A simplified calculation method for safety and stability of pile-supported structures

Abstract

The application provides a simplified calculation method for safety stability of a pile buttress structure, which comprises equivalent of a surrounding pile to an underground continuous wall and equivalent of each group of pile buttresses to a sheet pile; a group of pile buttresses is selected as a calculation object, a center of the group of pile buttresses is taken as a symmetric center, and a half of a buttress spacing on each side is selected to form a calculation unit, and a moment of inertia of the calculation unit is calculated; the calculation unit is equivalent to an underground continuous wall as a whole; displacement and internal force of the selected pile buttresses are calculated according to the equivalent underground continuous wall, so that the safety stability of the pile buttress structure is judged. The calculation method can perform segmented calculation on each group of pile buttresses, optimizes the number of rows of supporting piles and the number of supporting piles in each row in each group of pile buttresses while considering the safety stability, and can effectively reduce the engineering cost, save the construction time and improve the construction efficiency.

Description

Technical Field

[0001] This invention relates to the field of deep foundation pit engineering, and specifically to a simplified calculation method for the safety and stability of a pile-support structure. Background Technology

[0002] In deep foundation pit engineering, a reasonable support design is crucial for the safety of surrounding buildings, ground settlement control, and foundation pit deformation control. Currently, for deep foundation pit projects with strict deformation control requirements, internal support systems (such as steel or concrete supports) or double-row pile support structures are mainly used. The disadvantages of double-row pile support structures include a large construction space requirement; the disadvantages of internal support systems include a long construction period, occupation of foundation pit working space, the need to install column piles (which may pose a risk to the quality of the main structure), and certain safety risks during the replacement of internal supports. These problems increase the complexity of underground engineering implementation. In recent years, with the advancement of urbanization and the increasing demand for underground space development, foundation pit support faces higher technical requirements. Many scholars have begun to explore alternative support forms that do not require internal support, such as straight and inclined piles, inclined bracing, and pile stacks. For example, patent CN109723063A discloses a clustered pile stack support structure, which adds clustered pile stacks at regular intervals in the middle of the long side of a wide foundation pit, achieving both supportless operation and not requiring an increase in the cross-sectional size of the support piles. However, in this patent, the clustered piles are located outside the retaining piles (outside the foundation pit), as shown in the appendix of the patent. Figure 3 For foundation pits with limited space, this method has limited practicality. The patent also provides a calculation method based on a clustered pile support structure. This method calculates the stress on the clustered pile support structure by treating the front and rear rows of piles in each clustered pile structure as a single high-stiffness support pile with a zero-angle rotation at the pile top. Then, by considering the spatial effect of the capping beam at the pile top, it performs a collaborative stress analysis with the front row of cantilever support piles outside the clustered pile structure area. Based on the equilibrium and deformation coordination conditions of the capping beam, it establishes the relationship between shear force and displacement at the pile top of each support pile, and then uses the elastic resistance method to solve for the bending moment, shear force, and horizontal displacement of each pile. This calculation method is relatively complex and has a certain computational difficulty, requiring the assistance of software programming and other methods, making it difficult to promote. Summary of the Invention

[0003] This invention provides a simplified calculation method for the safety and stability of a pile-support structure. This method can perform segmented calculations for each pile stack, and while considering safety and stability, optimizes the number of rows of support piles and the number of support piles in each row of pile stacks, which can effectively reduce costs and construction time.

[0004] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0005] A simplified calculation method for the safety and stability of a pile-support structure is provided. The pile-support structure includes a row of retaining piles arranged along the edge of the foundation pit and multiple sets of pile stacks arranged parallel to the retaining piles at equal intervals within the foundation pit. The retaining piles are composed of several first support piles arranged at equal intervals, and the tops of the first support piles are connected as a whole by a capping beam. Each set of pile stacks consists of 1 to 3 rows of support piles, and each row of piles consists of 2 to 3 second support piles arranged at equal intervals. The tops of the retaining piles and the multiple sets of pile stacks are covered with cap plates, so that the retaining piles and the multiple sets of pile stacks are connected as a whole.

