: (6) After determining the location of the next point, calculate the equivalent soil height at that point. and equivalent self-weight per unit width of the slide band , (7) (8) in, The soil weight is [not specified].

[0052] Based on the equivalent unit weight, the effective normal stress at this point on the slip surface is calculated as follows: (9) in Let be the angle between the normal at the slip surface point and the vertical direction. According to the relevant flow rules, we get... (10) Substituting the above information into the formula for calculating the internal friction angle of the loss, we can obtain the closed-loop expression. (11) In the above formula (11), the right side excluding All other quantities can be calculated directly, and the instantaneous internal friction angle at that point can be solved using an iterative method. Then, the values ​​are substituted into the instantaneous cohesion calculation formula to obtain the complete instantaneous parameter information for that point. This iterative process continues until a certain node is reached. Satisfy the vertical coordinate If the slope reaches the top, the failure path configuration is considered complete. If it is slightly higher than the top, the final segment is closed towards the top using a linear interpolation correction method, forming a complete potential failure surface (sliding surface). The closed area enclosed by the potential sliding surface and the slope surface is defined as the potential sliding body.

[0053] like Figure 5The diagram illustrates the element partitioning and energy calculation of a sliding body. The sliding body is divided into several vertical strips, each considered a rigid body element i. In the energy calculation, the external power (work done by gravity) of each element depends on its weight, rotational angular velocity, and geometric parameters. Internal energy dissipation occurs on the sliding surface segment at the bottom of the element, depending on the instantaneous cohesion, relative displacement rate, and length of that segment. This discretization allows complex slope stability problems to be solved numerically.

[0054] For example, in step S120 above, calculating the external work power and internal energy dissipation power of the rigid body element and constructing the power balance equation includes the following steps: S121. Confirm the motion parameters in the potential sliding body, including the weight of the sub-block, displacement power, shear stress, and relative displacement rate of the sliding surface.

[0055] S122. Calculate the external work power and internal energy dissipation power of the rigid body element based on motion parameters. The calculation method is as follows: (12) (13) In the above formulas, formula (5) is used to calculate external work power, and formula (6) is used to calculate internal energy dissipation power, that is, sliding surface dissipation power. Among them, For the weight of the sub-block, This corresponds to the displacement power. For shear stress, The relative displacement rate of the sliding surface.

[0056] S123. Construct a power residual function based on the external power and internal energy dissipation power. The power residual function is shown below: (14) Among them, W ext Indicates external power, W dis R represents the internal energy dissipation power, and R represents the residual. Power balance is achieved when the residual is less than the set tolerance. The value can be 10 -6 .

[0057] The aforementioned optimization algorithms, including Sequential Quadratic Programming (SQP) or the bisection method, are used to solve for the position of the rotation center. With critical height .

[0058] For example, in step S140 above, the evolution towards the target height is gradually advanced from the critical height corresponding to the initial critical state, including the following steps: Confirm the position of the rotation center and the critical height in the initial critical state.

[0059] The altitude evolution path is determined based on the target altitude, the position of the rotation center, and the critical altitude, as shown below: (15) in, This is the path advancement coefficient. This indicates that it is in the initial state. ; This indicates that the target height has been reached, that is... ;when hour, and its corresponding center of rotation of the sliding surface Given that the starting state is used for path advancement, and with small step sizes... Gradually increase.

[0060] For example, in step S140, constraining the search domain of the current height based on the critical state of the previous height includes: constraining the initial safety factor and the rotation center contraction domain of the current height, wherein the initial safety factor is as follows: (16) The rotation center contraction region is shown below: (17) in, This represents the initial safety factor at the current altitude. This indicates the contraction zone of the rotation center at the current altitude. It is the convergent solution of the previous height safety factor and the center of rotation. The safety factor is relative to the disturbance amplitude. For Center, radius The rotation center trust region.

[0061] In the above process, to avoid the missed detection mechanism from abruptly changing due to an excessively small tightening domain, this method also sets up an expansion and rollback mechanism. When preset conditions are met, the relative disturbance amplitude of the safety factor is dynamically increased. and the radius of the trust region of the rotation center If the evolution process fails to converge, a global rotation center search is triggered for re-initialization; the preset conditions include at least one of the following: 1. No rotation center satisfying the power balance condition can be found within the contraction domain; 2. The safety factor and the sliding surface morphology undergo abrupt changes; 3. The energy residual decreases non-monotonically.

[0062] For example, in step S140, a consistency reduction is performed under the nonlinear strength envelope constraint for iterative correction, including the following steps: S141. Confirm the reduction factor and reduce it according to the instantaneous cohesion and the instantaneous internal friction angle, ensuring that the strength parameters after reduction are consistent with the original nonlinear envelope; the reduction process is as follows: (18) in, This represents the instantaneous cohesion after reduction. This represents the instantaneous friction angle after reduction. This represents the reduction factor.

[0063] S142. Iterative correction is performed using the bisection method. Based on the sliding surface adaptive generation strategy, a sliding path under the current reduction coefficient is constructed. A reduction coefficient F that satisfies the power balance condition is searched. If it exists, then F is the upper limit solution of the safety factor.

