Method for calculating anti-upheaval stability of narrow foundation pit

Abstract

The invention discloses a narrow foundation pit upheaval resistance stability calculation method, which comprises the following steps: acquiring actual length, width and depth dimensions of a foundation pit and a consolidation undrained strength index, cohesion ccu and an internal friction angle phi cu of a field soil layer, and calculating a type critical width according to an improvement formula considering the internal friction angle of soil and a first width calculation coefficient, and whether the foundation pit is the narrow foundation pit or not is determined according to the comparison result of the actual foundation pit width and the type critical width. When the actual foundation pit is determined to be the narrow foundation pit, the width of a sinking soil body on the side face of the foundation pit is reversely solved through an improvement formula considering the internal friction angle of soil and the width of the actual foundation pit, and the upheaval-resistant stability coefficient of the narrow foundation pit based on the foundation bearing capacity mode is calculated and compared with the upheaval-resistant stability coefficient of the arc sliding mode. And taking the smaller value as the anti-upheaval stability coefficient of the narrow foundation pit so as to evaluate the anti-upheaval stability of the pit bottom of the foundation pit. Therefore, the problems that in the related technology, the judgment standard of the narrow foundation pit and selection of the slip plane are unreasonable, preconditions for checking calculation according to the narrow foundation pit design are unknown, and the friction angle in the stratum is not considered are solved.

Description

Technical Field

[0001] The present application relates to the technical field of foundation pit engineering, and in particular to a calculation method for the anti-uplift stability of a narrow foundation pit in a saturated clay layer or a layer with a small internal friction angle. Background Art

[0002] Foundation pit refers to the space below the ground excavated for the construction of building (structure) foundation and underground building (structure). The calculation of foundation pit stability usually includes overall stability, anti-uplift stability, anti-overturning stability, anti-horizontal sliding stability and anti-seepage stability. The uplift of the bottom of the foundation pit is due to the elastic-plastic uplift deformation of the bottom soil of the pit under the gravity of the soil outside the pit or the uniformly distributed load on the surface after the overburden pressure of the bottom soil and the lateral soil pressure in the pit are unloaded during the excavation of the foundation pit. Therefore, the uplift of the bottom of the foundation pit will cause the soil at the bottom of the foundation pit to arch up, the ground around the foundation pit to collapse and settle unevenly, thus endangering the safety of nearby existing buildings (structures) and other facilities. When the bottom of the foundation pit is severely uplifted, it will lead to the destruction of the foundation of the proposed building (structure), and it may also cause the deformation of the support system to be too large or even fail, resulting in excessive deformation or collapse of the foundation pit. Therefore, the anti-uplift verification of the foundation pit is a key content of the foundation pit support design.

[0003] The current industry specifications and regulations mainly verify the anti-uplift stability of foundation pits based on the ultimate bearing capacity failure mode and the arc sliding failure mode. However, in recent years, in the practice of foundation pit engineering, it has been found that the calculation method of the anti-uplift stability of foundation pits in the current specifications and regulations is insufficient. Although a large number of scholars have improved the calculation method of the anti-uplift stability coefficient of wide foundation pits involved in the specifications, neither the method in the specifications nor the improved method by scholars considers the influence of the width of the foundation pit on the stability of the foundation pit, that is, it is only applicable to the anti-uplift stability verification of foundation pits with large width or negligible width.

[0004] The anti-uplift stability of the foundation pit is affected by many factors, such as the lithology of the site, the length of the foundation pit, the width of the foundation pit, the depth of the foundation pit, the combination of the retaining structure and the depth of the embedded section. The width of the common foundation pits such as subway stations, integrated pipe corridors, underground pipelines and trench pipe corridors is usually small. The potential sliding surface when the bottom of this narrow foundation pit is damaged by uplift is often limited by the width of the foundation pit and is different from that of a wide foundation pit. This type of foundation pit belongs to the category of narrow foundation pit stability analysis. Due to the influence of the opposite side rock and soil and retaining structure, the anti-uplift stability coefficient of a narrow foundation pit is generally higher than that of a wide foundation pit. Therefore, the design calculation method of a traditional wide foundation pit will underestimate the anti-uplift stability coefficient, resulting in an overly conservative design and increased investment.

[0005] In the prior art, the following methods can be used to verify the stability of narrow foundation pits against heave: Prior art 1. The anti-uplift stability coefficient of the foundation pit is determined according to the calculation method in the current specifications and regulations, including a verification mode based on the ultimate bearing capacity of the foundation and a verification mode based on arc sliding. However, as mentioned above, these two verification methods are not suitable for narrow foundation pits.

[0006] First, the calculation model does not consider the influence of the width of the foundation pit on the radius of the sliding surface of the foundation pit bottom uplift failure, and implies the assumption that the width of the foundation pit is very large relative to the excavation depth. Therefore, it is only applicable to foundation pits with a sufficiently large width or a sufficiently large width-to-depth ratio, but not to narrow foundation pits. For narrow foundation pits, a relatively small stability coefficient will be given; second, when the embedding depth of the retaining structure is small, the stability coefficient of the foundation pit bottom uplift calculated under the arc sliding mode will be seriously large because the resistance of the support structure is considered in the numerator of the calculation formula, and the influence of different arc sliding modes on the maximum embedding depth is not considered; third, saturated clay is divided into clay and silty clay. When the soil layer is silty clay, the internal friction angle of the soil is generally considered to be non-zero. Therefore, the specifications and regulations recommend that for saturated clay, the strength index of the soil body should be the consolidated undrained strength index when checking the stability. At this time, it is more reasonable to consider that the internal friction angle is not zero for calculation; finally, the calculation result of the ultimate bearing capacity failure mode of the foundation is too conservative when the embedding depth is small. Because the shear force between the subsidence soil outside the foundation pit and the surrounding stable soil is ignored in the basic assumption, and the coefficient term related to the foundation width in the foundation bearing capacity formula is ignored. In the case of a large embedded depth, because it is still assumed that the embedded section has a large enough stiffness and does not cause kicking rotation failure, the calculated stability coefficient will be too large.

