A method for determining the position of the slip shear outlet of a narrow and long foundation pit

Abstract

The present invention provides a method for determining the position of the slip shear outlet suitable for the bottom heave failure of narrow and long foundation pits. This method uses the contour map of the stress yield proximity of the bottom soil to determine the position of the slip shear outlet, solving the problems that the existing failure modes of the bottom heave of narrow and long foundation pits lack scientific demonstration and may bring insecurity and economic waste to the design.

Description

Technical Field

[0001] The present invention relates to the field of geotechnical engineering design, and particularly to a method for determining the slip shear outlet position of a narrow and long foundation pit. Background Art

[0002] With the gradual development of underground space, narrow and long foundation pits are increasing in subway stations, open-cut tunnels in sections, and underground pipeline construction.

[0003] At present, the arc sliding mode is generally adopted for the anti-heave stability analysis of foundation pits in the foundation pit code. This mode believes that the wall below the excavation surface can play a role in resisting the heave at the bottom of the pit, and assumes that the soil slides along the ground of the retaining wall, and the sliding surface is an arc. However, this mode cannot consider the influence of the foundation pit size and is only applicable to foundation pits with a larger width and is not applicable to narrow and long foundation pits.

[0004] For the anti-heave stability analysis of narrow and long foundation pits, many scholars have conducted research and proposed corresponding failure modes, mainly including the following three: trapezoidal mode (Wang Chenghua, Failure mode and stability analysis of narrow and long foundation pit heave, 2017), triangular mode (Wang Hongxin, Improvement of the safety factor for anti-heave stability of foundation pits, 2014), and improved arc sliding mode (Peng Kongshu, Research on the anti-heave stability problem of narrow strip foundation pits, 2015). However, these three modes lack scientific demonstration and may bring risks such as insecurity and economic waste to the design. Summary of the Invention

[0005] In order to solve the problem that the existing failure modes of the bottom heave of narrow and long foundation pits lack scientific demonstration and may bring risks such as insecurity and economic waste to the design, the present invention provides a method for determining the slip shear outlet position of a narrow and long foundation pit.

[0006] To solve the above technical problems, the present invention provides the following technical solution: A method for determining the slip shear outlet position of a narrow and long foundation pit, characterized in that the method includes the following steps:

[0007] A. First, calculate the stress distribution of the narrow and long foundation pit under the action of a vertical strip uniform load;

[0008] B. Secondly, calculate the principal stress of the soil mass at any point below the bottom of the pit;

[0009] C. Thirdly, calculate the yield proximity of the soil mass at any point below the bottom of the pit;

[0010] D. Then, draw an isogram of the yield proximity according to the yield proximity of each point of the soil mass at the bottom of the pit;

[0011] E. Finally, determine the slip shear outlet position according to the isogram of the yield proximity.

[0012] The yield proximity is expressed as

[0013]

[0014] Where: σ equ and σ Y are the equivalent stress of the soil skeleton and the yield stress under this stress state respectively, σ1 and σ3 are the maximum and minimum principal stresses of the soil skeleton (compression is positive), c, are the cohesion and internal friction angle of the soil respectively. When η < 1, the soil is in an elastic state, and when η ≥ 1, the soil is in a plastic state.

[0015] In step E, the only intersection point of the contour line with a yield proximity equal to 1 at the limit state and the bottom of the pit is the position of the slip shear outlet.

[0016] As can be seen from the above disclosed technical solutions, compared with the prior art, the beneficial effects of the present invention are as follows:

[0017] (1) The theory is reliable, scientific and reasonable.

[0018] (2) Applicable to all soil layers.

[0019] (3) For narrow and long foundation pits, the pile length of the retaining pile can be reduced.

[0020] (4) Reduce the retaining cost and shorten the construction period. Description of the Drawings

[0021] Figure 1 is a schematic diagram of a narrow and long foundation pit model according to an embodiment of the present invention;

[0022] Figure 2 is a schematic diagram of the stress distribution when a strip uniform load is applied in a semi-infinite body according to an embodiment of the present invention;

[0023] Figure 3 is a contour line diagram of the yield proximity drawn under the conventional load according to an embodiment of the present invention.

