Supporting type foundation pit stability safety coefficient calculation method

Abstract

The invention discloses a supporting type foundation pit stability safety coefficient calculation method, and belongs to the technical field of foundation pit stability calculation. The supporting type foundation pit stability safety coefficient calculation method comprises the steps that stratum information, supporting structure information and foundation pit information are input; determining a slip line circle center search range and a search depth under the pit bottom; drawing a slip line; calculating the anti-sliding torque Mri of the soil body, the sliding torque Msi on a sliding line, the anti-sliding torque M'ri and the sliding torque M'si on the sliding arc slope of the ith soil strip, the anti-sliding torque M 'ri and the sliding torque M' si on the sliding arc slope of the ith soil strip under the action of additional stress, and the anti-sliding torque Mf generated by side friction; calculating a safety coefficient K; and outputting the minimum safety coefficient Kmin and the slip line. By means of the supporting type foundation pit stability safety coefficient calculation method, the calculation efficiency is remarkably improved; various factors influencing the foundation pit stability safety coefficient calculation are covered in the calculation process, and the objectivity and accuracy of the calculation result are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of foundation pit stability calculation, and in particular to a method for calculating the safety factor of a supported foundation pit stability. Background Art

[0002] With the acceleration of my country's urbanization process, the above-ground space can no longer meet the needs of social development, and more and more underground space is being developed. Foundation pit engineering plays an important role in the evolution of cities, but the increasing complexity of urban space has brought many challenges to foundation pit construction. The unloading effect generated during foundation pit excavation will inevitably cause stress redistribution in the surrounding strata, resulting in large displacement of the surrounding strata and leading to foundation pit instability. Therefore, the design and construction of foundation pit engineering are becoming more and more challenging, and the accompanying risks are gradually increasing. The control standards for foundation pit stability are becoming more and more stringent. The improvement of foundation pit stability calculation methods is of great significance to ensuring construction safety and understanding the mechanism of foundation pit instability.

[0003] Chinese patent application number 201610912559.0 proposes a method for calculating the safety factor of soft soil foundation pit stability, which belongs to the field of foundation pit stability. The method includes: (1) establishing an excavation finite element model; (2) simulating the soil excavation process; and (3) obtaining the stability safety factor of the foundation pit. The method uses the large-scale finite element software ABAQUS to establish a finite element model to simulate and analyze the foundation pit construction process. It simulates details such as the ground stress balance, the construction of the retaining structure, and the earth excavation during the foundation pit excavation process. Finally, by reducing the strength parameters of the soil, the stability safety factor of the foundation pit is obtained. However, the above calculation method does not consider the influence of the support structure system on the safety factor calculation. In actual foundation pit projects, changes in excavation depth will change the stress state of the support structure, causing the safety factor to change continuously during the dynamic construction process. Therefore, the safety factor calculation method described in this patent is inaccurate for the assessment of foundation pit stability.

[0004] The Chinese patent application number 201811045050.6 proposes a method for analyzing the embedded stability of narrow foundation pits, which belongs to the field of geotechnical engineering technology. The method includes: (1) using support piles and internal supports to determine whether the foundation pit is a narrow foundation pit: through conventional analysis methods and analysis results, if the opposite side support piles are located within the sliding surface range, it is a narrow foundation pit; (2) searching all potential sliding surfaces, calculating the embedded stability of each sliding surface, and the sliding surface with the smallest arc sliding stability safety factor is the most unfavorable sliding surface. This method improves the accuracy of the calculation results for safety evaluation by considering the contribution of the friction resistance and active earth pressure between the opposite side support piles and the sliding soil to the anti-sliding stability. This method is mainly based on static analysis and does not consider the impact of dynamic factors on stability during the foundation pit construction process, resulting in inaccurate evaluation of foundation pit stability. During the construction process, the excavation sequence of the soil, the construction time of the support structure, and the construction process will cause changes in the stress state of the soil, thereby affecting the stability of the foundation pit.

[0005] Chinese patent application number 201811483667.6 proposes a method for calculating the safety factor of foundation pit stability under the action of seismic waves, which belongs to the field of foundation pit stability. The method includes: (1) establishing an excavation finite element model and simulating the soil excavation process; (2) correcting the baseline of the seismic wave and adjusting the effective peak value of acceleration; (3) adding seismic waves; and (4) obtaining the stability safety factor of the foundation pit by reducing the strength parameters of the soil. However, the above patent relies on large-scale finite element software to calculate the safety factor, which is computationally expensive and affects the computational efficiency. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for calculating the safety factor of the stability of a supported foundation pit, which abandons finite element or finite difference software and significantly improves the calculation efficiency; in the calculation process, various factors affecting the calculation of the safety factor of the foundation pit stability are covered, thereby improving the objectivity and accuracy of the calculation results.