[0007] Prior art 2: Generally, the sliding surface when the foundation pit is uplifted is approximated as a combined sliding surface of a circular arc surface and a vertical surface. The essence is to move the rotation center of the circular arc sliding surface downward, so that the arc at the lower end of the embedded section of the retaining structure is reduced, so that the width of the narrow foundation pit can accommodate this circular arc sliding surface without being affected by the opposite stratum. However, whether analyzed from the principle of mechanics or verified by numerical simulation calculation, the retaining structure above the assumed rotation center in the calculation will also produce a certain deformation into the pit, that is, the entire embedded section will rotate around the fulcrum of the lowest support in the foundation pit.

[0008] The above method determines whether the foundation pit is a narrow foundation pit based on the relative size of the embedded depth of the retaining structure and the width of the foundation pit. However, because this method ignores the different failure modes corresponding to the foundation bearing capacity verification, the judgment of the narrow foundation pit is not completely accurate. When the embedded depth of the retaining structure is small, the narrow foundation pit will be judged as a wide foundation pit; secondly, the position of the center of the arc sliding failure surface is specified at the bottom of the retaining structure, rather than the fulcrum position of the lowest support of the foundation pit. After that, the anti-uplift moment and the uplift moment of the foundation pit are calculated based on this artificially specified center position, but in fact, since the retaining structure is not infinitely stiff, the retaining structure should rotate around the fulcrum position of the lowest support, so this assumption does not conform to the principles of mechanics. And this verification method is not calculated for saturated clay layers, which makes it inapplicable.

[0009] Prior art 3: Whether a foundation pit is narrow is determined only by whether the foundation pit width can accommodate the edge of the circular arc sliding surface when checking the wide foundation pit. If it cannot accommodate, it means that the radius of the circular arc is greater than the width of the foundation pit, and the foundation pit is narrow. Then, it is assumed that the center of the circular arc can be moved so that the edge of the sliding surface does not pass through the opposite pit wall. After that, for multiple potential circular arc sliding surfaces corresponding to different centers, the ratio of the corresponding anti-sliding moment to the sliding moment is calculated by the strip method as the trial value of the stability coefficient, and the sliding surface corresponding to the minimum stability coefficient is taken as the most unfavorable sliding surface. The corresponding stability coefficient is the anti-uplift stability coefficient in the foundation pit stability verification.

[0010] In the above technology, the size of the arc sliding radius relative to the width of the foundation pit during the stability verification of the wide foundation pit is used as the judgment standard for the width and narrowness of the foundation pit. When the embedding depth of the retaining structure is small, the narrow foundation pit may be judged as a wide foundation pit, because the failure mode at this time is likely to be not the arc sliding surface mode, but the sliding line mode; secondly, it is believed that the center position of the arc sliding surface moves in the horizontal plane where the lowest support is located, so the imaginary possible arc sliding surface is not reasonable. As mentioned above, according to the analysis of mechanical principles, it can be known that the deformation of the retaining structure is a rotation around the support point of the lowest support; thirdly, this technical solution simultaneously searches for sliding surfaces corresponding to the two types of centers in the horizontal plane where the lowest support is located and in the horizontal plane of the top surface of the foundation pit, but does not consider the actual possible foundation ultimate bearing capacity failure mode, nor does it consider the possible critical embedding depth problem; fourthly, this technical solution also does not clearly select the consolidation undrained strength index when performing stability verification on saturated clay layers, and there are certain defects in the calculation of saturated clay strength.

[0011] Existing technology 4, for narrow foundation pits on saturated soft soil foundations, a calculation method for the anti-uplift stability of foundation pits based on the ultimate bearing capacity failure mode of the foundation is proposed. Based on the ultimate bearing capacity failure mode of the foundation, the stress state of the underlying soil is analyzed, and the relationship curve between the width of the sunken soil and the anti-uplift stability coefficient of the foundation pit is obtained through the strength reduction method. The width of the foundation pit is classified into narrow and narrow according to the critical width of the foundation pit when the stability coefficient is the smallest, and the anti-uplift stability coefficient corresponding to the narrow foundation pit is calculated.

[0012] In the above-mentioned prior art 4, it is assumed that the soil layer is a saturated soft clay layer, so it is necessary to obtain the consolidated undrained shear strength of the soil layer, and it is only necessary to obtain the cohesion c value. However, in the case of a soil layer with a small internal friction angle and a shallow embedding depth, the foundation pit uplift failure mode is also mainly based on the ultimate bearing capacity failure mode of the foundation. Secondly, when constructing the limit equilibrium equation, only the balance of soil stress is taken into account without considering the different sizes of the soil bodies under stress, so the limit equilibrium equation needs to be corrected. Thirdly, saturated clay includes clay and silty clay. In actual engineering, the internal friction angle of saturated silty clay is generally not zero, so this method needs to be improved.

[0013] In summary, the relevant existing technologies have problems such as unreasonable selection of the judgment criteria for narrow foundation pits and the uplift failure sliding surface, unclear preconditions for design verification of narrow foundation pits, and the calculation method of the anti-uplift stability coefficient of narrow foundation pits under the ultimate bearing capacity failure mode of the foundation needs to be improved. Summary of the invention

[0014] The present application provides a method for calculating the anti-uplift stability of a narrow foundation pit, so as to solve the technical problems in the related art, such as unreasonable selection of judgment criteria and failure sliding surface for narrow foundation pits, unclear preconditions for design and verification of narrow foundation pits, and lack of improved calculation method for anti-uplift stability coefficient of narrow foundation pits according to the ultimate bearing capacity failure mode of foundation, so as to provide a judgment method for accurately identifying the wide and narrow foundation pit types for the foundation pits with embedded depth less than the actual foundation pit width, solve the problem that the foundation pits with "small embedded depth" are still classified as wide foundation pits in the related art, and lack of corresponding judgment method for wide and narrow foundation pit types, and propose an improved calculation method for anti-uplift stability coefficient of the ultimate bearing capacity failure mode of foundation corresponding to narrow foundation pits.