[0024] Figure 4 is a contour line diagram of the yield proximity drawn under the transition load according to an embodiment of the present invention.

[0025] Figure 5 is a contour line diagram of the yield proximity drawn under the ultimate load according to an embodiment of the present invention. Detailed Embodiments

[0026] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. According to the following description and claims, the advantages and features of the present invention will become clearer. The technical content and features of the present invention will be described in detail below with reference to the listed embodiments in conjunction with the accompanying drawings. It should be noted that the accompanying drawings are in a very simplified form and use non-precise scales, only for the purpose of facilitating and clearly assisting in explaining the embodiments of the present invention. For the convenience of description, the "upper" and "lower" directions mentioned below are consistent with the upper and lower directions of the accompanying drawings, but this should not be a limitation to the technical solution of the present invention.

[0027] Embodiment 1

[0028] This embodiment discloses a method for determining the position of the slip shear outlet of the bottom heave failure suitable for a narrow and long foundation pit. The method includes the following steps:

[0029] 1. Calculate the stress distribution of the narrow and long foundation pit under the action of vertical strip uniform load

[0030] Wang Hongxin (Stress calculation formula for vertical rectangular and strip uniform loads in a semi-infinite elastic body, 2016) derived an analytical expression for the stress distribution of a narrow and long foundation pit under the action of a vertical strip uniform load in a semi-infinite body through integration based on the Mindlin solution. This formula can consider the influence of the foundation pit width, foundation pit depth, and wall bottom depth.

[0031] The specific calculation formula for the additional stress component of the soil mass caused by foundation pit excavation unloading is

[0032]

[0033] In the formula: μ is the Poisson's ratio of the soil mass, is the internal friction angle of the soil mass, b is half of the foundation pit width, z is the wall bottom depth, H is the foundation pit excavation depth, p is the load caused by foundation pit excavation, p = γH, σ x ’, σ z ’ respectively represent the horizontal and vertical components of the additional stress of the soil mass, τ zx ’ represents the additional shear stress of the soil mass.

[0034] The specific calculation formula for the total stress (sum of self-weight stress and additional stress) component of the soil mass at the bottom of the pit is

[0035]

[0036] σ z = γz - 2σ’ z

[0037] τ zx = τ’ zx左 - τ’ zx右

[0038] In the formula: μ is the Poisson's ratio of the soil mass, γ is the unit weight of the soil mass, z is the depth of the wall bottom, and σ x , σ z respectively represent the total horizontal and vertical stresses of the soil mass at the bottom of the pit, and τ zx represents the total shear stress of the soil mass at the bottom of the pit.

[0039] 2. Calculate the principal stresses of the soil mass at any point below the bottom of the pit

[0040] According to the Mohr-Coulomb strength theory, the maximum principal stress and the minimum principal stress of the soil mass in the elastic state are respectively

[0041]

[0042] 3. Calculate the yield proximity of the soil mass at any point below the bottom of the pit

[0043] Cao Linwei (Static Stability Analysis of Tailings Dam Based on the Concept of Yield Proximity and Its Comparison with Strength Reduction Coefficient Method, 2010) introduced the yield proximity η to quantitatively evaluate the safety of the analysis object. For the stress state of the soil mass, the yield proximity η can be used to judge whether the soil stress is in the elastic state or the plastic state. The yield proximity η can be expressed as

[0044]

[0045] In the formula: σ equ , σ Y are respectively the equivalent stress of the soil skeleton and the yield stress under this stress state, σ1 and σ3 are respectively the maximum and minimum principal stresses of the soil skeleton (compression is positive), c, are respectively the cohesion and the internal friction angle of the soil mass. When η < 1, the soil mass is in the elastic state, and when η ≥ 1, the soil mass is in the plastic state.

