The application discloses a method and device for calculating anti-heave stability of a foundation pit considering pit bottom reinforcement and a storage medium.

Abstract

The application discloses a kind of pit anti-heave stability calculation method and device considering pit bottom reinforcement, storage medium, constructs by region I conventional soil subsidence translation zone, region II conventional soil logarithmic spiral shear zone, region III reinforced soil logarithmic spiral shear zone and region IV reinforced soil upper heave translation zone Composed of four regional kinematics allowing mechanism, and keep position continuous, velocity continuous at the common radial line EF of region II and region III;The work done by gravity and pit outside ground surface additional load of each region, the internal energy consumption of each velocity discontinuity surface and segmented shear zone is calculated respectively, the critical anti-heave stability coefficient is determined by power balance and mechanism parameter optimization, and the minimum effective replacement rate meeting target stability coefficient can be inversely calculated.The application introduces pit bottom reinforcement replacement rate simultaneously into material parameter, velocity field, failure profile and power balance process, and can be used for un-reinforced scheme checking, different reinforcement arrangement comparison and minimum reinforcement demand determination.

Description

Technical Field

[0001] This invention belongs to the field of foundation pit engineering stability analysis and foundation reinforcement design technology, specifically involving a foundation pit heave stability calculation method and device, and storage medium that considers pit bottom reinforcement. Background Technology

[0002] In soft cohesive soil layers, silty clay layers, and other strata where shear strength is simultaneously controlled by cohesion and friction, deep foundation pit excavation can cause downward movement of the soil outside the pit and upward heave of the soil inside the pit. When the insertion depth of the retaining wall, the strength of the soil at the bottom of the pit, or the passive zone resistance are insufficient, the foundation pit may experience overall heave instability, leading to increased deformation at the bottom of the pit, displacement of the retaining structure, and additional deformation of surrounding buildings and structures.

[0003] In engineering projects, cement-soil mixing piles, high-pressure jet grouting piles, grouting reinforcement, or other composite reinforcement methods are often used to reinforce the potential uplift zone at the bottom of the pit before excavation, either as a whole or in a grid pattern. Reinforcement design typically involves factors such as the area ratio of the reinforcement body, construction effectiveness, strength of the reinforcement materials, and parameters of the composite soil after reinforcement. Therefore, stability calculations not only need to determine whether the unreinforced foundation pit is safe, but also need to quantify the impact of different reinforcement levels on the critical failure mechanism and stability coefficient, and calculate the minimum reinforcement requirements to meet the design specifications.

[0004] Existing methods for calculating heave resistance often employ bearing capacity models, Prandtl models, circular arc sliding models, or predefined rigid block models. These methods typically rely on homogeneous soil and fixed failure profiles, often simplifying the bottom reinforcement effect to shear strength increments, additional resistance, or empirical correction coefficients. This fails to reflect the combined impact of changes in the internal friction angle after reinforcement on the velocity field exponential rate, shear zone curvature, the extent of moving soil, and internal energy distribution. While finite element strength reduction methods can simulate complex reinforced zones, they require repeated modeling and iteration in scheme comparison and replacement rate back-calculation, resulting in high computational costs. Furthermore, the critical mechanism is affected by the mesh, constitutive model, and convergence criteria.

[0005] Furthermore, there are existing upper limit analysis methods for soils characterized by cohesion and internal friction angle, mainly targeting unreinforced homogeneous strata. When the potential uplift zone within the pit is reinforced as a whole, the conventional soil and the reinforced soil have different effective strength parameters; if a single exponential shear fan is still used, or if only the reinforcement gain is superimposed on the final stability coefficient, the continuity of velocity on both sides of the common diameter EF cannot be guaranteed, nor can the critical failure profile be updated synchronously.

[0006] Therefore, there is a need for a method to calculate the heave stability of a pit bottom reinforcement level directly to the composite soil parameters and to construct the velocity field of a conventional soil-reinforced soil combination under kinematically permissible conditions, so as to uniformly solve the problems of unreinforced verification, reinforcement scheme evaluation and minimum reinforcement requirement back calculation. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a method, device, and storage medium for calculating the heave stability of a foundation pit considering bottom reinforcement. It acquires parameters such as the foundation pit geometry, effective strength of the conventional soil, layout of the bottom reinforcement, additional surface loads, and design objectives. The effective replacement rate is determined by the reinforcement area ratio and construction effectiveness coefficient, and the effective cohesion, effective internal friction angle, and effective unit weight of the reinforced soil are obtained accordingly. A four-region kinematic permissible mechanism is constructed, consisting of a conventional soil settlement and translation zone in Region I, a logarithmic spiral shear zone in Region II, a logarithmic spiral shear zone in Region III, and a heave and translation zone in Region IV. Positional and velocity continuity is maintained at the common radius EF of Regions II and III. The power generated by gravity and additional surface loads outside the pit in each region, the internal energy dissipation of each velocity discontinuity, and the segmented shear zone are calculated separately. The critical heave stability coefficient is determined through power balance and mechanism parameter optimization, and the minimum effective replacement rate to meet the target stability coefficient can be calculated in reverse. This invention incorporates the pit bottom reinforcement replacement rate into material parameters, velocity field, failure profile, and power balance process simultaneously. It can be used for verifying unreinforced schemes, comparing different reinforcement arrangements, and determining minimum reinforcement requirements. It solves the problem that existing simplified methods cannot simultaneously consider the reinforcement replacement rate, changes in reinforced soil strength, continuity of the segmented velocity field, and updating of the critical failure profile. To achieve the above objectives, the present invention provides the following solution: A method for calculating the heave stability of a foundation pit considering bottom reinforcement includes: Obtain the excavation depth of the foundation pit, the insertion depth of the retaining wall, the effective strength parameters of the conventional soil, the soil weight, the reinforcement layout parameters of the pit bottom, the reinforcement material parameters, and the additional load on the ground surface outside the pit; The effective replacement rate is determined based on the reinforcement layout parameters at the bottom of the pit, and the effective cohesion, effective internal friction angle, and effective unit weight of the reinforced soil in the pit are determined based on the effective replacement rate. Strength reduction was applied to both conventional soil and reinforced soil to obtain mobilization strength parameters under a given trial stability coefficient; An anti-heave failure mechanism is constructed, which includes the conventional soil settlement and displacement zone in region I, the logarithmic spiral shear zone in region II, the logarithmic spiral shear zone in region III, and the heave and displacement zone in region IV; Construct velocity fields for regions II and III respectively, so that the positions and velocities of the two shear zones at the common radius EF are continuous, and the velocities of the two translation zones along the wall normal are compatible with the horizontal translation velocity of the rigid wall; Based on the anti-heave failure mechanism and the segmented velocity field, calculate the power of the external load and the internal energy dissipation power. The stability coefficient under given mechanism parameters is determined by making the power exerted by the external load equal to the power dissipated by the internal energy. The coefficient is then optimized within the feasible region of the mechanism parameters that satisfy velocity compatibility, associated flow, and geometrically effective conditions to obtain the critical anti-uplift stability coefficient.