[0007] To achieve the above object, the present invention provides a method for calculating the safety factor of a supported foundation pit stability, comprising the following steps:

[0008] S1. Input stratum information, support structure information and foundation pit information;

[0009] S2. Determine the search range of the center of the slip line and the search depth below the pit bottom, determine the center position and calculate the depth;

[0010] S3. Determine the radius of the slip line according to the center position of the circle and the calculated depth, and draw the slip line;

[0011] S4. Calculate the soil anti-sliding moment M ri and the sliding moment M on the slip line si; Calculate the anti-sliding moment M' on the sliding arc slope of the i-th soil strip according to whether there is a ground load above the soil strip ri and sliding moment M' si According to the positional relationship between the slip line and the underground continuous wall, calculate the anti-slip moment M" on the sliding arc slope of the i-th soil strip under the action of additional stress ri and sliding moment M" si ; According to whether the slip line extends to the opposite wall of the foundation pit, calculate the anti-slip torque M generated by the side friction resistance of the opposite wall f ;

[0012] S5, determine whether the calculation of the soil strips above the slip line has been completed. If not, repeat S4; if completed, according to the anti-slip moment M ri , sliding torque M si , Sliding torque M' ri , sliding torque M' si , anti-slip torque M" ri , sliding torque M" si and anti-slip torque M f Calculate the safety factor K;

[0013] S6, minimum storage safety factor K min and minimum safety factor K min The corresponding center position and calculated depth;

[0014] S7, determine whether the search of the circle center search range and search depth is completed, if not, repeat S4-S6; if completed, execute S8;

[0015] S8, output minimum safety factor K min and slip lines.

[0016] Preferably, in said S1, the stratum information includes: the depth h of each soil layer i , each soil layer weight γ i , cohesion c i , internal friction angle Active earth pressure coefficient K ai , static earth pressure coefficient K 0i , passive earth pressure coefficient K pi ,

[0017] Support structure information includes: underground continuous wall depth H w ,

[0018] Foundation pit information includes: foundation pit excavation depth H e , foundation pit excavation width W e .

[0019] Preferably, in S2, the search range of the center of the sliding line is: with the free surface of the top of the ground-connected wall as the origin A (0, 0), the area formed by the origin A extending toward the free surface by p and extending directly above by q; the initial center position is the origin A, the horizontal offset of the center is Δp, and the vertical offset of the center is Δq;

[0020] Initial calculation depth H c is the foundation pit excavation depth H e , calculate the depth offset as Δh.

[0021] Preferably, in S3, the radius of the slip line is the distance between the center of the circle O(m,n) and the point S where the pit bottom and the underground continuous wall intersect. The slip line equation is:

[0022] (xm) 2 +(yn) 2 =R 2 ;

[0023] Among them, x is the horizontal coordinate of the slip line, y is the vertical coordinate of the slip line, m is the horizontal coordinate of the center of the circle, n is the vertical coordinate of the center of the circle, and R is the radius of the slip line.

[0024] Preferably, in said S4, the soil anti-slip moment M ri and the sliding moment M on the slip line si The expression is:

[0025]

[0026] M si =W i sinβ i ·R;

[0027] Among them, c i is the soil cohesion at the sliding surface of soil strip i, l i is the length of the sliding surface of soil strip i, is the internal friction angle of soil at the sliding surface of soil strip i, W i is the gravity of soil strip i, β i is the angle between the inclined section of the sliding surface of soil strip i and the x-axis, R is the radius of the sliding arc, and when soil strip i is located to the left of the center of the circle, the sliding moment M si is a negative value.

[0028] Preferably, in said S4, if there is no ground load, the vertical additional stress is 0; if there is a ground load, the anti-slip moment M' on the sliding arc slope of the i-th soil strip is ri , sliding torque M' si Respectively expressed as:

[0029]

[0030] M' si =q i b i sinβ i ·R;

[0031] Among them, q i is the size of the uniformly distributed load per unit length, b i is the width of soil strip i.

[0032] Preferably, in said S4, when the slip line is located above the underground continuous wall, the anti-slip moment M" on the sliding arc slope of the i-th soil strip is ri and sliding moment M" si The calculation process is:

[0033] S411. The displacement of the soil behind the underground continuous wall is expressed as:

[0034] δ l =f(h);

[0035] Among them, δ l is the displacement of the soil behind the underground continuous wall, and h is the depth from the ground surface to the underground continuous wall measuring point;

[0036] S412. Calculate the static earth pressure e0 of the soil at depth h:

[0037] e0=K 0i ·σ h ;

[0038] Among them, K 0i is the static earth pressure coefficient at the depth h from the surface to the underground continuous wall measuring point, σ h is the vertical stress at the depth h from the ground surface to the measuring point of the underground continuous wall;

[0039] S413. Calculate the active earth pressure e of the soil at depth h. a :

[0040]