[0015] The technical solution of the embodiment of the present application is as follows: A calculation method for the anti-uplift stability of a narrow foundation pit is applied to the calculation of the anti-uplift stability of a narrow foundation pit in a saturated clay layer or a layer with a small internal friction angle, wherein: The method comprises the following steps: (1) Obtain the actual length, width, and depth of the foundation pit and the undrained strength index of the site soil layer (cohesion) c cu and internal friction angleφ cu ; (2) Based on the consolidated undrained strength index, the first sinking soil width corresponding to the ultimate bearing capacity failure mode of the wide foundation pit is calculated according to the improved formula considering the internal friction angle of the soil and the first width calculation coefficient, and the corresponding type critical width is calculated based on the first sinking soil width; (3) comparing the actual foundation pit width with the critical width of the type to obtain the width type of the foundation pit, and when the width type of the foundation pit is a narrow foundation pit type, based on the actual foundation pit width, inversely calculating the second sinking soil width corresponding to the narrow foundation pit foundation ultimate bearing capacity failure mode according to an improved formula that considers the internal friction angle of the soil; (4) Based on the width of the second sunken soil mass, the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit foundation is calculated according to an improved formula that takes into account the internal friction angle of the soil; (5) Calculate the anti-uplift stability coefficient of the circular arc sliding failure mode of the foundation pit, and compare the anti-uplift stability coefficient of the circular arc sliding failure mode with the anti-uplift stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit. Take the smaller value as the anti-uplift stability coefficient of the narrow foundation pit, and evaluate the anti-uplift stability of the foundation pit based on this calculation result.

[0016] Preferably, the calculation of the corresponding critical foundation pit width based on the width of the first sunken soil body includes: acquiring foundation parameters, foundation pit parameters and retaining structure parameters, and analyzing and calculating the foundation pit width according to the stress conditions of the soil body and the retaining structure.

[0017] Furthermore, when constructing the improved formula considering the internal friction angle of soil, the soil range and parameters of the passive zone of the base are considered and η As a correction factor.

[0018] Furthermore, the analysis and calculation of the foundation pit width according to the stress conditions of the soil and the retaining structure includes using the first sinking soil width, the consolidated undrained strength index, the foundation parameters, and the dimensionless parameters and width calculation coefficient corresponding to the first sinking soil width, and obtaining the anti-uplift stability coefficient K corresponding to the critical foundation pit width by considering the improved formula of the internal friction angle of the soil. b ~B' curve, and determine the critical width of the type of foundation pit at the moment of instability based on the tangent line of the curve at the point of maximum curvature.

[0019] Furthermore, the stability coefficient calculation formula of the narrow foundation pit ultimate bearing capacity failure mode is: , Among them, K b is the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit, N cis the foundation bearing capacity coefficient in the Prandtl-Reithner foundation bearing capacity formula, c 01 is the undrained strength of the soil at the embedded end of the retaining structure, β2 is the calculation coefficient of the bearing capacity width, c inc is the growth rate of undrained strength with depth, Z max，2 F is the depth of the slip surface when the foundation bearing capacity fails. Q is the resultant shear force of the inclined sliding surface, θ is the angle between the fracture surface and the horizontal plane, B2 is the width of the second sinking soil, W is the load caused by the sinking soil outside the pit, Q is the load caused by the ground load, γ′ is the buoyant weight of the soil, D is the depth of the embedded section, and η2 is the second width calculation coefficient.

[0020] The embodiment of the present application can be based on cohesion c cu and internal friction angle φ cu , the width of the first subsidence soil corresponding to the ultimate bearing capacity failure mode of the wide foundation pit is calculated, and K b ~B' curve, and according to K b The tangent of the maximum curvature point of the ~B' curve determines the critical width of the type of foundation pit facing the moment of instability. The width type of the foundation pit is obtained by comparing the size of the critical width of the type and the actual foundation pit width, which solves the problem of difficulty in judging the width and narrowness of the foundation pit. When the foundation pit type is a narrow foundation pit type, based on the actual foundation pit width, the width of the second sinking soil body is inversely calculated according to the improved formula that considers the internal friction angle of the soil, so as to calculate the stability coefficient of the narrow foundation pit based on the ultimate bearing capacity failure mode of the foundation, and by comparing it with the stability coefficient calculated by the arc sliding mode, the anti-uplift stability coefficient of the narrow foundation pit is obtained, and the anti-uplift stability of the narrow foundation pit is evaluated. In this way, the problems in the relevant technology such as unreasonable selection of the judgment criteria and sliding surface for narrow foundation pits, unclear preconditions for design and verification of narrow foundation pits, and the calculation method of the anti-uplift stability coefficient of narrow foundation pits according to the ultimate bearing capacity failure mode of the foundation are solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which: Figure 1 A flowchart of a method for calculating the anti-uplift stability of a narrow foundation pit provided according to an embodiment of the present application; Figure 2 A schematic diagram of calculating the stability coefficient of a wide foundation pit foundation ultimate bearing capacity failure mode considering the internal friction angle of the soil according to a specific embodiment of the present application; Figure 3 A schematic diagram of calculating the stability coefficient according to a foundation ultimate bearing capacity failure mode referred to in a specific embodiment of the present application; Figure 4 A schematic diagram of calculating the stability coefficient of the failure mode of the foundation ultimate bearing capacity by inversely calculating the width of the sunken soil body according to a specific embodiment of the present application through the narrow foundation pit width; Figure 5 A schematic diagram of the relationship between the stability coefficient and the critical width when calculating the stability coefficient according to the wide foundation pit stability verification according to a specific embodiment of the present application; Figure 6 It is a flow chart of a method for calculating the anti-uplift stability of a narrow foundation pit according to a specific embodiment of the present application; Figure 7 The figure is a numerical simulation result of a calculation method for the anti-uplift stability of a narrow foundation pit according to a specific embodiment of the present application. DETAILED DESCRIPTION

[0022] Embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0023] The following describes the calculation method of the anti-uplift stability of the narrow foundation pit in the embodiment of the present application with reference to the accompanying drawings. In view of the problems mentioned in the above background technology, the judgment criteria of the narrow foundation pit and the selection of the sliding surface are unreasonable, the preconditions for the design and verification of the narrow foundation pit are unclear, and the calculation method of the anti-uplift stability coefficient of the narrow foundation pit according to the ultimate bearing capacity failure mode of the foundation needs to be improved. The present application provides a calculation method for the anti-uplift stability of a narrow foundation pit, which is applied to the calculation of the anti-uplift stability of a narrow foundation pit in a saturated clay layer or a layer with an internal friction angle within a predetermined range. In this method, the consolidation undrained strength index of the stratum in the foundation pit site and the actual length, width and height of the foundation pit can be obtained. The consolidation undrained strength index includes at least cohesion. c cu and internal friction angle φ cu , so that the uplift failure sliding surface of the foundation pit is rationalized, based on the above-mentioned consolidated undrained strength index, the first sinking soil width corresponding to the ultimate bearing capacity failure mode of the wide foundation pit is calculated according to the improved formula considering the internal friction angle of the soil and the first width calculation coefficient, and the corresponding type critical width is calculated based on the first sinking soil width.