[0006] The simplified calculation method for the safety and stability of the pile-support structure includes the following steps:

[0007] (1) Based on the basic conditions of the foundation pit, determine the pile diameter d1 and pile spacing t1 of the first support pile, the pile diameter d2 and pile spacing t2 of the second support pile, the pile spacing x of two adjacent pile stacks, the center distance y between the retaining pile and the second support pile closest to the retaining pile in the pile stack, and the number of rows, quantity and row spacing c of the second support pile in each pile stack.

[0008] (2) According to the equivalent bending stiffness method, the pile spacing t1 of the first support pile is taken as the calculation length, and the retaining pile is equivalent to a diaphragm wall with a thickness of h1; the actual width of the pile stack is taken as the calculation length, and each pile stack is equivalent to a sheet pile with a thickness of h2. The center distance between the equivalent diaphragm wall and the sheet pile is taken as the center distance y between the retaining pile and the second support pile closest to the retaining pile in the pile stack.

[0009] (3) Select a set of piles as the calculation object, and select half of the pile spacing x on both sides of the center of the piles as the center of symmetry to form a calculation unit, and calculate the moment of inertia of the calculation unit.

[0010] (4) Then, according to the equivalent bending stiffness method, the calculation unit in step (3) is equivalent to a diaphragm wall with a thickness of H.

[0011] (5) Calculate the displacement and internal force of the piles selected in step (3) based on the equivalent underground continuous wall in step (4);

[0012] (6) Repeat steps (3) to (5) to calculate the displacement and internal force of other pile groups;

[0013] (7) Determine the safety of the pile support structure based on the calculated displacement and internal force of the pile.

[0014] The diameter d2 of the second support pile is not less than the diameter d1 of the first support pile.

[0015] When each pile group consists of three rows of piles, the row spacing c between adjacent rows of piles in each pile group is equal.

[0016] The center distance y between the retaining pile and the second support pile closest to the retaining pile in the pile stack is 1-2 times the pile diameter d2 of the second support pile.

[0017] The spacing x between two adjacent pile groups is 6-12 times the diameter d2 of the second support pile.

[0018] The spacing c between two adjacent rows of piles in the pile stack is 1-2 times the diameter d2 of the second support pile.

[0019] The thickness of the cover plate is not less than the pile diameter d2 of the second support pile.

[0020] The number of pile rows in the middle pile stack of the foundation pit support structure shall not be less than the number of pile rows in the pile stacks on both sides of the foundation pit support structure; the number of support piles in each row of the pile stack in the middle pile stack of the foundation pit support structure shall not be less than the number of support piles in each row of the pile stacks on both sides of the foundation pit support structure.

[0021] In step (2) of the simplified calculation method for the safety and stability of the pile support structure, the following assumptions are made during the calculation process: a) it is assumed that the elastic modulus of the first support pile and the equivalent underground continuous wall are equal; b) it is assumed that the elastic modulus of the second support pile and the equivalent sheet pile are equal.

[0022] In step (2) of the simplified calculation method for safety and stability based on pile stack support structure: when each row of piles in the pile stack consists of two second support piles, the actual width of the pile stack l = d2 + t2 is equivalent to sheet piles; when each row of piles consists of three second support piles, the actual width of the pile stack l = d2 + 2t2 is equivalent to sheet piles.

[0023] Compared with the prior art, the beneficial effects of the present invention are:

[0024] 1. The calculation method provided by this invention can perform segmented calculations for each pile stack. While considering safety and stability, it optimizes the number of rows of support piles and the number of support piles in each row of pile stacks, which can effectively reduce costs and construction time. Under the premise of the same deformation conditions, it can optimize the pile spacing and pile diameter, thereby achieving a balance between safety and economy.