[0008] Preferably, the effective replacement rate is determined by the area occupied by the reinforcing material in the equivalent calculation unit and the construction effectiveness coefficient; the construction effectiveness coefficient is used to characterize construction deviation, reinforcement overlap, strength dispersion and reinforcement effectiveness.

[0009] Preferably, the effective cohesion, friction coefficient, and effective unit weight of the reinforced soil are respectively equivalent to conventional soil parameters and reinforcement material parameters according to the effective replacement rate, and nonlinear equivalent relationships obtained by field tests, laboratory tests, or numerical inversion are allowed to replace linear equivalent relationships.

[0010] Preferably, regions II and III have different mobilization internal friction angles, velocity exponential rates, and logarithmic spiral growth rates. The two shear zones share the velocity at point F and the extreme radius EF, so that no velocity jump occurs at the common radius EF. EF is the boundary between regions II and III, but does not constitute a velocity discontinuity, and its interface energy consumption is zero.

[0011] Preferably, the power exerted by the external load includes the gravity power of the conventional soil settlement and displacement zone in Region I, the gravity power of Region II, the gravity power of Region III, the gravity power of the reinforced soil uplift and displacement zone in Region IV, and the power of the additional surface load outside the pit; the internal energy dissipation power includes the energy dissipation at the velocity discontinuity outside the pit, the energy dissipation at the velocity discontinuity inside the pit, and the energy dissipation in Regions II and III.

[0012] As a preferred option, when the effective replacement rate is zero, the parameters of the reinforced soil are restored to those of the conventional soil, and the common diameter EF is degenerated into a regional boundary line without strength abrupt changes or velocity jumps, so as to obtain the heave stability coefficient of the unreinforced foundation pit.

[0013] Preferably, the method further includes: given a target heave stability coefficient, repeatedly performing composite soil parameter calculation, segmented velocity field construction, power balance solution and mechanism optimization within the range of effective replacement rate, to determine the minimum effective replacement rate that satisfies the target heave stability coefficient.

[0014] Preferably, the additional load on the ground outside the pit is a vertically uniformly distributed load, and its power is determined according to the smaller value between the actual width of the additional load and the width of the moving ground outside the pit.

[0015] The present invention also provides a calculation device for the anti-heave stability of a foundation pit considering bottom reinforcement, comprising: The parameter acquisition module is used to acquire parameters such as the geometry of the foundation pit, the effective strength of the conventional soil, the layout of the reinforcement at the bottom of the pit, the reinforcement materials, and the additional load on the ground surface outside the pit. The module for determining replacement rate and composite soil parameters is used to determine the effective replacement rate from the reinforcement area ratio and the construction effectiveness coefficient, and to determine the reinforcement soil parameters from the effective replacement rate. The strength reduction module is used to reduce the strength of conventional soil and reinforced soil respectively. The failure mechanism construction module is used to construct the subsidence and displacement zone of conventional soil in Region I, the shear zone of conventional soil in Region II, the shear zone of reinforced soil in Region III, and the heave and displacement zone of reinforced soil in Region IV. The kinematics allowance check module is used to construct the velocity fields of region II and region III respectively, and to ensure the continuity of position and velocity at the common track EF; The power calculation module is used to calculate the power exerted by external loads in each region and the internal energy dissipation power at each velocity discontinuity. The root-finding and optimization module is used to solve for the stability coefficient through power balance and search for critical values ​​within the feasible region of kinematically permissible mechanism parameters; The results output module is used to back-calculate the minimum effective permutation rate to achieve the target stability coefficient as needed.

[0016] The present invention also provides a storage medium storing a computer program, which, when running, executes a method for calculating the stability of a foundation pit considering bottom reinforcement.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: The reinforcement of the pit bottom is transformed from external resistance or empirical coefficients into composite soil material parameters and velocity field parameters, so that the reinforcement effect enters the failure mechanism formation process; Regions II and III adopt velocity exponential rates corresponding to their respective internal friction angles, and maintain position and velocity continuity at the common trajectory EF; For each effective replacement rate, the composite soil parameters, critical mechanism geometry, external power, and internal energy dissipation are recalculated to reflect the changes in the failure profile with the degree of reinforcement. When the effective replacement rate is zero, it naturally degenerates into an unreinforced homogeneous soil condition, and benchmark verification and reinforcement scheme evaluation can be completed within the same calculation framework; It can output critical stability coefficient, failure profile, power components and kinematic residuals, and can back-calculate the minimum effective replacement rate to meet the design objectives; The calculation parameters can be obtained from conventional surveys, indoor tests, and reinforcement design data. The calculation workload is lower than that of repetitive three-dimensional numerical modeling, making it suitable for rapid comparison and selection during the scheme stage. Attached Figure Description