[0024] The type of foundation pit is obtained by comparing the critical width of the type and the actual foundation pit width, which solves the problem of difficulty in judging the width of the foundation pit. When the width type of the foundation pit is a narrow foundation pit type, based on the actual foundation pit width, the second sinking soil width corresponding to the narrow foundation pit foundation ultimate bearing capacity failure mode is inversely calculated according to the improved formula that considers the internal friction angle of the soil, and by comparing it with the stability coefficient of the arc sliding mode, the anti-uplift stability coefficient of the narrow foundation pit is obtained, and the anti-uplift stability of the narrow foundation pit is judged. In this way, the problems in the related technology such as the unreasonable selection of the judgment criteria and sliding surface for narrow foundation pits, the unclear preconditions for the design and verification of narrow foundation pits, and the calculation method of the anti-uplift stability coefficient of narrow foundation pits under the foundation ultimate bearing capacity failure mode need to be improved are solved.

[0025] Specifically, Figure 1 A schematic flow chart of a method for calculating the anti-uplift stability of a narrow foundation pit provided in an embodiment of the present application.

[0026] like Figure 1 As shown, the calculation method of the anti-uplift stability of the narrow foundation pit is applied to the verification of the stability of the narrow foundation pit in the saturated clay layer or the small internal friction angle layer, wherein the method comprises the following steps: In step S101, the actual length, width and depth of the foundation pit and the consolidation undrained strength index of the site soil layer are obtained. The consolidation undrained strength index includes at least cohesion c cu and internal friction angle φ cu .

[0027] In the actual implementation process, the embodiment of the present application can obtain the cohesion of the consolidation undrained strength index of the soil layer in the foundation pit site through the site geotechnical engineering survey report. c cu The cohesion can also be directly obtained through the undrained consolidation test of the original soil sample or the in-situ undrained test. c cu , where c cu It can increase approximately linearly with depth.

[0028] , Where c0 is the value of undrained shear strength at the top of the soil layer, c inc is the rate of increase of undrained shear strength with depth, c0, c inc is the undrained strength parameter of soil, and z is the calculation depth.

[0029] When there is a lack of consolidation undrained test data, the present embodiment can also use the consolidation undrained test results to calculate c0 and c inc Make an estimate.

[0030] In this step, the actual foundation pit width B should be obtained for subsequent determination of the width type of the foundation pit.

[0031] In step S102, based on the consolidated undrained strength index, the first sinking soil width corresponding to the wide foundation pit ultimate bearing capacity failure mode is calculated according to an improved formula considering the internal friction angle of the soil and a first width calculation coefficient, and the corresponding type critical width is calculated based on the first sinking soil width; Specifically, the embodiment of the present application can solve the stability coefficient K in the case of a wide foundation pit. b1 The relationship between the width of the first sinking soil B1 and its corresponding critical foundation pit width B', where the stability coefficient K b1 The width of the first subsidence soil body B1 should satisfy the following improved formulas (1), (2), (3), and (4) considering the internal friction angle of the soil: (1) , (2) , (3) , (4) , The failure slip surface assumed in the above formula can be expressed as Figure 2 The improved formula considering the internal friction angle of soil is a combination of the above four formulas, where: W is the deadweight of the soil; Q is the force caused by the surface load; F Q is the resultant shear force of the inclined sliding surface, which can be calculated by integrating the friction force and the cohesion force at depth; θ is the angle between the fracture surface and the horizontal plane; K b1 is the stability coefficient corresponding to the width B1 of the first subsided soil body; B1 is the width of the first subsided soil body; , is the undrained strength of the soil at the embedded end of the retaining structure; , is the bearing capacity correction factor; c inc is the rate of increase of undrained shear strength with depth; , is the depth of the slip surface when the foundation bearing capacity fails; , is the first dimensionless parameter required to calculate the bearing capacity of the foundation; is the foundation bearing capacity coefficient in the Prandtl-Reithner foundation bearing capacity formula, where ;γ′ is the floating weight of the soil; D is the depth of the embedded section; η1 is the width calculation coefficient, which will be given in the following section; H is the depth of the foundation pit; , is the distance between the sliding fracture surface on the ground and the outer edge of the foundation pit; γ w is the weight of water; q0 is the surface load; , is the cohesion value varying with depth; , is the length of the sliding surface above the retaining structure; K a is the active earth pressure coefficient, ; , is the resultant force of self-weight stress; φ cu It is the internal friction angle in the consolidated undrained strength index of soil.

[0032] It is understandable that when the foundation reaches the ultimate bearing capacity and fails, the proportional relationship between the foundation width and the sliding surface width can be expressed by a width calculation coefficient. It should be pointed out that according to relevant technology, the calculation formula of this width calculation coefficient is: , Where η is the calculation coefficient representing the proportional relationship between the width of the sliding surface and the width of the foundation in the bearing capacity problem (e.g. Figure 3 As shown); k is a dimensionless parameter, ; c inc，0 is the growth rate of soil shear strength with depth; B0 is the foundation width; c 0，0 is the undrained shear strength of the soil at the depth of the foundation bottom. After conceptual analysis and verification by a large number of numerical tests, the dimensionless parameter It can comprehensively characterize soil strength parameters c 0，0 、c inc，0 The influence of the foundation width B0 is taken into account, and the calculation coefficient η can be uniquely determined by the dimensionless parameter k. In the foundation bearing capacity verification of anti-uplift stability, the foundation width B0 should be determined by the width of the subsidence soil outside the pit, c 0，0 、c inc，0 It should be determined based on the properties of the soil at the embedded end of the retaining structure.

[0033] Therefore, the embodiment of the present application can be based on the above formula, based on the undrained strength c of the soil at the embedded end of the retaining structure 01 and c inc , the first dimensionless parameter k1 is calculated in combination with the first sinking soil width B1, and the first width calculation coefficient η1 is obtained based on the first dimensionless parameter, and then the first width calculation coefficient η1 and the sinking soil width B1 are multiplied to obtain the type critical width B'.

[0034] Optionally, in one embodiment of the present application, the calculation formula of the first width calculation coefficient is: , Wherein, η1 is the first width calculation coefficient, and k1 is the first dimensionless parameter.