[0025] 2. The arrangement of pile stacks can be flexibly considered in this invention. The number of pile rows or the number of support piles per row in the middle of the foundation pit support structure is set to be large. That is, the rigidity of the pile stacks is appropriately strengthened in the middle of the foundation pit support structure with large deformation to ensure the safety and stability of the middle of the foundation pit support structure.

[0026] 3. The pile stack support structure provided by the present invention can be used to replace the pile bracing support structure composed of one internal support + support pile or the double row pile support structure in the foundation pit support, and the pile stack replaces the internal support node to achieve the purpose of controlling deformation.

[0027] 4. The equivalent thickness of the underground continuous wall is obtained by analytical method in this invention, which is relatively simple to calculate; and this calculation method can be combined with existing foundation pit calculation software, which is convenient to use. Attached Figure Description

[0028] Figure 1 This is a plan view of the pile support structure provided by the present invention;

[0029] Figure 2 The plan layout of the pile support structure provided by the present invention after step (1) is equivalent;

[0030] Figure 3 This is a plan view of the actual layout of the pile support structure in the foundation pit in the application example;

[0031] Figure 4 This is a schematic diagram showing various arrangement shapes of piles in the pile support structure in the application example;

[0032] Figure 5 The calculated displacement diagram of the pile support structure after the application example is shown.

[0033] Figure 6 The calculation bending moment envelope diagram of the pile support structure after the application example is shown.

[0034] Figure 7 The calculated earth pressure curve of the pile-support structure after the application example is shown.

[0035] Figure 8 The calculation shear force envelope diagram of the pile support structure after the application example is shown.

[0036] In the diagram: 1-First support pile, 2-Second support pile, 3-Cover plate. Detailed Implementation

[0037] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0038] In this invention, the pile spacing refers to the center-to-center distance between two adjacent support piles in the same row, the stack spacing refers to the center-to-center distance between two adjacent sets of pile stacks, and the row spacing refers to the center-to-center distance between two adjacent rows of support piles within a pile stack. The pile stack support structure in this invention includes a row of retaining piles arranged along the edge of the foundation pit and multiple sets of pile stacks located within the foundation pit and arranged at equal intervals parallel to the retaining piles. The retaining piles consist of several first support piles 1 arranged at equal intervals, and the tops of the first support piles are connected as a whole by a capping beam. Each pile stack consists of 1 to 3 rows of piles, and each row of piles consists of 2 to 3 second support piles 2 arranged at equal intervals. A cover plate 3 is poured onto the tops of the retaining piles and the multiple pile stacks, connecting the retaining piles and the multiple pile stacks into a single unit. Figure 1 As shown.

[0039] Furthermore, the diameter d2 of the second support pile is not less than the diameter d1 of the first support pile; preferably, the diameter d2 of the second support pile is the same as the diameter d1 of the first support pile.

[0040] Furthermore, when each pile group consists of three rows of piles, the row spacing c between adjacent rows of piles in each pile group is equal; preferably, each row of piles consists of three second support piles.

[0041] Furthermore, the center distance y between the retaining pile and the second support pile closest to the retaining pile in the pile stack is 1-2 times the pile diameter d2 of the second support pile; preferably, the center distance y between the retaining pile and the second support pile closest to the retaining pile in the pile stack is 2 times the pile diameter d2 of the second support pile.

[0042] Furthermore, the pile spacing x between two adjacent pile groups is 6-12 times the pile diameter d2 of the second support pile; preferably, the pile spacing x between two adjacent pile groups is 6 times the pile diameter d2 of the second support pile.

[0043] Furthermore, the row spacing c between two adjacent rows of piles in the pile stack is 1-2 times the pile diameter d2 of the second support pile; preferably, the row spacing c between two adjacent rows of piles in the pile stack is 2 times the pile diameter d2 of the second support pile.

[0044] Furthermore, the thickness of the cover plate shall not be less than the pile diameter d2 of the second support pile.