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

[0019] Figure 1 To illustrate the four-zone anti-heave failure mechanism of overall pit bottom reinforcement according to an embodiment of the present invention; Figure 2 According to the embodiments of the present invention, the equiangular rigid triangular block sector of region II and region III, the velocity triangle of adjacent blocks, and their corresponding symbols are shown. Figure 3 This is a flowchart illustrating the method for calculating the anti-heave stability of a foundation pit considering bottom reinforcement, as described in an embodiment of the present invention. Figure 4 This is a schematic diagram of the structure of a foundation pit heave stability calculation device considering pit bottom reinforcement according to an embodiment of the present invention; Figure 5 This is a comparison between the method and existing numerical results when the effective substitution rate is zero according to an embodiment of the present invention; Figure 6 The critical stability coefficient and its increase are given by the effective substitution rate according to an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] Example 1 This invention provides a method for calculating the heave stability of a foundation pit considering bottom reinforcement. First, a trial stability coefficient is calculated. F As inner-layer variables, stability coefficients under given mechanism parameters are obtained through intensity reduction, mechanism construction, kinematic permissibility verification, and power balance root finding; secondly, the expansion angle of region II is used. I 2 is a mid-level variable; the critical failure mechanism is searched within the kinematically permissible parameter domain, and the minimum stability coefficient is taken. When it is necessary to determine the minimum reinforcement level, the effective replacement rate is then used. orFor the outer variables, the minimum effective permutation rate that satisfies the target stability coefficient is calculated inversely. Therefore, the following steps are not a linear list of independent variables, but rather follow a sequential order. Figure 3 The nested relationship between the inner root finding, the middle optimization, and the outer inverse calculation is shown.

[0023] This embodiment employs a two-dimensional plane strain condition, with soil values ​​determined based on either drainage or effective stress conditions. Shear strength is characterized by effective cohesion and effective internal friction angle. Potential uplift zones within the pit are assumed to be reinforced holistically; therefore, regions III and IV utilize the same set of reinforced soil parameters. c 2. , c 2; The same set of conventional soil parameters was used for both Region I and Region II. c 1. , c 1. The enclosure wall, as a rigid body that does not undergo bending energy dissipation, undergoes horizontal translation. The normal velocities of the contact sections between the enclosure wall and the wall in regions I and IV are both equal to the horizontal translation velocity of the rigid wall.

[0024] Furthermore, the method for calculating the heave stability of a foundation pit considering bottom reinforcement according to the present invention specifically includes: Step 1: Obtain calculation parameters. Obtain the excavation depth. H The insertion depth of the retaining wall below the bottom of the pit. d Effective cohesion of conventional soil c 1. Effective internal friction angle of conventional soil Effective unit weight of conventional soil c 1. Uniformly distributed additional load outside the pit q and load width b_q; obtain the effective cohesion of the reinforcing material. c g Effective internal friction angle of reinforcing materials Effective weight of reinforcement materials c g Equivalent calculation unit area A c Effective reinforcement area A g and construction effective coefficient x .

[0025] Step 2: Determine the effective replacement rate and reinforced soil parameters. Combine the reinforced area ratio with the construction effectiveness into the effective replacement rate, allowing the design layout and construction quality to be included as unified variables in the stability calculation.

[0026] In the formula, or For effective replacement rate; x This is the effective construction coefficient, and its value ranges from 0 to 1. A gThe effective area of ​​the reinforcing material within the equivalent calculation unit; A c This represents the total area of ​​the equivalent calculation unit.

[0027] In the formula, c 2( or () represents the effective replacement rate or The corresponding effective cohesion of the reinforced soil; c 1 represents the effective cohesion of conventional soil; c g To reinforce the effective cohesion of materials or to fully strengthen the soil; or The effective replacement rate.

[0028] In the formula, ( ) represents the effective internal friction angle of the reinforced soil; This is the effective internal friction angle of conventional soil; To reinforce the material or fully reinforce the soil's effective internal friction angle; or The effective replacement rate.

[0029] In the formula, c 2( or ( ) represents the effective unit weight of the reinforced soil; c 1 represents the effective unit weight of conventional soil; c g To reinforce the material or fully reinforce the effective unit weight of the soil; or The effective replacement rate.

[0030] The above equivalent relationship is a basic implementation method for convenient engineering applications. When laboratory tests, field core tests, or numerical inversion show that the composite soil parameters and replacement rate have a nonlinear relationship, a function calibrated by experiments can be used. c 2( or ), )and c 2( or Substitute equations (2) to (4), and the subsequent calculation steps remain unchanged.

[0031] Step 3: Reduce the strength of conventional soil and reinforced soil respectively. Calculate the stability coefficient using trial calculations. F Strength reduction was applied to both types of materials to obtain results comparable to current strength. F and or The corresponding mobilization intensity parameters.

[0032] In the formula, c 1m For conventional soil mobilization cohesion;c 1 represents the effective cohesion of conventional soil; F To calculate the stability coefficient.

[0033] In the formula, This is the internal friction angle of conventional soil mobilization; This is the effective internal friction angle of conventional soil.

[0034] In the formula, c 2m To strengthen soil cohesion; c 2( or () represents the effective replacement rate or The corresponding effective cohesion of the reinforced soil; F To calculate the stability coefficient.

[0035] In the formula, To reinforce the soil, the internal friction angle is increased; () represents the effective replacement rate or The corresponding effective internal friction angle of the reinforced soil.

[0036] In the formula, t 1 represents the friction coefficient of conventional soil mobilization; t 2 represents the mobilization friction coefficient of the reinforced soil; and These are the internal friction angles of conventional soil and reinforced soil, respectively.

[0037] Step 4: Construct an anti-bulging failure mechanism. For example... Figure 1 As shown, the origin of the coordinate system is the intersection point O1 of the pit bottom and the retaining wall, and the coordinate system is the direction from the retaining wall outwards from the pit. x The positive direction of the axis is vertically upward. y Positive axis direction; wall toe E is located below O1 at a distance d The regions are as follows: Region I is the conventional soil settlement and displacement zone ABCE; Region II is the conventional soil logarithmic spiral shear zone CEF with point E as the pole; Region III is the reinforced soil logarithmic spiral shear zone FEM with the same point E as the pole; Region IV is the reinforced soil uplift and displacement zone O1-NME within the pit. EF is the common radius of Regions II and III, and F is the common point of the two regions; the position and velocity at EF are continuous, not a velocity discontinuity, and the energy dissipation at its interface is zero.