[0035] Specifically, the embodiment of the present application can utilize the width B1 of the first sunken soil body, the undrained strength c of the soil body at the embedded end of the retaining structure, and the 01 and soil strength parameter c incThe first dimensionless parameter k1 is obtained, and the first width calculation coefficient η1 is obtained based on the first dimensionless parameter k1, wherein the first width calculation coefficient η1 refers to the ratio of the width of the sliding surface of the ultimate bearing capacity failure mode of the foundation to the width of the submerged soil body; the first width calculation coefficient η1 is multiplied by the width of the submerged soil body B1 to obtain the corresponding critical foundation pit width B'. Figure 2 As shown in the figure, the width of the sliding surface B' where the bearing capacity of the wide foundation pit fails can be regarded as the critical foundation pit width. The calculation formula is as follows: , , Among them, η1 is the ratio of the width of the sliding surface of the wide foundation pit where the bearing capacity fails to work and the width of the first sinking soil. η1 is related to the soil strength parameter c 01 and c inc It is related to the width B1 of the first sinking soil body.

[0036] Optionally, in one embodiment of the present application, the calculation formula of the first dimensionless parameter is: , Among them, c inc is the growth rate of undrained strength with depth; B1 is the width of the first sinking soil; c 01 The first dimensionless parameter k1 can comprehensively characterize the undrained strength parameter c of the soil at the embedded end of the retaining structure. 01 and c inc And the influence of the width B1 of the first sinking soil body.

[0037] In the process of solving the above formula, the embodiment of the present application can solve it by iterative search and trial calculation. For example, the embodiment of the present application can calculate B' and K by inputting B1=0.1m. b1 Then gradually increase the value of B1 until B1 is equal to T, that is, when the inclined fracture surface turns into a vertical fracture surface, K is obtained. b1 ~B' curve, take the tangent line at the maximum curvature of the curve and K b1 =1 at the intersection of B L The value is the critical width value for determining the foundation pit type, that is, the critical width of the type, corresponding to B1 as the width of the first sinking soil body.

[0038] In step S103, the actual foundation pit width is compared with the type critical width B L , obtain the width type of the foundation pit, and when the width type of the foundation pit is a narrow foundation pit type, based on the actual foundation pit width, inversely calculate the width of the second sinking soil body corresponding to the narrow foundation pit foundation ultimate bearing capacity failure mode according to an improved formula that considers the internal friction angle of the soil; Specifically, in the embodiment of the present application, the actual foundation pit width B is compared with the type critical width B L , the width type of the foundation pit can be obtained, when B L , it can be judged that the width type of the foundation pit is a narrow foundation pit type.

[0039] When the width type of the foundation pit is a narrow foundation pit type, the embodiment of the present application can solve the sinking soil width B2 corresponding to the maximum foundation bearing capacity failure and damage sliding surface that can be accommodated according to the actual foundation pit width B, that is, the second sinking soil width B2.

[0040] Optionally, in one embodiment of the present application, the calculation formula for the width of the second sinking soil body is: , , , Among them, B2 is the width of the second sunken soil; B is the width of the foundation pit; η2 is the second width calculation coefficient, and k2 is the second dimensionless parameter.

[0041] like Figure 4 As shown, the embodiment of the present application can inversely calculate the second sinking soil width B2 corresponding to the narrow foundation pit foundation ultimate bearing capacity failure mode based on the actual foundation pit width B, and the solution formula is as follows: , , , Among them, η2 is the second width calculation coefficient, which is related to the variable B2 to be solved. Therefore, B2 can be solved by the above formula through the iterative method.

[0042] In step S104, based on the width of the second sunken soil body, the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit foundation is calculated according to an improved formula that takes into account the internal friction angle of the soil.

[0043] In the actual implementation process, the embodiment of the present application can calculate the stability coefficient K of the ultimate bearing capacity failure mode of the foundation in the case of a narrow foundation pit. b .

[0044] like Figure 4 As shown, the embodiment of the present application can use the preset formula for calculating the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit, that is, the anti-uplift stability coefficient K of the foundation ultimate bearing capacity failure mode corresponding to the narrow foundation pit is calculated by the strength reduction method. b .

[0045] Optionally, in one embodiment of the present application, the stability coefficient calculation formula of the ultimate bearing capacity failure mode of the narrow foundation pit foundation is:​ , Among them, K b is the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit, N c is the foundation bearing capacity coefficient in the Prandtl-Reithner foundation bearing capacity formula, c 01 is the undrained strength of the soil at the embedded end of the retaining structure, β2 is the calculation coefficient of the bearing capacity width, c inc is the growth rate of undrained strength with depth, Z max，2 F is the depth of the slip surface when the foundation bearing capacity fails. Q is the resultant shear force of the inclined sliding surface, θ is the angle between the fracture surface and the horizontal plane, B2 is the width of the second sinking soil, W is the load caused by the sinking soil outside the pit, Q is the load caused by the ground load, γ′ is the buoyant weight of the soil, D is the depth of the embedded section, and η2 is the second width calculation coefficient.

[0046] Furthermore, if Figure 4 As shown in the figure, based on the failure slip surface, the calculation formula for the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit foundation can be derived as follows: When solving, the embodiment of the present application can calculate the bearing capacity p according to the width B2 of the second sinking soil body and the reduced undrained soil strength parameters and foundation pit parameters. u , the shear force F of the inclined sliding surface is calculated using the reduced undrained strength parameters of the soil Q , and calculate the downward pressure load p1, and then calculate the stability coefficient K by solving the following formula b : , Among them, p1 is the downward pressure load; p u (K b ) refers to p u It's K b function.

[0047] Bearing capacity u After considering the soil strength reduction, it can be written as: , in, is the foundation bearing capacity coefficient in the Prandtl-Reithner foundation bearing capacity formula, where ; , is the undrained strength of the soil at the embedded end of the retaining structure; c inc is the rate of increase of undrained shear strength with depth; K is the depth of the slip surface where the foundation bearing capacity fails; b is the stability coefficient corresponding to B2; D is the depth of the embedded section, To calculate the correction factor for the bearing capacity, This is the dimensionless parameter required to calculate the bearing capacity of the foundation. This dimensionless parameter does not change with the strength parameter c 01 、c inc The resultant shear force of the inclined sliding surface can be: , The load caused by the subsidence of soil outside the pit and the surface load q0 is: , , , In summary, , Since only K b An unknown number, so it can be sorted as: , Thus, a stability coefficient calculation method based on the foundation bearing capacity instability mode suitable for narrow foundation pits is obtained.