[0041] Among them, K ai is the active earth pressure coefficient at the depth h from the surface to the underground continuous wall measuring point, c ai is the cohesion at the depth h from the ground surface to the underground continuous wall measuring point;

[0042] S414. Calculate the unloading value P of the soil on the right side of the underground continuous wall in the foundation pit excavation x :

[0043]

[0044] Among them, δ ais the displacement required for the active limit state of the soil behind the retaining structure;

[0045] S415. Calculate the stress change at a point in the soil under the action of a horizontal force;

[0046]

[0047] Among them, Δσ x , Δσ z , Δτ zx The additional normal stress in the x-axis direction, the additional normal stress in the z-axis direction, and the shear stress in the zx plane of a point in the soil at the sliding line at the depth c on the right side of the underground continuous wall are calculated using the Mindlin solution. i is the angle between the inclined section of the sliding surface of soil strip i and the x-axis, is the internal friction angle of soil at the sliding surface of soil strip i, Δσ i , Δτ i , Δτ fi are the total normal stress change at a point in the soil, the total shear stress change at a point in the soil, and the total shear strength increment at a point in the soil;

[0048] S416, anti-sliding moment M" on the sliding arc slope of the i-th soil strip under additional stress ri and sliding moment M" si They are:

[0049] M” ri =Δτ fi ·l i ·R;

[0050] M” si =Δτ i ·l i ·R.

[0051] Preferably, in said S4, when the slip line is located below the underground continuous wall, the anti-slip moment M" on the sliding arc slope of the i-th soil strip is ri and sliding moment M" si The calculation process is:

[0052] S421. Calculate the passive earth pressure e of the soil at depth h. p :

[0053]

[0054] Among them, K pi is the passive earth pressure coefficient at depth h, c pi is the cohesion at the depth h from the surface to the underground continuous wall measuring point, σ ph is the vertical soil stress from the excavation surface to the depth h;

[0055] S422. Calculate the soil loading value P on the left side of the underground continuous wall caused by foundation pit excavation xp :

[0056]

[0057] Among them, δ p is the displacement required for the passive limit state of the soil below the foundation pit excavation surface;

[0058] S423. Use Mindlin's solution to calculate the additional normal stress Δσ in the x-axis direction at a point in the sliding line soil at depth c of the right underground continuous wall. x , additional normal stress Δσ in the z-axis direction” z , shear stress Δτ in the zx plane” zx , when calculating, use the loading value P xp Replace the uninstall value P in the formula x ;

[0059] Calculate the additional stress Δσ"' at a point on the sliding line of the underground continuous wall at the depth c on the left side of the foundation pit using Mindlin's solution z , Δσ”' x and Δτ'' zx ;

[0060] S424. The lateral friction resistance generated by the stress released by the retaining structure on the pit bottom is:

[0061]

[0062] P' x =P xp +e0

[0063] Among them, P' x is the horizontal stress acting on the retaining structure at the bottom of the foundation pit. is the effective internal friction angle of the contact surface between the soil at the bottom of the foundation pit and the retaining structure;

[0064] S425. Calculate the equivalent load on the soil at the bottom horizontal plane of the retaining structure after excavation and unloading:

[0065]

[0066] Among them, σ zz is the vertical soil stress from the surface to the excavation surface of the foundation pit, α is the residual stress coefficient,

[0067]

[0068] Among them, h r is the residual stress influence depth, h0 is the vertical distance from soil strip i to the excavation surface of the foundation pit, α0 is the initial residual stress coefficient;

[0069] S426, use Mindlin solution to calculate the excavation surface H e Additional normal stress Δσ' in the x-axis direction at a point in the lower soil x , additional normal stress Δσ' in the z-axis direction z , shear stress Δτ' in the zx plane zx ;

[0070] S427. Calculate the stress change at a point in the soil, considering only the stress change on the left slip line of the underground continuous wall:

[0071]

[0072] S428, anti-sliding moment M" on the sliding arc slope of the i-th soil strip under additional stress ri And sliding torque M" si They are:

[0073] M” ri =Δτ fi ·l i ·R;

[0074] M” si =Δτ i ·l i ·R.

[0075] Preferably, in said S4, if the slip line does not extend to the opposite side wall of the foundation pit, the frictional resistance between the opposite side wall and the soil in the pit is not considered; if the slip line extends to the opposite side wall of the foundation pit, the frictional resistance between the opposite side wall and the soil in the pit is considered; the anti-slip torque M generated by the side friction resistance f for:

[0076]

[0077] Wherein, θ is the angle between the arc radius R and the vertical direction when the slip line acts on the opposite wall.

[0078] Preferably, in S5, the calculation formula of the safety factor K is:

[0079]

[0080] The advantages and positive effects of the method for calculating the safety factor of the supported foundation pit stability described in the present invention are:

[0081] 1. The calculation method described in the present invention abandons the traditional large-scale finite element or finite difference software, and significantly improves the calculation efficiency of the safety factor of foundation pit stability.