[0038] Step 5: Construct the velocity field of Region II. Referring to the isoangular rigid triangular block construction in Section 3.4.2 of Chen (1975), the continuous shear region of Region II is first discretized into... nTwo points with E as their common vertex and both having a central angle of Δ β The rigid triangular block is then used to establish a recursive relationship based on the velocity triangles of adjacent blocks. Let the EF radius be vertically downwards, and the local angular coordinates... β Measured from EC to EF.

[0039] In the formula, i F For the EF meridian relative x The polar angle of the axis; i C EC Meridians Relative x The polar angle of the axis; I 2 represents the total expansion angle of region II from EC to EF; π is pi. The above angles are in... Figure 1 The polar angle and the unfolding angle are shown in the magnified diagram.

[0040] In the formula, n 2 represents the number of discrete rigid triangular blocks in region II; Δ β The central angle between two adjacent radii; β j For the first j The cumulative local angle of the stripe relative to EC; j Number the discrete blocks in region II. Figure 2 (a) indicates Δ β , β j Passing the exam j A rigid triangular block.

[0041] Adjacent number j -1 block and the first j Tangential relative sliding occurs between blocks you 2,j According to the Mohr-Coulomb associated flow conditions, this tangential velocity increment must be accompanied by a normal separation velocity. dv 2,j The relationship is as follows:

[0042] In the formula, you 2,j This represents the component of the velocity difference between adjacent blocks in region II along the tangential direction of their common radial line; dv 2,j Its normal component; This is the internal friction angle of conventional soil mobilization; t 1 represents the friction coefficient of conventional soil mobilization. Figure 2 (b) gives v 2,j-1 , v2,j , you 2,j , d v 2,j Δ β and The velocity triangle formed.

[0043] When Δ β When the velocity is sufficiently small, the velocity magnitude and the corresponding polar radius have the same first-order growth rate, as can be seen from the velocity triangle of adjacent blocks.

[0044] In the formula, v 2,j-1 and v 2,j They are respectively the second region II j -1 block and the first j The speed of the block; r 2,j-1 and r 2,j These are the polar radii from the corresponding outer edge point to the pole E. Take point EC. v 2,0 = v 1. r 2,0 = r C By iterating through each block, we can obtain:

[0045] In the formula, v 1 represents the reference velocity on the starting radial line EC of Region I and Region II; r C For EC length. With n 2 tends to infinity, Δ β Approaching zero and maintaining β = j Δ β Unchanged, the discrete rigid triangular block sector converges to a continuous logarithmic spiral shear region:

[0046] In the formula, v 2( β ( ) represents the local angular coordinates of region II. β The magnitude of the velocity at that point; r 2( β ) represents the polar radius at the same location; exp is the natural exponential function. This equation shows that both the velocity and polar radius change from EC to EF at a constant angle. t1. Controlled exponential growth. Following Chen's logarithmic spiral shear region construction, the velocity magnitude remains constant along each radial line, and the velocity direction is perpendicular to the corresponding radial line; the velocity magnitude and polar radius increase exponentially from EC to EF. Let... β = I 2. The velocity and polar radius at the common point F can be obtained:

[0047] In the formula, v F Let F be the magnitude of the velocity at the common point. r F The length of EF; v 1. r C , I 2 and t The meaning of 1 is the same as before.

[0048] Step Six: Construct the velocity field for Region III. Region III adopts the same isoangular rigid triangular block limit structure as Region II, but the material parameters are changed to the mobilization strength of reinforced soil. The velocity field at the endpoint F of Region II is used as the starting point. v F and r F As the starting value for region III, local angular coordinates x Measured from EF to EM.

[0049] In the formula, i M For EM diameter relative x The polar angle of the axis; i F The polar angle of the EF radial line; I 3 represents the total development angle of region III from EF to EM.

[0050] In the formula, n 3 represents the number of discrete rigid triangular blocks in region III; Δ x The central angle between adjacent radii; x k For the first k The cumulative local angle of the radii relative to EF; k Number the discrete blocks in region III. Figure 2 (c) indicates Δ x , x k Passing the exam k A rigid triangular block.

[0051] Adjacent number k -1 block and the first kTangential velocity increment between blocks you 3,k and normal separation velocity dv 3,k The associated flow conditions for the reinforced soil are satisfied:

[0052] In the formula, you 3,k and dv 3,k These are the tangential and normal components of the velocity difference between adjacent blocks in Region III, respectively. To reinforce the soil, the internal friction angle is increased; t 2 represents the mobilization friction coefficient of the reinforced soil. Figure 2 (d) gives the velocity triangles of adjacent blocks in region III.

[0053] When Δ x When the size is sufficiently small, the block-by-block recursive relationship between the velocity magnitude and polar radius of region III is as follows:

[0054] In the formula, v 3,k-1 , v 3,k and r 3,k-1 , r 3,k These represent the velocity magnitudes and corresponding polar radii of adjacent rigid blocks in region III. Take point EF... v 3,0 = v F , r 3,0 = r F ,get:

[0055] In the formula, v F and r F Let F be the initial velocity and initial polar radius shared by regions II and III at their common point F. Let n 3 tends towards infinity, Δ x Approaching zero and maintaining x = k Δ x Without changing the parameters, we obtain the continuous velocity field and logarithmic spiral radius of region III:

[0056] In the formula, v 3( x )and r 3( x The coordinates of region III are respectively the local angular coordinates. x The magnitude of the velocity and the polar radius at each point. According to Chen's construction, the magnitude of the velocity remains constant along each radial line, and the velocity direction is perpendicular to the corresponding radial line; the magnitude of the velocity and the polar radius increase exponentially from EF to EM. Let... x = I 3. Obtain the velocity magnitude of point M and region IV, and the length of EM:

[0057] In the formula, v 4 represents the velocity magnitude of point M and region IV; r M Let be the length of EM. From equation (15) in... β = I 2 places and equation (22) in x = 0 can be obtained v 2( I 2) = v 3(0) = v F , r 2( I 2) = r 3(0) = r F Therefore, Region II and Region III are continuous in position and velocity at their common path EF; EF is only used to distinguish them. c 1. , c 1 and c 2. , c 2. It does not form a velocity discontinuity, and its interface energy consumption is zero.