[0048] In step S105, the stability coefficient of the circular sliding mode of the foundation pit is calculated, and by comparing the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit foundation with the stability coefficient of the circular sliding mode of the foundation pit, the smaller value between the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit foundation and the stability coefficient of the circular sliding mode is taken as the anti-uplift stability coefficient of the narrow foundation pit, so as to judge the anti-uplift stability of the foundation pit based on the anti-uplift stability coefficient of the narrow foundation pit.

[0049] As a possible implementation method, the embodiment of the present application can calculate the second stability coefficient K of the arc sliding mode: c , and compare it with the stability coefficient of the foundation bearing capacity model, take the smaller value to get the anti-uplift stability coefficient of the narrow foundation pit, and judge the anti-uplift stability of the foundation pit based on the anti-uplift stability coefficient of the narrow foundation pit.

[0050] Among them, the calculation formula of the stability coefficient of the arc sliding mode is: , Among them, K c is the stability coefficient of the arc sliding mode, D is the depth of the embedded section, l0 is the distance from the lowest support to the bottom of the pit, c 02 is the undrained shear strength of the soil layer corresponding to the lowest support plane, , M0 is the ultimate bending strength of the retaining structure.

[0051] Optionally, in one embodiment of the present application, the actual foundation pit width is compared with the type critical width BL , and obtain the width type of the foundation pit, and also include: if the width type of the foundation pit is a wide foundation pit type, then calculate the stability coefficient of the foundation bearing capacity mode according to the wide foundation pit; compare the stability coefficient of the circular arc sliding mode of the foundation pit with the stability coefficient of the foundation bearing capacity mode, and take the smaller value between the stability coefficient of the circular arc sliding mode of the foundation pit and the stability coefficient of the foundation bearing capacity mode as the anti-uplift stability coefficient of the wide foundation pit, so as to judge the anti-uplift stability of the foundation pit based on the anti-uplift stability coefficient of the wide foundation pit.

[0052] Furthermore, the embodiment of the present application can compare the actual foundation pit width B and the type critical width B corresponding to B1. L , when B ≥ B L When, the embodiment of the present application can determine that the width type of the foundation pit is a wide foundation pit type.

[0053] At this time, the embodiment of the present application can verify the bearing capacity failure mode of the wide foundation pit foundation to obtain the stability coefficient of the foundation bearing capacity verification.

[0054] The embodiment of the present application can compare the stability coefficient of the arc sliding mode and the stability coefficient of the foundation bearing capacity mode, take the smaller value to obtain the anti-uplift stability coefficient of the wide foundation pit, and judge the anti-uplift stability of the foundation pit based on the anti-uplift stability coefficient of the wide foundation pit.

[0055] Combination Figures 2 to 6 As shown, a method for calculating the anti-uplift stability of a narrow foundation pit according to an embodiment of the present application is described in detail using an embodiment.

[0056] like Figure 6 As shown, the embodiment of the present application may include the following steps: Step S501: Obtain the actual width of the foundation pit and the consolidated undrained shear strength index of the soil layer: cohesion c cu and internal friction angle φ cu In the embodiment of the present application, the consolidated undrained shear strength index c of the soil layer in the foundation pit site can be obtained through the site survey report. cu In the embodiment of the present application, c can be directly obtained by a consolidation undrained test of an original soil sample under self-weight stress or an in-situ undrained test. cu , where c cu It can increase approximately linearly with depth.

[0057]

[0058] Where c0 is the value of undrained shear strength at the top of the soil layer, c inc is the rate of increase of undrained shear strength with depth, i.e. c0, c inc is the undrained strength parameter of soil, and z is the depth.

[0059] When there is a lack of consolidated undrained test data, the present application embodiment can also use the unconsolidated undrained test results to calculate c0 and c inc Make an estimate.

[0060] Furthermore, the embodiment of the present application should obtain the actual foundation pit width B for subsequent determination of the width type of the foundation pit.

[0061] Step S502: Calculate the width of the first subsidence soil body corresponding to the ultimate bearing capacity failure mode of the wide foundation pit. The embodiment of the present application can solve the stability coefficient K in the case of a wide foundation pit. b1 The relationship between the width of the first sinking soil B1 and its corresponding critical foundation pit width B', where the stability coefficient K b1 The width of the first sinking soil body B1 should satisfy the following improved formula considering the internal friction angle of the soil: , , , , Where W is the deadweight of the soil; Q is the force caused by the surface load; F Q is the resultant shear force of the inclined sliding surface, which can be calculated by integrating the friction force and the cohesion force at depth; θ is the angle between the fracture surface and the horizontal plane; K b1 is the stability coefficient corresponding to B1; B1 is the width of the first sinking soil body; , is the undrained strength of the soil at the embedded end of the retaining structure; , is the bearing capacity correction factor; c inc is the rate of increase of undrained shear strength with depth; , is the depth of the slip surface when the foundation bearing capacity fails; , is the first dimensionless parameter required to calculate the bearing capacity of the foundation; is the foundation bearing capacity coefficient in the Prandtl-Reithner foundation bearing capacity formula, where ;γ′ is the floating weight of the soil; D is the depth of the embedded section; η1 is the width calculation coefficient, which will be given in the following section; H is the depth of the foundation pit; , is the distance between the sliding fracture surface on the ground and the outer edge of the foundation pit; γ w is the weight of water; q0 is the surface load; , is the cohesion value varying with depth; , is the length of the sliding surface above the retaining structure; K a is the active earth pressure coefficient, ; , is the resultant force of self-weight stress; φ cuIt is the internal friction angle in the consolidated undrained strength index of soil.

[0062] The critical foundation pit width is calculated based on the width of the first subsidence soil mass. Figure 2 As shown in the figure, it is the sliding surface B' corresponding to the wide foundation pit. The embodiment of the present application can be based on the undrained strength parameter c of the soil at the embedded end of the retaining structure 01 and c inc , the first dimensionless parameter k1 is calculated in combination with the first sinking soil width B1, and the first width calculation coefficient η1 is obtained based on the first dimensionless parameter. The critical foundation pit width B' is obtained by multiplying the first width calculation coefficient η1 and the sinking soil width B1. The calculation formula can be as follows: , , , Among them, η1 is the ratio between the width of the sliding surface where the bearing capacity of the wide foundation pit fails and the width of the first sinking soil. η1 should be related to the soil strength parameter c 01 and c inc It is related to the width B1 of the first sinking soil body.