[0082] 2. This method comprehensively considers multiple factors, including soil parameters, ground loads, wall resistance, and the effects of cross bracing, encompassing as many factors as possible that influence the calculation of the safety factor for foundation pit stability, thereby significantly improving the objectivity and accuracy of the calculation results. This calculation method not only ensures the correctness and effectiveness of stability factor calculations in actual projects, but also helps reduce project risks and provides more reliable technical support for the stability assessment of foundation pit projects.

[0083] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 This is a flow chart of the method for calculating the safety factor of the supported foundation pit stability according to the present invention;

[0085] Figure 2 Schematic diagram of circle center search for the method for calculating the safety factor of stability of a supported foundation pit according to the present invention;

[0086] Figure 3 This is a schematic diagram of the calculation of the foundation pit slip line located above the wall of the present invention;

[0087] Figure 4 Schematic diagram of calculation of Mindlin solution under horizontal concentrated stress of the present invention;

[0088] Figure 5 This is a schematic diagram of the calculation of the supported foundation pit sliding line located below the wall of the present invention;

[0089] Figure 6 Schematic diagram of calculation of Mindlin solution under vertical concentrated stress of the present invention;

[0090] Figure 7 Schematic diagram of the stress state calculation of a point in the soil of a supported foundation pit according to the present invention;

[0091] Figure 8 This is a schematic diagram of the calculation of the supported foundation pit of the present invention without considering the friction resistance of the opposite wall;

[0092] Figure 9 This is a schematic diagram of the calculation of the friction resistance of the opposite wall of the supported foundation pit of the present invention. DETAILED DESCRIPTION

[0093] In this application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this application belongs. In the event of any inconsistency, the meaning described in this specification or the meaning derived from the contents recorded in this specification shall prevail. In addition, the terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0094] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0095] like Figure 1 A method for calculating the safety factor of a supported foundation pit stability includes the following steps:

[0096] S1. Input stratum information, support structure information and foundation pit information.

[0097] Stratum information includes: depth of each soil layer h i , each soil layer weight γ i , cohesion c i , internal friction angle Active earth pressure coefficient K ai , static earth pressure coefficient K 0i , passive earth pressure coefficient K pi .

[0098] Support structure information includes: underground continuous wall depth H w .

[0099] Foundation pit information includes: foundation pit excavation depth H e , foundation pit excavation width W e .

[0100] S2, such as Figure 2 Determine the search range of the center of the slip line and the search depth below the pit bottom, determine the center position and calculate the depth.

[0101] The search range for the center of the slipline circle is: origin A(0,0) at the top free surface of the ground-connected wall, and the area formed by extending from origin A to the free surface by a distance p and directly above it by a distance q. The initial center position is origin A, the horizontal offset of the center is Δp, and the vertical offset of the center is Δq.

[0102] Initial calculation depth H c is the foundation pit excavation depth H e , calculate the depth offset as Δh.

[0103] S3. Determine the radius of the slip line according to the center position of the circle and the calculated depth, and draw the slip line.

[0104] The radius of the slip line is the distance between the center of the circle O(m,n) and the point S where the pit bottom and the underground continuous wall intersect. Point S is any point extending downward from the intersection of the pit bottom and the underground continuous wall. The specific downward extension depth can be determined based on the subsequent trend of the safety factor or the engineer's experience. The slip line equation is:

[0105] (xm) 2 +(yn) 2 =R 2 ;

[0106] Among them, x is the horizontal coordinate of the slip line, y is the vertical coordinate of the slip line, m is the horizontal coordinate of the center of the circle, n is the vertical coordinate of the center of the circle, and R is the radius of the slip line.

[0107] S4. Calculate the soil anti-sliding moment M ri and the sliding moment M on the slip line si ; Calculate the anti-sliding moment M' on the sliding arc slope of the i-th soil strip according to whether there is a ground load above the soil strip ri and sliding moment M' si According to the positional relationship between the slip line and the underground continuous wall, calculate the anti-slip moment M" on the sliding arc slope of the i-th soil strip under the action of additional stress ri and sliding moment M" si ; According to whether the slip line extends to the opposite wall of the foundation pit, calculate the anti-slip torque M generated by the side friction resistance of the opposite wall f .

[0108] Soil anti-slip moment M ri and the sliding moment M on the slip line si The expression is:

[0109]

[0110] M si =W i sinβ i ·R;

[0111] Among them, c i is the soil cohesion at the sliding surface of soil strip i, l i is the length of the sliding surface of soil strip i, is the internal friction angle of soil at the sliding surface of soil strip i, W i is the gravity of soil strip i, β i is the angle between the inclined section of the sliding surface of soil strip i and the x-axis, R is the radius of the sliding arc, and when soil strip i is located to the left of the center of the circle, the sliding moment M si is a negative value.