[0058] Step 7: Determine the rigid body velocity compatibility relationship and mechanistic mechanism. Region I... v 1. A rigid body is translated, with its velocity direction perpendicular to EC; Region IV is... v 4. A rigid body is translated, with its velocity direction perpendicular to EM. The retaining wall moves horizontally with a velocity... v w Translation. Based on the non-penetration condition of the wall-soil contact surface, the projections of the velocities in regions I and IV onto the wall's normal direction should both be equal to the horizontal velocity of the wall:

[0059] In the formula, v 1 represents the magnitude of the velocity in region I; v 4 represents the velocity magnitude of region IV; i C and i M Relative to the diameters EC and EM, respectively. xPolar angle in the positive direction of the axis; v w For the wall along x The signed horizontal velocities in the direction. Since the velocities of regions I and IV are perpendicular to EC and EM, respectively, their wall normal projections are respectively... v 1sin i C and v 4sin i M This equation indicates that the normal velocity of the wall is equal to that of the adjacent soil on both sides of the wall.

[0060] In the formula, I 2 and I 3 represents the expansion angles of region II and region III, respectively; t 1 and t 2 represents the friction coefficients of the two materials; this formula is used to obtain the friction coefficients of the two materials given by the given equation. I 2. Find the wall surface that is compatible with the normal direction. I 3.

[0061] In this embodiment, to avoid the EC length becoming an unconstrained independent dimension, a closure condition is adopted where the geometric angle between EC and the vertically downward wall line is equal to the conventional soil mobilization internal friction angle, resulting in:

[0062] In the formula, l Insertion depth of EC and enclosure wall d The ratio; EC is the distance from point E to point C; d The length is O1E; This is the internal friction angle of conventional soil mobilization; i C This is the polar angle of the EC radial line.

[0063] In the formula, ( x C , y C ), ( x F , y F )and( x M , y M ) are respectively C , F and M The plane coordinates of the point; x E , y E ( ) is the toe pole of the wall.E Plane coordinates; r C , r F and r M They are respectively EC , EF and EM Length; i C and i M They are respectively EC and EM Relative diameters x The polar angle of the axis.

[0064] In the formula, d B The direction angle of the velocity discontinuity BC outside the pit relative to the x-axis; d N The velocity discontinuity MN within the pit is relative to x The direction angle of the axis; i C and i M These are the EC and EM polar angles, respectively. and These are the internal friction angles of conventional soil and reinforced soil, respectively.

[0065] In the formula, L BC and L MN These are the lengths of the velocity discontinuity BC outside the pit and the velocity discontinuity MN inside the pit, respectively. H This refers to the depth of the foundation pit excavation. y C and y M Here are the y-coordinates of points C and M, respectively. d B and d N These are the BC and MN direction angles, respectively.

[0066] In the formula, B and N These are the intersections of the velocity discontinuities outside and inside the pit with the ground surface or the bottom of the pit, respectively; x B , y B )and( x N , yN ) are respectively B Point and N The plane coordinates of the point; x C , y C )and( x M , y M ) are respectively C Point and M The plane coordinates of a point; L BC and L MN velocity sections BC and MN Length; d B and d N They are respectively BC and MN relatively x The direction angle of the axis.

[0067] To avoid selecting conjugate branches that contract inwards from the angle solely based on their positive or negative values, the outward branch criterion should be explicitly applied: BC intersects the surface outside the pit from point C to the upper right, and MN intersects the bottom of the pit from point M to the upper left.

[0068] In the formula, d B Let C be the directed angle from C to B. d N Let M be the directed angle from M to N; the above angle intervals respectively ensure that BC is located in the first quadrant and MN is located in the second quadrant.

[0069] In the formula, x B , x C , x N and x M Let B, C, N, and M be the x-coordinates of the points respectively. This formula ensures that B is located outside the pit of C and N is located inside or outside the pit of M, thus eliminating geometric branches that contract into the mechanism.

[0070] Step 8: Calculate the power exerted by external loads. The power exerted by external loads includes the gravity power of Region I, the gravity power of Region II, the gravity power of Region III, the gravity power of Region IV, and the additional load power from the surface outside the pit.

[0071] In the formula, P 1 represents the gravitational power in region I; c 1 represents the effective unit weight of conventional soil; A 1 represents the area of ​​region I; v 1cos i C This is the projection of the velocity in region I along the vertically downward direction.

[0072] In the formula, P 4 represents the gravitational power of region IV; c 2 represents the effective unit weight of the reinforced soil; A 4 represents the area of ​​region IV; v 4cos i M The signed projection of the velocity in region IV along the vertically downward direction.

[0073] In the formula, f 2( β ) is the integrand of the gravitational power in region II; β These are the local angular coordinates of a typical soil section; t 1 represents the friction coefficient of conventional soil mobilization; i C This is the EC polar angle.

[0074] In the formula, I 2 represents the integral coefficient of gravity power in region II; I 2 represents the expansion angle of region II; f 2( β ) is the integrand of the gravitational power in region II; β It is the integral variable.

[0075] In the formula, P 2 represents the gravitational power in region II; c 1 represents the effective unit weight of conventional soil; v 1 represents the reference speed for Region I; r C EC length; I 2 represents the integral coefficient of gravity power in region II.

[0076] In the formula, f 3( x ) is the integrand of the gravitational power in region III; x The local angular coordinates of the reinforced section; t2 represents the mobilization friction coefficient of the reinforced soil; i F The polar angle of the EF radial line.

[0077] In the formula, I 3 represents the integral coefficient of gravity power in region III; I 3 represents the unfolding angle of region III; f 3 ( x ) is the integrand of the gravitational power in region III; x It is the integral variable.

[0078] In the formula, P 3 represents the gravitational power in region III; c 2 represents the effective unit weight of the reinforced soil; v F and r F These represent the velocity and polar radius at point F, respectively. I 3 represents the integral coefficient of gravity power in region III.