[0063] In the process of solving the above formula, the embodiment of the present application can solve it by iterative search and trial calculation. For example, the embodiment of the present application can calculate B' and K by inputting B1=0.1m. b1 Then gradually increase the value of B1 until B1 is equal to T, that is, when the inclined fracture surface turns into a vertical fracture surface, K is obtained. b1 ~B' curve, take the tangent line at the maximum curvature of the curve and K b1 =1 is the value of the intersection point of type critical width B L , corresponding to B1 is the width of the first sinking soil body.

[0064] Step S503: Compare the actual foundation pit width with the category critical width. If the actual foundation pit width is less than the category critical width, proceed to step S504; if the actual foundation pit width is greater than or equal to the category critical width, proceed to step S506.

[0065] Step S504: If the width type of the foundation pit is a narrow foundation pit type, the width of the second submerged soil body is calculated. In this embodiment of the application, the actual foundation pit width B and the critical width B of the type can be compared. L Get the width type of the foundation pit, when B L When, the embodiment of the present application can determine that the width type of the foundation pit is a narrow foundation pit type.

[0066] ​When the width type of the foundation pit is a narrow foundation pit type, the embodiment of the present application can use the actual foundation pit width B to solve the sinking soil width B2 corresponding to the maximum sliding surface that the actual foundation pit width can accommodate when the foundation bearing capacity fails, that is, the second sinking soil width B2.

[0067] like Figure 4 As shown, in the embodiment of the present application, B2 can be obtained by solving the following formula and using B to inversely calculate: , , , Among them, B2 is the width of the second sunken soil; B is the width of the foundation pit; η2 is the second width calculation coefficient; k2 is the second dimensionless parameter.

[0068] Step S505: Calculate the stability coefficient of the ultimate bearing capacity failure mode of the foundation in the case of a narrow foundation pit. Figure 4 As shown, the embodiment of the present application can use the preset formula for calculating the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit, that is, the anti-uplift stability coefficient K of the foundation ultimate bearing capacity failure mode corresponding to the narrow foundation pit is calculated by the reduced strength method. b .

[0069] Furthermore, based on the calculation of the failure slip surface, the derivation process of the stability coefficient calculation formula of the ultimate bearing capacity failure mode of the narrow foundation pit foundation can be as follows: When solving, the embodiment of the present application can calculate the bearing capacity p using the second sinking soil width B2 and the reduced soil undrained strength parameters and foundation pit parameters. u , the shear force F of the inclined sliding surface is calculated using the reduced undrained strength parameters of the soil Q , and the downward pressure load p1 of the sinking soil, and then the stability coefficient K is calculated by solving the following formula b : , Among them, p1 is the downward pressure load; p u (K b ) refers to p u It's K b function.

[0070] Bearing capacity u After considering the soil strength reduction, it can be written as: , in, is the foundation bearing capacity coefficient in the Prandtl-Reithner foundation bearing capacity formula, where ; , is the undrained strength of the soil at the embedded end of the retaining structure; cinc is the rate of increase of undrained shear strength with depth; K is the depth of the slip surface where the foundation bearing capacity fails; b is the stability coefficient corresponding to B2; D is the depth of the embedded section, To calculate the correction factor for the bearing capacity, This is the dimensionless parameter required to calculate the bearing capacity of the foundation. This dimensionless parameter does not change with the strength parameter c 01 、c inc The resultant shear force of the inclined sliding surface can be: , The load caused by the subsidence of soil outside the pit and the surface load q0 is: , , , In summary, , Since only K b An unknown number, so it can be sorted as: , Thus, the stability coefficient calculation method for the foundation bearing capacity instability mode suitable for narrow foundation pits is obtained.

[0071] Step S506: If the width type of the foundation pit is a wide foundation pit type, the stability coefficient of the foundation bearing capacity verification is calculated according to the calculation method of the wide foundation pit based on the foundation bearing capacity model. L , when B ≥ B L When, the embodiment of the present application can determine that the width type of the foundation pit is a wide foundation pit type.

[0072] Among them, the calculation formula of the stability coefficient of the arc sliding mode is: , Among them, K c is the stability coefficient of the arc sliding mode, D is the depth of the embedded section, l0 is the distance from the lowest support to the bottom of the pit, c 02 is the undrained shear strength of the soil layer on the lowest supporting plane, , M0 is the ultimate bending strength of the retaining structure.

[0073] The effectiveness of the embodiments of the present application is verified by an embodiment below.

[0074] The embodiment of the present application can be verified by a site with a stratum with a small internal friction angle. The embedding depth of the foundation pit support structure is 2m, which is suitable for the situation mentioned in the embodiment of the present application. The site soil layer parameters, foundation pit size and support structure parameters can be shown in Tables 1 and 2, wherein Table 1 is a table of site soil layer parameters, and Table 2 is a table of foundation pit size and support structure parameters.

[0075] Table 1

[0076] Table 2

[0077] Step S1: In the present embodiment, the consolidated undrained strength parameters of the soil layer can be obtained through the geotechnical physical and mechanical parameter table in the site survey report. In this embodiment, c0=25 kPa, c inc =3.0kPa / m,φ=20°.

[0078] Step S2: Use B1=0.1m to perform trial calculation and gradually iterate the value B1 to be equal to T to obtain K b1 ~B' curve, take the tangent line at the point of maximum curvature of the curve: , Tangent and K b1 = 1, the B' value of the intersection is the type critical width, and B L =1.63m.

[0079] Step S3: Compare the actual foundation pit width B and the type critical width B L Since B = 1.5m is less than the critical width B L , so the width type of this foundation pit is a narrow foundation pit type.

[0080] Step S4: The second subsided soil width B2 is calculated by inversely calculating the actual foundation pit width B. At this time, substitute the formula: , , , Available , and the solution is B2=1.61m.

[0081] Step S5: Calculate the first stability coefficient K of the ultimate bearing capacity failure mode of the foundation in the case of narrow foundation pit b , based on the formula , get K b =1.72.

[0082] Step S6: Based on the formula , get K c=16.7.