[0064] Specifically: Construct a sliding path under the current reduction factor based on the sliding surface adaptive generation strategy, and search for a path that satisfies the power residual. As explained earlier, the power balance condition is satisfied when the energy residual is less than the set tolerance; if this condition exists, then... To find the upper bound solution for the safety factor, the bisection method is used to update the interval until the upper bound solution with the smallest value within the tightening threshold is obtained. .

[0065] S143. Update the interval using the bisection method until the minimum upper limit solution within the tightening threshold is obtained, which is used as the final safety factor. When At that time, the path propulsion outputs the safety factor at the target height and the corresponding potential sliding surface.

[0066] For example, the method in this application embodiment can be combined with a slope monitoring system to input the measured pore pressure and stress parameters into the system model and update the slip surface evolution and safety factor calculation results in real time.

[0067] like Figure 6 The diagram shown is a flowchart of the safety factor calculation process in an embodiment of this application. The following is a summary of the process. Figure 6 The calculation process will now be explained: First, after the method starts, the initial condition parameters are obtained or set, including cohesion. internal friction angle Nonlinear coefficients slope angle Severe Parameters such as these.

[0068] Based on the critical height convergence of the bisection method described above and the generation of the adaptive nonlinear strength-driven slip surface (potential slip surface).

[0069] The rotation center is searched using the quadratic programming method described above, so that the residual is not greater than the set tolerance and the difference between the current height and the previous height is less than a preset value. If the conditions are not met, the process returns to the step of generating a potential sliding surface.

[0070] Construct a continuous path from the critical altitude to the target altitude and advance it in predetermined increments.

[0071] A tight domain with a safety factor and rotation center is defined and adjusted using a nonlinear reduction method to achieve a potential sliding surface after adaptive parameter reduction.

[0072] The search is performed around the center of rotation, and the interval of the reduction coefficient is bisected to obtain the solution with the minimum coefficient upper bound. It is then determined whether the reduction coefficient converges and whether the following conditions are met. (Indicates the target height). If the conditions are met, the potential sliding surface (related information) and the corresponding safety factor are output as stability evaluation indicators.

[0073] The method in this application employs the technical features of establishing nonlinear strength criteria and nonlinear strength envelopes, fundamentally abandoning the distorted linear strength assumption. This allows for a more realistic reflection of the nonlinear law of soil strength changing with stress state, laying a correct physical foundation for subsequent accurate analysis. Based on the nonlinear strength criterion and related flow laws, the feature of generating a potential sliding surface from the slope toe completely eliminates the dependence on a pre-set sliding surface shape. The sliding surface morphology is dynamically determined by the soil's constitutive relationship (nonlinear criterion) and mechanical laws (flow laws), thus automatically capturing the critical sliding surface that best matches the actual stress state, significantly improving the prediction accuracy of the sliding surface location and morphology. By calculating external force power and internal energy dissipation power to construct a power balance equation and confirm the critical state, this invention replaces the potentially incomplete force or moment balance assumptions in the traditional limit equilibrium method with a strict energy conservation principle, making the solution of the safety factor have a more solid mechanical foundation and the results more reliable. Furthermore, through a highly evolutionary strategy, the solution of complex problems is transformed into a gradual and continuous convergence process. This greatly narrows the scope of the optimization search and avoids the blindness of traditional global search, thus significantly improving computational efficiency while effectively ensuring the stability and convergence of the iteration process.

[0074] Furthermore, this method ensures that the reduced parameters always lie on the original nonlinear envelope when performing strength reduction, thus solving the problem that traditional reduction methods would disrupt the consistency of the original strength model. This makes the final safety factor completely match the adopted nonlinear strength criterion, resulting in a more scientific and accurate evaluation result.

[0075] In summary, the slope stability analysis method based on nonlinear strength criteria provided in this application embodiment can significantly improve the effectiveness and accuracy of slope stability analysis calculation.

[0076] This application also provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described slope stability analysis method based on nonlinear strength criteria.

[0077] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0078] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0079] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0080] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A slope stability analysis method based on a nonlinear strength criterion, characterized in that, The slope stability analysis method based on nonlinear strength criteria includes: Obtain the state parameters of the slope, establish a nonlinear strength criterion and a nonlinear strength envelope based on the state parameters, and generate a potential sliding surface from the toe of the slope based on the nonlinear strength criterion and related flow rules. Based on the potential sliding surface, the potential sliding body is identified, and the potential sliding body is divided into several rigid body elements. The external work power and internal energy dissipation power of the rigid body elements are calculated to construct the power balance equation. Based on the power balance equation, the critical sliding surface and safety factor under the power balance condition are determined by an optimization algorithm and used as the initial critical state. Starting from the critical height corresponding to the initial critical state, the process gradually evolves towards the target height. The search domain of the current height is constrained based on the critical state of the previous height, and consistency reduction is performed under the nonlinear strength envelope constraint for iterative correction. When the height evolution progresses to the target height and the strength reduction iteration converges, the stability evaluation index of the target slope is output.