[0046] 4. Draw the yield proximity contour map according to the yield proximity of each point at the bottom of the pit

[0047] Select points at different depths and distances at the bottom of the pit as characteristic points, and calculate the yield proximity of the soil mass under normal load (load ratio 1:1, Figure 3 ), transitional load (load ratio 1:1.25, Figure 4 ), and ultimate load (load ratio 1:1.353, Figure 5 ) respectively. Draw the yield proximity contour map according to the yield proximity of each point.

[0048] 5. Determine the position of the slip shear outlet according to the yield proximity contour map

[0049] From the contour maps of the yield proximity under normal load, transition load, and ultimate load, it can be seen that the only intersection point of the contour line with a yield proximity of 1 at the ultimate state and the bottom of the pit is the position of the slip shear outlet. Through calculation, it is determined that this point is the midpoint of the bottom of the pit.

[0050] Example 2

[0051] Adopt the calculation method for the anti-heave stability of the foundation pit as described in Example 1. Taking a narrow and long foundation pit in a sandy soil area as an example, the specific steps are as follows:

[0052] The depth of the foundation pit is 6m, the width of the foundation pit is 10m, and the soil layer parameters are: unit weight 18.5kN / m 3 , cohesion 8kPa, internal friction angle 19°, and the surcharge outside the pit is taken as 20kPa.

[0053] Now, taking the calculation of the yield proximity at a point 0.5m below the midpoint of the bottom of the foundation pit as an example, the calculation process is as follows

[0054] (1) Calculate the additional stress at the corner point

[0055]

[0056] (2) Calculate the total stress at the center point

[0057]

[0058] σ z =γz - 2σ' z =18.5×6.5 - 2×44.7=30.8

[0059] τ zx =τ’ zx左 - τ’ zx右 =0

[0060] (3) Calculate the maximum principal stress and the minimum principal stress

[0061]

[0062] (4) Calculate the yield proximity

[0063]

[0064] According to the above method, select points at different depths (0 - 4m, at intervals of 0.5m) and different distances (0 - 10m, at intervals of 0.5m) at the bottom of the pit as characteristic points, and calculate the yield proximity of each point in turn. Draw the contour map of the yield proximity based on the yield proximity of each point.

[0065] Gradually increase the load caused by the foundation pit excavation, so that the yield proximity gradually increases, and the soil at the bottom of the pit gradually changes from elastic to plastic. When the contour line where the yield proximity is equal to 1 intersects the bottom of the pit at a point, this point is the position of the slip shear outlet, and through calculation, it is determined that this point is the midpoint of the bottom of the pit.

[0066] The above description is only a description of the preferred embodiments of the present invention, and does not limit the scope of the present invention in any way. Any changes and modifications made by those of ordinary skill in the art of the present invention based on the above disclosure shall fall within the protection scope of the claims.

Claims

1. A method for determining the slip shear outlet position of a narrow and long foundation pit, characterized in that The method comprises the following steps: First, calculate the stress distribution of a narrow and long foundation pit under a vertical strip uniform load; Second, calculate the principal stress of the soil mass at any point below the bottom of the pit; Third, calculate the yield proximity of the soil mass at any point below the bottom of the pit; Fourth, draw an isogram of the yield proximity according to the yield proximity of each point of the soil mass at the bottom of the pit; Fifth, determine the position of the slip shear outlet according to the isogram of the yield proximity; The yield proximity is expressed as where: σ equ , σ Y are the equivalent stress of the soil skeleton and the yield stress under this stress state respectively, σ1 and σ3 are the maximum and minimum principal stresses of the soil skeleton respectively, with compression being positive, c, are the cohesion and internal friction angle of the soil respectively. When η < 1, the soil is in an elastic state, and when η ≥ 1, the soil is in a plastic state.

2. The method for determining the slip shear outlet position of a narrow and long foundation pit according to claim 1, characterized in that In the fifth step, the only intersection point of the isogram with a yield proximity equal to 1 and the bottom of the pit under the ultimate state is the position of the slip shear outlet.

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