[0079] In the formula, P q Additional load power to the surface outside the pit; q The additional vertical load is uniformly distributed outside the pit; x B Let B be the x-coordinate, representing the width of the ground surface outside the pit. b q The actual width of the additional load; v 1cos i C This is the projection of the velocity in region I along the vertically downward direction.

[0080] In the formula, P 23 The gravitational power is for regions II and III; P 2 and P 3 represents the gravitational power of regions II and III, respectively.

[0081] In the formula, P ext Power applied to the total external load; P 1. P 23 and P 4 represents the sum of regions I, II, and III, and the gravitational power of region IV, respectively. Pq Additional load power to the surface outside the pit.

[0082] Step 9: Calculate the internal energy dissipation power. The internal energy dissipation power is generated by the velocity discontinuity BC outside the pit, the velocity discontinuity MN inside the pit, and the radial velocity discontinuities and logarithmic spiral outer edges of regions II and III, respectively.

[0083] In the formula, D BC Energy dissipation at velocity discontinuity BC outside the pit; c 1m For conventional soil mobilization cohesion; L BC The length of BC; v 1 represents the magnitude of the velocity in region I; This is the internal friction angle of conventional soil mobilization.

[0084] In the formula, D MN Energy consumption of velocity discontinuity MN within the pit; c 2m To strengthen soil cohesion; L MN MN is the length; v 4 represents the velocity magnitude of region IV; To reinforce the soil, the internal friction angle is adjusted.

[0085] In the formula, K 2 represents the energy consumption index factor for Region II; I 2 represents the expansion angle of region II; t 1 represents the friction coefficient of conventional soil mobilization.

[0086] In the formula, D 2 represents the energy dissipation of a set of radially discontinuous lines or logarithmic spiral outer edges in region II; c 1m For conventional soil mobilization cohesion; v 1 represents the magnitude of the velocity in region I; r C EC length; t 1 represents the friction coefficient of conventional soil mobilization; K 2 represents the energy consumption index factor for Region II.

[0087] In the formula, K 3 represents the energy consumption index factor for Region III; I3 represents the unfolding angle of region III; t 2 represents the mobilization friction coefficient of the reinforced soil.

[0088] In the formula, D 3 represents the energy dissipation of a set of radially discontinuous lines or logarithmic spiral outer edges in region III; c 2m To strengthen soil cohesion; v F and r F These represent the velocity and polar radius at point F, respectively. t 2 represents the mobilization friction coefficient of the reinforced soil; K 3 represents the energy consumption index factor for Region III.

[0089] In the formula, D 23 The internal energy dissipation power of regions II and III; D 2 and D 3 represents a set of energy consumption for regions II and III respectively; coefficient 2 indicates that the energy consumption of the radial discontinuity line and the energy consumption of the outer edge of the logarithmic spiral are both included in regions II and III.

[0090] In the formula, D total This represents the total internal energy dissipation power. D BC and D MN These represent the energy consumption at velocity discontinuities outside and inside the pit, respectively.

[0091] Step 10: Solve for the critical stability coefficient. For a given effective substitution rate... or and the expansion angle of Region II I 2. First, obtain the compatibility equation using the wall method. I 3. Then solve using the power balance equation. F .

[0092] In the formula, R For power residual; D total For a given trial stability coefficient F Region II Expansion Angle I 2 and effective replacement rate or Total internal energy dissipation power at that time; P ext The power applied to the total external load under the same trial calculation condition.

[0093] In the formula, F cr ( or () represents the effective replacement rate or The corresponding critical uplift stability coefficient; F ( I 2, or ) is given I 2 and or The minimum feasible positive root of the power balance equation; Ω represents the condition satisfying velocity compatibility, associated flow, non-penetration, and geometric efficiency. I 2. Feasible region.

[0094] In the specific solution process, you can first use the preset... I Perform a coarse grid scan within a 2-range; for each I 2, in F Within the positive interval, the power residual sign-changing interval is searched, and the minimum feasible positive root is obtained using the bisection method, Brent method, or other one-dimensional root-finding algorithms; mechanisms such as node out-of-bounds, non-positive region area, non-positive discontinuity length, incompatible wall normal, or soil penetration are eliminated; finally, the minimum of all feasible mechanisms is selected. F As F cr .

[0095] Step 11: Back-calculate the minimum effective replacement rate. When the design task specifies the target heave stability coefficient, in or Repeat steps two through ten within the range of values, and find the minimum value that satisfies the objective value. or .

[0096] In the formula, g ( or ) represents the replacement rate or The corresponding stability margin; F cr ( or () represents the corresponding critical resistance to uplift stability coefficient; F target The target is the anti-uplift stability coefficient.

[0097] In the formula, e A feasible set of effective permutation rates to meet the design objectives; or To calculate the effective replacement rate; g ( or ) represents the corresponding stability margin.

[0098] In the formula, ormin The minimum effective replacement rate to meet the design objectives.

[0099] like F cr (0) Not less than F target Then output or min = 0; if F cr (1) Still less than F target If the current reinforcement material parameters and reinforcement range are insufficient, a prompt will be output indicating that the target cannot be met simply by increasing the replacement rate.

[0100] Example 1: Degradation Verification in Unreinforced Conditions This embodiment is used to verify that when the bottom of the pit is not reinforced, the segmented failure mechanism constructed by the present invention can naturally degenerate into a homogeneous soil failure mechanism, and to verify the rationality of the corresponding power calculation and stability coefficient solution results.

[0101] make or = 0, based on the calculation relationship of composite soil parameters, we can obtain: c 2= c 1. and c 2= c 1.

[0102] exist or Under the condition of 0, Region II and Region III use the same soil strength and unit weight parameters. The positions and velocities of the two regions remain continuous at the common meridian EF; there is no velocity jump at EF, and the interface energy dissipation is zero. Therefore, the common meridian EF serves only as the boundary of the calculation segment, and Region II and Region III degenerate together into a continuous logarithmic helical shear zone in homogeneous soil in terms of material and kinematic relationships. The failure mechanism for reinforced conditions constructed in this invention thus naturally degenerates into the failure mechanism for unreinforced homogeneous soil.