[0112] Determine whether there is a ground load above soil strip i. If there is no ground load, the vertical additional stress is 0. If there is a ground load, the anti-slip moment M' on the sliding arc slope of the i-th soil strip is ri , sliding torque M' si Respectively expressed as:

[0113]

[0114] M' si =q i b i sinβ i ·R;

[0115] Among them, q i is the size of the uniformly distributed load per unit length, b i is the width of soil strip i.

[0116] Determine the relative position of the drawn slip line and the diaphragm wall. When the slip line is above the diaphragm wall, shear failure is unlikely due to the wall's high stiffness. Therefore, soil slip below the excavation surface is not considered. A fitting formula is derived using the diaphragm wall's lateral displacement and the distance from the diaphragm wall's measuring point to the ground surface. Because unloading during the excavation causes the diaphragm wall and the soil behind it to deform in concert, the displacement of the soil behind the pit is assumed to be consistent with the lateral displacement of the diaphragm wall.

[0117] The anti-sliding moment M" on the sliding arc slope of the i-th soil strip ri and sliding moment M" si The calculation process is:

[0118] S411. The displacement of the soil behind the underground continuous wall is expressed as:

[0119] δ l =f(h);

[0120] Among them, δ l is the displacement of the soil behind the underground continuous wall, and h is the depth from the ground surface to the underground continuous wall measuring point.

[0121] S412. Calculate the static earth pressure e0 of the soil at depth h:

[0122] e0=K 0i ·σ h ;

[0123] Among them, K 0i is the static earth pressure coefficient at the depth h from the surface to the underground continuous wall measuring point, σ h is the vertical stress at the depth h from the ground surface to the measuring point of the underground continuous wall.

[0124] S413. Calculate the active earth pressure e of the soil at depth h. a :

[0125]

[0126] Among them, K ai is the active earth pressure coefficient at the depth h from the surface to the underground continuous wall measuring point, c ai is the cohesion at the depth h from the ground surface to the measuring point of the underground continuous wall.

[0127] S414. Calculate the unloading value P of the soil on the right side of the underground continuous wall in the foundation pit excavation x :

[0128]

[0129] Among them, δ a is the displacement required for the active limit state of the soil behind the retaining structure. a and excavation depth H e There is a proportional relationship, which is generally 0.001~0.004H in clay. e The specific proportion relationship can be found in relevant literature.

[0130] S415, such as Figure 4 As shown. The Mindlin solution is used to calculate the additional stress at a point in the soil below the depth c of the underground continuous wall:

[0131]

[0132] Where c is the horizontal concentrated force P acting on the soil in the local coordinate system x The depth of action; x and z are the coordinate values of the midpoint of the inclined section of soil strip i in the local coordinate system. The origin of the local coordinate system is established on the right side of the underground continuous wall away from the foundation pit side. The x-axis extends horizontally to the right, and the z-axis extends vertically downward; μ is the Poisson's ratio of the soil.

[0133] like Figure 7 Calculate the stress change at a point in the soil under the action of horizontal force. Since the slip line only appears on the right side of the underground continuous wall, only the additional stress of the soil on the right side of the slip line is calculated.

[0134]

[0135] Among them, Δσ x , Δσ z , Δτ zx The additional normal stress in the x-axis direction, the additional normal stress in the z-axis direction, and the shear stress in the zx plane of a point in the soil at the sliding line at the depth c on the right side of the underground continuous wall are calculated using the Mindlin solution. i is the angle between the inclined section of the sliding surface of soil strip i and the x-axis, is the internal friction angle of soil at the sliding surface of soil strip i, Δσ i , Δτ i , Δτ fi are the total normal stress change at a point in the soil, the total shear stress change at a point in the soil, and the total shear strength increment at a point in the soil;

[0136] S416, anti-sliding moment M" on the sliding arc slope of the i-th soil strip under additional stress ri and sliding moment M" si They are:

[0137] M” ri =Δτfi ·l i ·R;

[0138] M” si =Δτ i ·l i ·R.

[0139] like Figure 5 As shown in the figure. When the slip line is located below the diaphragm wall, since the slip line passes through the diaphragm wall, the sliding of the soil below the excavation surface is considered. The fitting formula is derived from the lateral displacement of the diaphragm wall and the distance from the diaphragm wall measuring point to the ground surface. Because the diaphragm wall and the soil behind it deform in concert with each other due to unloading during the excavation, the displacement of the soil behind the pit is assumed to be consistent with the lateral displacement of the diaphragm wall.

[0140] The anti-sliding moment M" on the sliding arc slope of the i-th soil strip ri and sliding moment M" si The calculation process is:

[0141] S421. Calculate the passive earth pressure e of the soil at depth h. p :

[0142]

[0143] Among them, K pi is the passive earth pressure coefficient at depth h, c pi is the cohesion at the depth h from the surface to the underground continuous wall measuring point, σ ph is the vertical soil stress from the excavation surface to the depth h.