[0083] like Figure 7 As shown, the stability coefficient of the embodiment of the present application is calculated using the finite element limit analysis software Plaxis 3D, and it can be seen that its stability coefficient is 1.727, and its failure slip surface is close to the failure mode of bearing capacity failure. It can be seen that the method of the embodiment of the present application has high accuracy. On the other hand, when the foundation pit in the embodiment of the present application is verified by the circular arc sliding method, the width of the foundation pit can accommodate the slip surface, and the calculation of the stability coefficient of the circular arc sliding method can also ignore the influence of the width of the foundation pit; but for its real sliding mode - the sliding mode of foundation bearing capacity failure, the influence of the width of the foundation pit must be considered, that is, the foundation pit of this embodiment should be calculated as a narrow foundation pit, which shows that the method of the embodiment of the present application can reasonably and correctly identify narrow foundation pits and give correct verification results.

[0084] According to the calculation method of the anti-uplift stability of the narrow foundation pit proposed in the embodiment of the present application, it is applied to the verification of the stability of the narrow foundation pit in the saturated clay stratum or the stratum with small internal friction angle, and the consolidation undrained shear strength index and the actual foundation pit width of the soil layer in the foundation pit site can be obtained, avoiding the large error that may be caused by directly verifying the consolidation undrained strength index, and based on the undrained shear strength index, the first sinking soil width corresponding to the wide foundation pit under the ultimate bearing capacity failure mode is calculated, thereby calculating the corresponding critical foundation pit width, and the type critical width is obtained according to the calculation. The foundation pit type is obtained by comparing the size of the type critical width and the actual foundation pit width, which solves the problem of difficulty in judging the wide and narrow foundation pits. When the foundation pit type is a narrow foundation pit type, the second sinking soil width is inversely calculated based on the actual foundation pit width, thereby calculating the stability coefficient of the narrow foundation pit foundation ultimate bearing capacity failure mode, and by comparing it with the stability coefficient of the arc sliding mode, the anti-uplift stability coefficient of the narrow foundation pit is obtained, and the anti-uplift stability of the narrow foundation pit is judged. Among them, when calculating the stability coefficient in the foundation bearing capacity mode, the influence of the width of the submerged soil must be considered. In the case of narrow foundation pits, the width of the submerged soil is inversely calculated using the actual foundation pit width based on the proportional relationship between the foundation width and the sliding surface width in the foundation bearing capacity problem. The physical concept is clear and correct, and the calculated stability coefficient is more accurate than the existing technical solution. As a result, technical problems in the related technology such as unreasonable judgment criteria for narrow foundation pits and selection of sliding surfaces, unclear preconditions for design verification of narrow foundation pits, and lack of calculation methods for anti-uplift stability coefficients of narrow foundation pits in the ultimate bearing capacity failure mode of the foundation are solved.

[0085] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms are not necessarily for the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0086] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0087] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

Claims

1. A method for calculating the anti-uplift stability of a narrow foundation pit, characterized in that: The method is applied to the calculation of the anti-uplift stability of a narrow foundation pit in a saturated clay layer or a layer with a small internal friction angle, wherein the method comprises the following steps: S101. Obtain the actual length, width and depth of the foundation pit and the consolidation undrained strength index of the site soil layer. The consolidation undrained strength index at least includes cohesion c cu and internal friction angle φ cu ; S102, based on the consolidated undrained strength index, according to an improved formula considering the internal friction angle of the soil and a first width calculation coefficient, a first sinking soil width corresponding to the side of the foundation pit under the ultimate bearing capacity failure mode of the wide foundation pit is calculated, and a corresponding type critical width is calculated based on the first sinking soil width; S103, comparing the actual foundation pit width obtained with the critical width of the type to obtain the width type of the foundation pit, and when the width type of the foundation pit is a narrow foundation pit type, based on the actual foundation pit width, inversely calculating the second sinking soil width corresponding to the narrow foundation pit foundation ultimate bearing capacity failure mode according to an improved formula that considers the internal friction angle of the soil; S104, based on the width of the second sunken soil body, calculating the anti-uplift stability coefficient corresponding to the ultimate bearing capacity failure mode of the narrow foundation pit foundation according to an improved formula that takes into account the internal friction angle of the soil; S105. Calculate the anti-uplift stability coefficient corresponding to the circular arc sliding failure mode of the foundation pit, and compare the anti-uplift stability coefficient corresponding to the circular arc sliding failure mode with the anti-uplift stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit, take the smaller value as the anti-uplift stability coefficient of the narrow foundation pit, and evaluate the anti-uplift stability of the foundation pit based on the calculation result.

2. The calculation method according to claim 1, characterized in that: The corresponding critical foundation pit width is calculated based on the width of the first sunken soil body, including: obtaining foundation parameters, foundation pit parameters and retaining structure parameters, and analyzing and calculating the critical foundation pit width according to the stress conditions of the soil body and the retaining structure.

3. The calculation method according to claim 1, characterized in that: When constructing the improved formula considering the internal friction angle of soil, the soil range and parameters of the passive zone of the base are considered and the η As a correction factor.

4. The calculation method according to claim 2, characterized in that: The analysis and calculation of the foundation pit width according to the stress conditions of the soil and the retaining structure includes using the first sinking soil width, the consolidated undrained strength index, the foundation parameters, and the dimensionless parameters and width calculation coefficient corresponding to the first sinking soil width, and obtaining the anti-uplift stability coefficient K corresponding to the critical foundation pit width by taking into account the improved formula of the internal friction angle of the soil. b ~B' curve, and determine the critical width of the type of foundation pit at the moment of instability based on the tangent line of the curve at the point of maximum curvature.

5. The calculation method according to claim 1, characterized in that: The calculation formula of the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit is: ， Among them, K b is the stability coefficient of the ultimate bearing capacity failure mode of the narrow foundation pit, N c is the foundation bearing capacity coefficient in the Prandtl-Reithner foundation bearing capacity formula, c 01 is the undrained strength of the soil at the embedded end of the retaining structure, β2 is the calculation coefficient of the bearing capacity width, c inc is the growth rate of undrained strength with depth, Z max，2 F is the depth of the slip surface when the foundation bearing capacity fails. Q is the resultant shear force of the inclined sliding surface, θ is the angle between the fracture surface and the horizontal plane, B2 is the width of the second sinking soil, W is the load caused by the sinking soil outside the pit, Q is the load caused by the ground load, γ′ is the buoyant weight of the soil, D is the depth of the embedded section, and η2 is the second width calculation coefficient.

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