[0103] To verify the computational rationality of the aforementioned degradation mechanism, the finite element limit analysis results published by Jin et al. (2024) were selected as comparative data. In this embodiment, the embedment depth of the retaining wall below the pit bottom is denoted as... d The common parameter for both sets of verification conditions is the excavation depth of the foundation pit. H = 10 m, effective unit weight of soil c 1 = 18 kN / m 3 Additional surface load outside the pit q = 0, relative insertion depth of the enclosure wall d / H It changed from 0.5 to 1.0. Wherein: Operating Condition 1: c1 = 7 kPa Operating Condition 2: c 1 = 10 kPa .

[0104] For each d / H The geometric parameters of the critical failure mechanism were redefined, the gravity power, velocity dissipation power, and energy dissipation power within the shear zone were calculated for each region, and the critical stability coefficient was obtained through power balance conditions. F cr The calculation results are shown in Table 1.

[0105] Table 1

[0106] The average absolute percentage error of the above 12 calculation points relative to the finite element limit analysis results is 2.11%, and the maximum relative error is 4.84%. d / H The calculation results for the two sets of working conditions within the range of 0.8 to 1.0 are quite similar, indicating that when or When the coefficient of soil is 0, the parameters of the reinforced composite soil can be correctly degraded to those of conventional soil. Regions II and III can form a continuous shear zone through the combination of the common diameter EF. The external force power, internal energy dissipation power, and power balance solution of the degradation mechanism have numerical consistency and can reasonably reflect the influence of the relative insertion depth of the retaining wall and the soil strength parameters on the heave stability of the foundation pit. This verifies the degradation capability of the calculation method of the present invention under the condition of unreinforced homogeneous soil and provides a benchmark for evaluating the reinforcement effect of the pit bottom under different effective replacement rates.

[0107] Example 2: Impact of Effective Replacement Rate and Back Calculation of Reinforcement Demand This embodiment illustrates the influence of the effective replacement rate on the anti-heave stability and critical failure mechanism of the foundation pit, and describes the process of determining the minimum effective replacement rate using the method of the present invention.

[0108] Set the excavation depth of the foundation pit H = 10 m, the insertion depth of the retaining wall below the bottom of the pit. d = 8 m, effective cohesion of conventional soil c 1 = 15 kPa, effective internal friction angle = 20°, effective severe c 1 = 20 kN / m 3 Additional surface load outside the pit q =20 kPa. The fully reinforced material parameters satisfy: c g / c 1 = 3.0, tan = 1.15、 c g / c 1 = 1.03, where, c g , and c g These are the effective cohesion, effective internal friction angle, and effective density of the fully reinforced material, respectively.

[0109] Let the effective replacement rate or The values ​​vary within the range of 0 to 0.60. For each effective replacement ratio, the parameters of the reinforced composite soil are first calculated based on the effective replacement ratio mapping relationship. c 2( or ), ) and γ2( or Subsequently, the strength parameters of conventional soil and reinforced composite soil were reduced to obtain the mobilization strength parameters under the corresponding trial stability coefficients. Then, the piecewise velocity fields of region II and region III were reconstructed to determine the expansion angle, EC length, coordinates of each geometric node, and critical failure profile. Finally, the external force power and internal energy dissipation power were calculated, and the critical stability coefficient was obtained through the power balance condition. F cr .

[0110] The composite soil parameters and critical stability coefficients corresponding to each effective replacement rate are shown in Table 2.

[0111] Table 2

[0112] The results above show that, under the parameter conditions of this embodiment, the critical stability coefficient is... F cr With effective replacement rate or It increases and increases. When or When the value is 0, the soil at the bottom of the pit degenerates into an unreinforced homogeneous soil condition. F cr = 1.7271; when or = 0.30, F cr =1.8186, an increase of 5.30% compared to the unreinforced condition; when or When = 0.60, F cr = 1.9092, an increase of 10.54% compared to the unreinforced condition.

[0113] like Figure 5 As shown, orThe critical failure profiles corresponding to 0, 0.30, and 0.60 are plotted on the same coordinate system. The failure profiles corresponding to different effective replacement rates do not coincide. As the effective replacement rate increases, the boundary of the uplift zone inside the pit, the lowest point of the shear zone, the velocity discontinuity outside the pit, and the location of the surface exit all change accordingly. Therefore, the effective replacement rate not only changes the strength parameters of the reinforced composite soil, but also alters the geometry of the critical failure mechanism through the velocity continuity relationship between region II and region III.

[0114] like Figure 6 As shown, the critical stability coefficient and its increase relative to the unreinforced condition both increase with the increase of the effective replacement rate. This result indicates that the present invention does not directly superimpose empirical gains on the unreinforced stability coefficient, but rather recalculates the composite soil parameters, mobilization intensity, failure mechanism geometry, segmented velocity field, external force power, and internal energy dissipation power for each effective replacement rate, thereby obtaining the critical stability coefficient corresponding to the current reinforcement state.

[0115] When the engineering design specifies a target stability coefficient F target When this is the case, the above calculation can be repeated within the range of effective substitution rates, and the minimum effective substitution rate that satisfies the following formula can be determined: F cr ( or ) ≥ F target .

[0116] The minimum that satisfies the above conditions or Recorded as or min . or min It is used to characterize the minimum effective reinforcement level required to achieve the target anti-heave stability under given soil parameters, foundation pit geometry, surface additional loads, and reinforcement material parameters.