[0144] S422. Calculate the soil loading value P on the left side of the underground continuous wall caused by foundation pit excavation xp :

[0145]

[0146] Among them, δ p is the displacement required for the passive limit state of the soil below the foundation pit excavation surface. p and excavation depth H e There is a proportional relationship, which is generally 0.02~0.05H in clay. e The specific proportion relationship can be found in relevant literature.

[0147] S423. Use the Mindlin solution in S415 to calculate the additional normal stress Δσ in the x-axis direction at a point in the sliding line soil at a depth c of the right underground continuous wall. x , additional normal stress Δσ in the z-axis direction” z , shear stress Δτ in the zx plane” zx When calculating, use the load value Pxp Replace the uninstall value P in the formula x .

[0148] The load value P calculated according to the formula in S421-S422 xp , using Mindlin's solution to calculate the additional stress Δσ"' at a point in the soil on the sliding line at the depth c of the underground continuous wall on the left side of the foundation pit z , Δσ”' x and Δτ'' zx .

[0149] S424. Due to the protective effect of the retaining structure at the bottom of the foundation pit, a shielding effect is formed. Therefore, the stress released from the pit bottom will be affected by the lateral friction resistance generated by the retaining structure. The lateral friction resistance generated by the retaining structure on the stress released from the pit bottom is:

[0150]

[0151] P x =P xp +e0

[0152] Among them, P' x is the horizontal stress acting on the retaining structure at the bottom of the foundation pit. It is the effective internal friction angle of the contact surface between the soil at the bottom of the foundation pit and the retaining structure.

[0153] S425. Calculate the equivalent load on the soil at the bottom horizontal plane of the retaining structure after excavation and unloading:

[0154]

[0155] Among them, σ zz is the vertical soil stress from the ground surface to the excavation surface of the foundation pit, that is, the weight of the soil under the excavation depth of the foundation pit; α is the residual stress coefficient,

[0156]

[0157] Among them, h r is the residual stress influence depth, h0 is the vertical distance from soil strip i to the excavation surface of the foundation pit, and α0 is the initial residual stress coefficient.

[0158] S426, such as Figure 6 As shown. Using Mindlin solution to calculate the excavation surface H e Additional normal stress Δσ' in the x-axis direction at a point in the lower soil x , additional normal stress Δσ' in the z-axis direction z , shear stress Δτ' in the zx plane zx .

[0159]

[0160] Where c and b are the vertical forces P z The coordinate values in the local coordinate system under the action of , x and z are the coordinate values of the midpoint of the inclined section of soil strip i in the local coordinate system. The origin of the local coordinate system is established on the right side of the underground continuous wall close to the foundation pit side, the x-axis extends horizontally to the right, and the z-axis extends vertically downward.

[0161] S427. Calculate the stress change at a point in the soil, considering only the stress change on the left slip line of the underground continuous wall:

[0162]

[0163] S428, anti-sliding moment M" on the sliding arc slope of the i-th soil strip under additional stress ri And sliding torque M" si They are:

[0164] M” ri =Δτ fi ·l i ·R;

[0165] M” si =Δτ i ·l i ·R.

[0166] like Figure 8 If the slip line does not extend to the opposite wall of the foundation pit, the friction between the opposite wall and the soil in the pit will not be considered. Figure 9 If the slip line extends to the opposite side wall of the foundation pit, the friction between the opposite side wall and the soil in the pit should be considered. The anti-slip torque M generated by the side friction f for:

[0167]

[0168] Wherein, θ is the angle between the arc radius R and the vertical direction when the slip line acts on the opposite wall.

[0169] S5, determine whether the calculation of the soil strips above the slip line has been completed. If not, repeat S4. If completed, according to the anti-slip moment M ri , sliding torque M si , Sliding torque M' ri , sliding torque M' si , anti-slip torque M" ri , sliding torque M" si and anti-slip torque M f Calculate the safety factor K. The calculation formula for the safety factor K is:

[0170]

[0171] The safety factor of the foundation pit below the slip line is calculated by calculating the sum of the anti-slip moment and sliding moment of all soil strips within the slip line, as well as the anti-slip moment of the wall.

[0172] S6. Calculate the safety factor of the foundation pit below the slip line by calculating the sum of the anti-slip moment and sliding moment of all soil strips within the slip line, as well as the anti-slip moment of the wall, and store the minimum safety factor K. min and minimum safety factor K min The corresponding center position and calculated depth.

[0173] S7. Determine whether the search of the circle center search range and search depth is completed. If not, repeat S4-S6; if completed, execute S8.

[0174] S8, output minimum safety factor K min and slip lines.

