A method for calculating the embedding depth of a deep-water open-bottom rock-embedded steel sheet pile cofferdam

Abstract

This invention relates to the field of methods for calculating the embedment depth of cofferdams, specifically a method for calculating the embedment depth of a deep-water, bottomless, rock-embedded steel sheet pile cofferdam, which includes the following steps: S1, Assumptions: critical failure state of the kicker, equivalent depth h of hard rock stress at the trench opening. e =1m, and the stress is uniformly distributed along the vertical equivalent depth; the influence of seepage on water pressure is not considered; the interaction between piles, backfill soil, and hard rock is not considered; define each symbol and its corresponding meaning; S2, establish the critical state equilibrium equation; S3, substitute into the calculation, divided into two cases: the embedment depth is greater than the equivalent depth of hard rock stress at the trench opening and the embedment depth is not greater than the equivalent depth of hard rock stress at the trench opening; S4, combine the two cases in S3 to obtain the calculation formula for the range of embedment depth. This invention can quickly provide a theoretically supported embedment depth range, which is consistent with the actual empirical value in engineering and the results of three-dimensional finite element simulation.

Description

Technical Field

[0001] This invention relates to the field of methods for calculating the embedment depth of cofferdams, specifically a method for calculating the embedment depth of deep-water, bottomless, rock-embedded steel sheet pile cofferdams. Background Technology

[0002] Bottomless, rock-embedded sheet pile cofferdams can be used for low-pile cap construction in deep-water bridge sites with hard rock foundations, providing a dry working environment for cap construction. For example, this cofferdam construction method was used in the Second Songhua River Bridge and the SZH-5 Dongjiang North Mainstream Bridge of the Guangdong-Shenzhen-Guangzhou Intercity Railway. The process involves first mechanically excavating trenches in the hard rock foundation, followed by backfilling with clay. This allows for the use of conventional piling equipment to drive sheet piles, while simultaneously grouting the backfill. To ensure the sealing of the cofferdam bottom and the stability of the borehole opening, engineering experience typically dictates increasing the length of the sheet piles embedded in the rock strata, i.e., increasing the sheet pile embedment depth. Insufficient embedment depth may lead to "kick-out failure" of the borehole opening, further causing leakage and instability in the foundation pit. However, excessive embedment depth increases construction difficulty and cost. There are currently no relevant standards or studies on how to determine the embedment depth of unsealed rock-socketed steel sheet piles. It is usually determined based on engineering experience, which lacks theoretical support and has poor reliability. Summary of the Invention

[0003] The purpose of this invention is to address the problem in the prior art that the embedment depth of unsealed rock-embedded steel sheet piles cannot be calculated, and to propose a method for calculating the embedment depth of deep-water unsealed rock-embedded steel sheet pile cofferdams.

[0004] The technical solution of this invention: A method for calculating the embedment depth of deep-water, bottomless, rock-embedded steel sheet pile cofferdams, comprising the following steps:

[0005] S1. Assumptions: Critical failure state of the kicker, equivalent depth of hard rock stress at the groove opening, h. e =1m, and the stress is uniformly distributed along the vertical equivalent depth; the effect of seepage on water pressure is not considered; the interaction between piles, backfill soil, and hard rock is not considered; define each symbol and its corresponding meaning: h q The embedment depth is the distance from the bottom of the sheet pile to the surface of the excavation pit; h z h is the height of the bottom support, i.e., the distance from the bottom support to the surface of the foundation pit. w The water depth is the distance from the water level to the surface of the pit; h e F1 represents the equivalent depth of hard rock stress at the trench opening; F1 represents the equivalent resultant force of the trapezoidal distributed water load. F2 is the equivalent resultant force of the triangularly distributed water load. h1 is the distance from the top surface of the trapezoid to the equivalent resultant force F1. h2 is the distance from the surface of the foundation pit to the equivalent resultant force F2. σ e For the equivalent stress in hard rock, the bearing capacity σ of hard rock can be taken as the critical equilibrium state. c γ is the specific gravity of water;

[0006] S2. Establish the critical state equilibrium equation. Taking the sheet pile as the object of study, to ensure its stability, take the moment about the support point o. Then we have: the moment generated by the ultimate stress of the rock mass ≥ the moment of the water pressure, that is:

[0007] S3. Substitute into the calculation. If the embedment depth is greater than the equivalent depth of hard rock stress at the groove opening, i.e., h q >h e =1m, then take h e =1m, Substituting into the equilibrium equation: σ c ·(h z +0.5)≥F1·h1+F2·(h2+h z The calculation yields:

[0008] If the embedment depth is not greater than the equivalent depth of hard rock stress at the groove opening, i.e., h q <h e =1m, then take h e =h q Substituting into the equilibrium equation: That is: (3σ) c -γh w )h q 2 +(6·σ c ·h z -3·γ·h w ·h z )·h q -γ·h z 2 ·(3·h w -h z For deep-water hard rock conditions, a ≥ 0, typically: a = 3σ c -γh w >0, axis of symmetry:

[0009] Discriminant: Δ=(6·σ c ·h z -3·γ·h w ·h z ) 2 +4·(3σ c -γh w )·γ·h z 2 ·(3·h w -hz Since ) > 0, the curve of the inequality opens upwards, and the embedment depth can only be a positive value. The solution to the inequality is:

[0010] S4. Determine the embedding depth range. Combining the two cases in S3, the comprehensive range of embedding depth is as follows:

[0011]

[0012] Compared with the prior art, the present invention has the following beneficial technical effects: it can quickly provide a theoretically supported range of embedment depth, which is consistent with the actual engineering experience value and the three-dimensional finite element simulation results, thus improving the reliability of embedment depth judgment. Attached Figure Description