[0117] Example 2 like Figure 4 As shown, the present invention also provides a foundation pit heave stability calculation device considering pit bottom reinforcement, comprising: The parameter acquisition module is used to acquire parameters such as the geometry of the foundation pit, the effective strength of the conventional soil, the layout of the reinforcement at the bottom of the pit, the reinforcement materials, and the additional load on the ground surface outside the pit. The module for determining replacement rate and composite soil parameters is used to determine the effective replacement rate from the reinforcement area ratio and the construction effectiveness coefficient, and to determine the reinforcement soil parameters from the effective replacement rate. The strength reduction module is used to reduce the strength of conventional soil and reinforced soil respectively. The failure mechanism construction module is used to construct the subsidence and displacement zone of conventional soil in Region I, the shear zone of conventional soil in Region II, the shear zone of reinforced soil in Region III, and the heave and displacement zone of reinforced soil in Region IV. The kinematics allowance check module is used to construct the velocity fields of region II and region III respectively, and to ensure the continuity of position and velocity at the common track EF; The power calculation module is used to calculate the power exerted by external loads in each region and the internal energy dissipation power at each velocity discontinuity. The root-finding and optimization module is used to solve for the stability coefficient through power balance and search for critical values ​​within the feasible region of kinematically permissible mechanism parameters; The results output module is used to back-calculate the minimum effective permutation rate to achieve the target stability coefficient as needed.

[0118] Example 3 The present invention also provides a storage medium storing a computer program, which, when running, executes a method for calculating the stability of a foundation pit considering bottom reinforcement.

[0119] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for calculating the heave stability of a foundation pit considering bottom reinforcement, characterized in that, include: Obtain the excavation depth of the foundation pit, the insertion depth of the retaining wall, the effective strength parameters of the conventional soil, the soil weight, the reinforcement layout parameters of the pit bottom, the reinforcement material parameters, and the additional load on the ground surface outside the pit; The effective replacement rate is determined based on the reinforcement layout parameters at the bottom of the pit, and the effective cohesion, effective internal friction angle, and effective unit weight of the reinforced soil in the pit are determined based on the effective replacement rate. Strength reduction was applied to both conventional soil and reinforced soil to obtain mobilization strength parameters under a given trial stability coefficient; An anti-heave failure mechanism is constructed, which includes the conventional soil settlement and displacement zone in region I, the logarithmic spiral shear zone in region II, the logarithmic spiral shear zone in region III, and the heave and displacement zone in region IV; Construct velocity fields for regions II and III respectively, so that the positions and velocities of the two shear zones at the common radius EF are continuous, and the velocities of the two translation zones along the wall normal are compatible with the horizontal translation velocity of the rigid wall; Based on the anti-heave failure mechanism and the segmented velocity field, calculate the power of the external load and the internal energy dissipation power. The stability coefficient under given mechanism parameters is determined by making the power exerted by the external load equal to the power dissipated by the internal energy. The coefficient is then optimized within the feasible region of the mechanism parameters that satisfy velocity compatibility, associated flow, and geometrically effective conditions to obtain the critical anti-uplift stability coefficient.

2. The method for calculating the heave stability of a foundation pit considering bottom reinforcement as described in claim 1, characterized in that, The effective replacement rate is determined by the area occupied by the reinforcing material in the equivalent calculation unit and the construction effectiveness coefficient; the construction effectiveness coefficient is used to characterize construction deviation, reinforcement overlap, strength dispersion and reinforcement effectiveness.

3. The method for calculating the heave stability of a foundation pit considering bottom reinforcement as described in claim 2, characterized in that, Regions II and III have different mobilization internal friction angles, velocity exponential rates, and logarithmic spiral growth rates. The two shear zones share the velocity at point F and the extreme radius EF, so that no velocity jump occurs at the common radius EF. EF is the boundary between Regions II and III, but it does not constitute a velocity discontinuity, and its interface energy consumption is zero.

4. The method for calculating the heave stability of a foundation pit considering bottom reinforcement as described in claim 3, characterized in that, The power generated by the external loads includes the gravity power of the conventional soil settlement and displacement zone in Region I, the gravity power of Region II, the gravity power of Region III, the gravity power of the reinforced soil uplift and displacement zone in Region IV, and the power of the additional surface load outside the pit; the internal energy dissipation power includes the energy dissipation at the velocity discontinuity outside the pit, the energy dissipation at the velocity discontinuity inside the pit, and the energy dissipation in Regions II and III.

5. The method for calculating the heave stability of a foundation pit considering bottom reinforcement as described in claim 4, characterized in that, When the effective replacement rate is zero, the parameters of the reinforced soil are restored to those of the conventional soil, and the common diameter EF is degenerated into a boundary line of the region without abrupt changes in strength and without velocity jumps, so as to obtain the heave stability coefficient of the unreinforced foundation pit.

6. The method for calculating the heave stability of a foundation pit considering bottom reinforcement as described in claim 5, characterized in that, The method further includes: given a target heave stability coefficient, repeatedly performing composite soil parameter calculation, segmented velocity field construction, power balance solution and mechanism optimization within the range of effective replacement rate, to determine the minimum effective replacement rate that satisfies the target heave stability coefficient.

7. A calculation device for the anti-heave stability of a foundation pit considering bottom reinforcement, characterized in that, include: The parameter acquisition module is used to acquire parameters such as the geometry of the foundation pit, the effective strength of the conventional soil, the layout of the reinforcement at the bottom of the pit, the reinforcement materials, and the additional load on the ground surface outside the pit. The module for determining replacement rate and composite soil parameters is used to determine the effective replacement rate from the reinforcement area ratio and the construction effectiveness coefficient, and to determine the reinforcement soil parameters from the effective replacement rate. The strength reduction module is used to reduce the strength of conventional soil and reinforced soil respectively. The failure mechanism construction module is used to construct the subsidence and displacement zone of conventional soil in Region I, the shear zone of conventional soil in Region II, the shear zone of reinforced soil in Region III, and the heave and displacement zone of reinforced soil in Region IV. The kinematics allowance check module is used to construct the velocity fields of region II and region III respectively, and to ensure the continuity of position and velocity at the common track EF; The power calculation module is used to calculate the power exerted by external loads in each region and the internal energy dissipation power at each velocity discontinuity. The root-finding and optimization module is used to solve for the stability coefficient through power balance and search for critical values ​​within the feasible region of kinematically permissible mechanism parameters; The results output module is used to back-calculate the minimum effective permutation rate to achieve the target stability coefficient as needed.

8. A storage medium, characterized in that, The storage medium stores a computer program, which, when running, executes the method for calculating the anti-heave stability of a foundation pit considering bottom reinforcement as described in any one of claims 1-6.

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