[0175] Therefore, the method for calculating the safety factor of the stability of a supported foundation pit described in the present invention abandons the finite element or finite difference software, significantly improving the calculation efficiency; various factors affecting the calculation of the safety factor of the stability of the foundation pit are covered in the calculation process, thereby improving the objectivity and accuracy of the calculation results.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for calculating the safety factor of a supported foundation pit stability, characterized in that: The following steps are involved: S1. Input stratum information, support structure information and foundation pit information; S2. Determine the search range of the center of the slip line and the search depth below the pit bottom, determine the center position and calculate the depth; S3. Determine the radius of the slip line according to the center position of the circle and the calculated depth, and draw the slip line; S4. Calculate the soil anti-sliding moment M ri and the sliding moment M on the slip line si ; According to whether there is ground load above the soil strip, calculate the anti-sliding moment M' on the sliding arc slope of the i-th soil strip ri and sliding moment M' si ; According to the positional relationship between the slip line and the underground continuous wall, the anti-slip moment M″ on the sliding arc slope of the i-th soil strip under the action of additional stress is calculated. ri and sliding torque M″ si ; According to whether the slip line extends to the opposite wall of the foundation pit, calculate the anti-slip torque M generated by the side friction resistance of the opposite wall f ; S5, determining whether the calculation of the soil strips above the slip line has been completed, if not, repeat S4; If completed, according to the anti-slip torque M ri , sliding torque M si , Sliding torque M' ri , sliding torque M' si , anti-slip torque M″ ri , sliding torque M″ si and anti-slip torque M f Calculate the safety factor K; S6. Storage minimum safety factor K min and minimum safety factor K min The corresponding center position and calculated depth; S7, determine whether the search of the circle center search range and search depth is completed, if not, repeat S4-S6; if completed, execute S8; S8, output minimum safety factor K min and slip lines.

2. A method for calculating the safety factor of a supported foundation pit stability according to claim 1, characterized in that: In S1, the stratum information includes: the depth h of each soil layer i , each soil layer weight γ i , cohesion c i , internal friction angle Active earth pressure coefficient K ai , static earth pressure coefficient K 0i , passive earth pressure coefficient K pi , Support structure information includes: underground continuous wall depth H w , Foundation pit information includes: foundation pit excavation depth H e , foundation pit excavation width W e .

3. A method for calculating the safety factor of a supported foundation pit stability according to claim 2, characterized in that: In S2, the search range of the center of the sliding line is: with the free surface of the top of the ground-connected wall as the origin A (0, 0), the area formed by the origin A extending toward the free surface p and directly above it extending q; the initial center position is the origin A, the horizontal offset of the center is Δp, and the vertical offset of the center is Δq; Initial calculation depth H c is the foundation pit excavation depth H e , calculate the depth offset as Δh.

4. A method for calculating the safety factor of a supported foundation pit stability according to claim 3, characterized in that: In S3, the radius of the slip line is the distance between the center of the circle O(m,n) and the point S where the pit bottom and the underground continuous wall intersect. The slip line equation is: (x-m) 2 +(y-n) 2 =R 2 ; Among them, x is the horizontal coordinate of the slip line, y is the vertical coordinate of the slip line, m is the horizontal coordinate of the center of the circle, n is the vertical coordinate of the center of the circle, and R is the radius of the slip line.

5. A method for calculating the safety factor of a supported foundation pit stability according to claim 4, characterized in that: In S4, the soil anti-sliding moment M ri and the sliding moment M on the slip line si The expression is: M si =W i ·sinβ i ·R; Among them, c i is the soil cohesion at the sliding surface of soil strip i, l i is the length of the sliding surface of soil strip i, is the internal friction angle of soil at the sliding surface of soil strip i, W i is the gravity of soil strip i, β i is the angle between the inclined section of the sliding surface of soil strip i and the x-axis, R is the radius of the sliding arc, and when soil strip i is located to the left of the center of the circle, the sliding moment M si is a negative value.

6. A method for calculating the safety factor of a supported foundation pit stability according to claim 5, characterized in that: In S4, if there is no ground load, the vertical additional stress is 0; If there is a ground load, the anti-sliding moment M' on the sliding arc slope of the i-th soil strip is ri , sliding torque M' si Respectively expressed as: M′ si =q i ·b i ·sinβ i ·R; Among them, q i is the size of the uniformly distributed load per unit length, b i is the width of soil strip i.