2. The slope stability analysis method based on nonlinear strength criterion according to claim 1, characterized in that, The state parameters include the slope height, slope angle, slope length, unit weight, cohesion, and internal friction angle of the slope. The nonlinear intensity criterion is in power function form, as shown below: in, and These represent the normal stress and shear stress on the sliding surface, respectively. The initial cohesion, For axial tensile strength, These are nonlinear coefficients.

3. The slope stability analysis method based on nonlinear strength criterion according to claim 2, characterized in that, The generation of a potential sliding surface from the toe of the slope, based on the nonlinear strength criterion and related flow rules, includes: Starting from the toe of the slope, the instantaneous internal friction angle at the starting point is calculated based on the nonlinear strength criterion and the nonlinear strength envelope. Based on the instantaneous internal friction angle of the starting point and the relevant flow rules, the position of the next node is determined through a discrete rotation-velocity discontinuity mechanism, thereby generating a slip surface path; Each new node is taken as the current point, and the slip surface path is iteratively advanced until it intersects with the top of the slope, forming a complete potential slip surface; The step of identifying a potential sliding body based on a potential sliding surface includes defining the closed area enclosed by the potential sliding surface and the slope surface as the potential sliding body.

4. The slope stability analysis method based on nonlinear strength criterion according to claim 2, characterized in that, After establishing the nonlinear intensity criterion and nonlinear intensity envelope based on the state parameters, the method further includes: Based on the nonlinear strength criterion in the form of a power function, a tangent is constructed at any stress point on the nonlinear strength envelope; The instantaneous cohesion and instantaneous internal friction angle are calculated based on the tangent and then locally linearized to obtain equivalent linear parameters that dynamically change with the stress state.

5. The slope stability analysis method based on nonlinear strength criterion according to claim 2, characterized in that, The calculation of the external work power and internal energy dissipation power of the rigid body element to construct the power balance equation includes: Identify the motion parameters in the potential sliding body, wherein the motion parameters include the weight of the sub-block, displacement power, shear stress, and relative displacement rate of the sliding surface; Calculate the external work power and internal energy dissipation power of the rigid body unit based on the motion parameters; A power residual function is constructed based on the external power and the internal energy dissipation power, as shown below: Among them, W ext The external power output is represented by W. dis R represents the internal energy dissipation power, and R represents the residual. When the residual is less than the set tolerance, power balance is achieved. The optimization algorithm includes sequential quadratic programming or bisection method, used to solve for the position of the rotation center and the critical height.

6. The slope stability analysis method based on nonlinear strength criterion according to claim 5, characterized in that, The process of gradually evolving towards the target height, starting from the critical height corresponding to the initial critical state, includes: Confirm the position of the rotation center and the critical height under the initial critical state; The height evolution path is determined based on the target height, the rotation center position, and the critical height, as shown below: in, This is the path advancement coefficient. This indicates that it is in the initial state. ; This indicates that the target height has been reached, that is... ;when hour, and its corresponding center of rotation of the sliding surface Given that the starting state is used for path advancement, and with small step sizes... Gradually increase.

7. The slope stability analysis method based on nonlinear strength criterion according to claim 2, characterized in that, The search domain for constraining the current height based on the critical state of the previous height includes: an initial safety factor constraining the current height and a rotation center contraction domain, wherein the initial safety factor is as follows: The rotation center contraction region is shown below: in, This represents the initial safety factor at the current altitude. This indicates the contraction zone of the rotation center at the current altitude. It is the convergent solution of the previous height safety factor and the center of rotation. The safety factor is relative to the disturbance amplitude. For Center, radius The rotation center trust region.

8. The slope stability analysis method based on nonlinear strength criterion according to claim 7, characterized in that, The search domain constrained by the critical state of the previous height for the current height also includes: when the preset conditions are met, dynamically expanding the relative disturbance amplitude of the safety factor and the radius of the rotation center trust domain; if the evolution process cannot converge, triggering a global rotation center search for re-initialization. The preset conditions include at least one of the following: no rotation center that satisfies the power balance condition can be found within the contraction domain; the safety factor and the sliding surface morphology undergo abrupt changes; and the energy residual decreases non-monotonically.

9. The slope stability analysis method based on nonlinear strength criterion according to claim 4, characterized in that, The consistency reduction under nonlinear strength envelope constraints for iterative correction includes: Confirm the reduction factor, and reduce it according to the instantaneous cohesion and the instantaneous internal friction angle, ensuring that the strength parameters after reduction are consistent with the original nonlinear envelope; The reduction process is as follows: in, This represents the instantaneous cohesion after reduction. This represents the instantaneous friction angle after reduction. Indicates the reduction factor; The bisection method is used for iterative correction. The sliding path under the current reduction coefficient is constructed according to the sliding surface adaptive generation strategy. The reduction coefficient F that satisfies the power balance condition is searched. If it exists, then F is the upper limit solution of the safety factor. The interval is updated using a bisection method until the minimum upper limit solution within the tightening threshold is obtained, which serves as the final safety factor.

10. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the slope stability analysis method based on the nonlinear strength criterion as described in any one of claims 1-9.

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