[0013] Figure 1 A simplified force diagram for steel sheet piles;

[0014] Figure 2 This is a graph of the inequalities in S3. Detailed Implementation

[0015] Example 1

[0016] like Figure 1-2 As shown, the present invention proposes a method for calculating the embedment depth of deep-water, bottomless, rock-embedded steel sheet pile cofferdams, comprising the following steps:

[0017] S1. Assumptions: Critical failure state of the kicker, equivalent depth of hard rock stress at the groove opening, h. e =1m, and the stress is uniformly distributed along the vertical equivalent depth; the effect of seepage on water pressure is not considered; the interaction between piles, backfill soil, and hard rock is not considered; define each symbol and its corresponding meaning: h q The embedment depth is the distance from the bottom of the sheet pile to the surface of the excavation pit; h z h is the height of the bottom support, i.e., the distance from the bottom support to the surface of the foundation pit. w The water depth is the distance from the water level to the surface of the pit; h e F1 represents the equivalent depth of hard rock stress at the trench opening; F1 represents the equivalent resultant force of the trapezoidal distributed water load. F2 is the equivalent resultant force of the triangularly distributed water load. h1 is the distance from the top surface of the trapezoid to the equivalent resultant force F1. h2 is the distance from the surface of the foundation pit to the equivalent resultant force F2. σ e For the equivalent stress in hard rock, the bearing capacity σ of hard rock can be taken as the critical equilibrium state. c γ is the specific gravity of water;

[0018] S2. Establish the critical state equilibrium equation. Taking the sheet pile as the object of study, to ensure its stability, take the moment about the support point o. Then we have: the moment generated by the ultimate stress of the rock mass ≥ the moment of the water pressure, that is:

[0019] S3. Substitute into the calculation. If the embedment depth is greater than the equivalent depth of hard rock stress at the groove opening, i.e., h q >h e =1m, then take h e =1m, Substituting into the equilibrium equation: σ c ·(h z +0.5)≥F1·h1+F2·(h2+h z The calculation yields:

[0020] If the embedment depth is not greater than the equivalent depth of hard rock stress at the groove opening, i.e., h q <h e =1m, then take h e =h q Substituting into the equilibrium equation: That is: (3σ) c -γh w )h q 2 +(6·σ c ·h z -3·γ·h w ·h z )·h q -γ·h z 2 ·(3·h w -h z For deep-water hard rock conditions, a ≥ 0, typically: a = 3σ c -γh w >0, axis of symmetry:

[0021] Discriminant: Δ=(6·σ c ·h z -3·γ·h w ·h z ) 2 +4·(3σ c -γh w )·γ·h z 2 ·(3·h w -h z Since ) > 0, the curve of the inequality opens upwards, and the embedment depth can only be a positive value. The solution to the inequality is:

[0022] S4. Determine the embedding depth range. Combining the two cases in S3, the comprehensive range of embedding depth is as follows:

[0023]

[0024] This embodiment can quickly provide a theoretically supported range of embedment depth, which is consistent with actual engineering experience values ​​and three-dimensional finite element simulation results, thus improving the reliability of embedment depth determination.

[0025] Example 2

[0026] This invention proposes a method for calculating the embedment depth of deep-water, bottomless, rock-embedded steel sheet pile cofferdams. Taking a specific practical engineering project as an example, h w =16m,h z =3.5m, σ c =400 kPa, γ = 9.8 × 10 3 N / m 3 Substitute h q In the expression:

[0027]

[0028] Direct calculation yields: 0.71m≤h q With a value of ≤2.15m, the embedment depth range can be quickly determined, and it has a theoretical basis. It complements the determination method based on engineering experience, thereby improving the reliability of the embedment depth value judgment.

[0029] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.

Claims

1. A method for calculating the embedment depth of a deep-water, bottomless, rock-embedded steel sheet pile cofferdam, characterized in that, Includes the following steps: S1. Assumptions: Critical failure state of the kicker, equivalent depth of hard rock stress at the groove opening. Furthermore, the stress is uniformly distributed along the vertical equivalent depth; the effect of seepage on water pressure is not considered; the interaction between the pile, backfill, and hard rock is not considered; the symbols and their corresponding meanings are defined as follows: The embedment depth is the distance between the bottom of the sheet pile and the surface of the pit. This refers to the height of the bottom support, which is the distance between the bottom support and the surface of the foundation pit. This refers to the water depth, which is the distance between the water level and the surface of the pit. The equivalent depth of hard rock stress at the groove opening; The equivalent resultant force of the trapezoidal water load distribution is... ; The equivalent resultant force of the triangularly distributed water load is... ; For equivalent resultant force Distance from the top surface of the trapezoid ; For equivalent resultant force Distance from the surface of the excavation pit, ; For the equivalent stress of hard rock, the bearing capacity of hard rock is taken at the critical equilibrium state. ; The specific gravity of water; S2. Establish the critical state equilibrium equation. Taking the sheet pile as the object of study, to ensure its stability, take the moment about the support point o. Then we have: the moment generated by the ultimate stress of the rock mass ≥ the moment of the water pressure, that is: ; S3. Substituting into the calculation, if the embedment depth is greater than the equivalent depth of hard rock stress at the groove opening, that is... Then take Substituting into the equilibrium equation: The calculation yields: If the embedment depth is not greater than the equivalent depth of hard rock stress at the groove opening, i.e. Then take Substituting into the equilibrium equation: ,Right now: , For deep-water hard rock conditions, we have: Axis of symmetry: , Discriminant: Therefore, the curve of the inequality opens upwards, and the embedment depth can only be a positive value. The solution to the inequality is: ; S4. Determine the embedding depth range. Combining the two cases in S3, the comprehensive range of embedding depth is as follows: 。

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