7. A method for calculating the safety factor of a supported foundation pit stability according to claim 6, characterized in that: In S4, when the slip line is above the underground continuous wall, the anti-slip moment M″ on the sliding arc slope of the i-th soil strip is ri and sliding torque M″ si The calculation process is: S411. The displacement of the soil behind the underground continuous wall is expressed as: d l =f(h); Among them, δ l is the displacement of the soil behind the underground continuous wall, and h is the depth from the ground surface to the underground continuous wall measuring point; S412. Calculate the static earth pressure e0 of the soil at depth h: e0=K 0i ·s h ; Among them, K 0i is the static earth pressure coefficient at the depth h from the surface to the underground continuous wall measuring point, σ h is the vertical stress at the depth h from the ground surface to the measuring point of the underground continuous wall; S413. Calculate the active earth pressure e of the soil at depth h. a : Among them, K ai is the active earth pressure coefficient at the depth h from the surface to the underground continuous wall measuring point, c ai is the cohesion at the depth h from the ground surface to the measuring point of the underground continuous wall; S414. Calculate the unloading value P of the soil on the right side of the underground continuous wall in the foundation pit excavation x : Among them, δ a is the displacement required for the active limit state of the soil behind the retaining structure; S415. Calculate the stress change at a point in the soil under the action of a horizontal force; Among them, Δσ x , Δσ z , Δτ zx The additional normal stress in the x-axis direction, the additional normal stress in the z-axis direction, and the shear stress in the zx plane of a point in the soil at the sliding line at the depth c on the right side of the underground continuous wall are calculated using the Mindlin solution. i is the angle between the inclined section of the sliding surface of soil strip i and the x-axis, is the internal friction angle of soil at the sliding surface of soil strip i, Δσ i , Δτ i , Δτ fi are the total normal stress change at a point in the soil, the total shear stress change at a point in the soil, and the total shear strength increment at a point in the soil; S416. Anti-sliding moment M″ on the sliding arc slope of the i-th soil strip under additional stress ri and sliding torque M″ si They are: M″ ri =Dt fi ·l i ·R; M″ si =Dt i ·l i ·R.

8. The method for calculating the safety factor of a supported foundation pit stability according to claim 7, wherein: In S4, when the slip line is below the underground continuous wall, the anti-slip moment M″ on the sliding arc slope of the i-th soil strip is ri and sliding torque M″ si The calculation process is: S421. Calculate the passive earth pressure e of the soil at depth h. p : Among them, K pi is the passive earth pressure coefficient at depth h, c pi is the cohesion at the depth h from the surface to the underground continuous wall measuring point, σ ph is the vertical soil stress from the excavation surface to the depth h; S422. Calculate the soil loading value P on the left side of the underground continuous wall caused by foundation pit excavation xp : Among them, δ p is the displacement required for the passive limit state of the soil below the foundation pit excavation surface; S423. Use Mindlin's solution to calculate the additional normal stress Δσ″ in the x-axis direction at a point in the sliding line soil at a depth c of the right underground continuous wall. x , additional normal stress Δσ″ in the z-axis direction z , shear stress Δτ″ in the zx plane zx ; When calculating, use the load value P xp Replace the uninstall value P in the formula x . Calculate the additional stress Δσ''' at a point on the sliding line of the underground continuous wall at the depth c on the left side of the foundation pit using Mindlin's solution z , Δσ''' x and Δτ''' zx ; S424. The lateral friction resistance generated by the stress released by the retaining structure on the pit bottom is: P' x =P xp +e0; Among them, P' x is the horizontal stress acting on the retaining structure at the bottom of the foundation pit. is the effective internal friction angle of the contact surface between the soil at the bottom of the foundation pit and the retaining structure; S425. Calculate the equivalent load on the soil at the bottom horizontal plane of the retaining structure after excavation and unloading: Among them, σ zz is the vertical soil stress from the surface to the excavation surface of the foundation pit, α is the residual stress coefficient, Among them, h r is the residual stress influence depth, h0 is the vertical distance from soil strip i to the excavation surface of the foundation pit, α0 is the initial residual stress coefficient; S426, use Mindlin solution to calculate the excavation surface H e Additional normal stress Δσ' in the x-axis direction at a point in the lower soil x , additional normal stress Δσ' in the z-axis direction z , shear stress Δτ' in the zx plane zx ; S427. Calculate the stress change at a point in the soil, considering only the stress change on the left slip line of the underground continuous wall: S428. Anti-sliding moment M″ on the sliding arc slope of the i-th soil strip under additional stress ri and sliding torque M″ si They are: M″ ri =Dt fi ·l i ·R; M″ si =Dt i ·l i ·R.

9. A method for calculating the safety factor of a supported foundation pit stability according to claim 8, characterized in that: In S4, if the slip line does not extend to the opposite side wall of the foundation pit, the frictional resistance between the opposite side wall and the soil in the pit is not considered; if the slip line extends to the opposite side wall of the foundation pit, the frictional resistance between the opposite side wall and the soil in the pit is considered; the anti-slip torque M generated by the side friction resistance f for: Wherein, θ is the angle between the arc radius R and the vertical direction when the slip line acts on the opposite wall.

10. A method for calculating the safety factor of a supported foundation pit stability according to claim 9, characterized in that: In S5, the calculation formula of the safety factor K is:

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