[0045] Furthermore, the number of pile rows in the middle of the foundation pit support structure should not be less than the number of pile rows in the pile rows on both sides of the foundation pit support structure; the number of support piles in each row of the pile row in the middle of the foundation pit support structure should not be less than the number of support piles in each row of the pile rows on both sides of the foundation pit support structure; that is, in the middle of the foundation pit support structure with large displacement, the number of pile rows or the number of piles in each row can be appropriately increased to strengthen the rigidity of the pile row, such as... Figure 4 As shown.

[0046] The simplified calculation method for the safety and stability of the pile-support structure includes the following steps:

[0047] (1) Based on the basic conditions of the foundation pit (foundation method and layout), determine the pile diameter d1 and pile spacing t1 of the first support pile, the pile diameter d2 and pile spacing t2 of the second support pile, the pile spacing x of two adjacent pile stacks, the center distance y between the retaining pile and the second support pile closest to the retaining pile in the pile stack, and the number of rows, quantity and row spacing c of the second support pile in each pile stack.

[0048] (2) Based on the equivalent bending stiffness method, the pile spacing t1 of the first retaining pile is taken as the calculation length, and the retaining pile is equivalent to a diaphragm wall with a thickness h1, such as... Figure 1 and Figure 2 As shown, the calculation formula is:

[0049]

[0050] In the formula, E1 and E1′ are the elastic moduli of the first support pile and the equivalent diaphragm wall, respectively; d1 is the pile diameter of the first support pile; b1 is the calculated length, which is taken here as the pile spacing t1 of the first support pile, i.e., b1=t1;

[0051] In the calculation process, it is assumed that the elastic modulus of the first support pile and the equivalent diaphragm wall are equal, i.e., E1=E1′. Since d1 and t1 are known, h1 can be calculated.

[0052] Taking the actual width of the pile stack as the calculated length, each pile stack is equivalent to a sheet pile with a thickness of h2; when the pile stack is set with a row of piles, the calculation formula is:

[0053]

[0054] In the formula, E2 and E2′ are the elastic moduli of the second support pile and the equivalent sheet pile, respectively; d2 is the pile diameter of the second support pile; n is the number of second support piles in the pile stack; b2 is the calculated length, which is taken as the actual width l of the pile stack.

[0055] When the pile pier has two rows of piles, the calculation formula is as follows:

[0056]

[0057] In the formula, c is the row spacing between the two rows of support piles within the pile stack; n is the number of the second support piles within the pile stack.

[0058] When the pile pier is equipped with three rows of piles, the calculation formula is as follows:

[0059]

[0060] In the formula, n1 is the number of the second row of support piles in the three rows of piles; n2 is the number of the second support piles in the other two rows;

[0061] Specifically, when a pile stack is set with one row of piles, and each row of piles consists of two second support piles, it is equivalent to sheet piles according to the actual width of the pile stack l = d2 + t2; when each row of piles consists of three second support piles, it is equivalent to sheet piles according to the actual width of the pile stack l = d2 + 2t2; there are a maximum of three rows of piles in the pile stack, and each row has a maximum of three second support piles.

[0062] In this embodiment, the pile stack consists of a row of two second support piles. Therefore, n is 2; b2 is the sum of the pile spacing t2 of the second support pile and the pile diameter d2 of the second support pile, i.e., b2 = l = t2 + d2.

[0063] In the calculation process, it is assumed that the elastic modulus of the second support pile and the equivalent sheet pile are equal, that is, E2=E2′. Since d2, t2 and n are known, h2 can be calculated.

[0064] The center-to-center distance between the equivalent diaphragm wall and the sheet pile is taken as the center-to-center distance y between the retaining pile and the second support pile closest to the retaining pile in the pile stack.

[0065] (3) Select a set of pile stacks as the calculation object, and take the center of the set of pile stacks as the center of symmetry, and select half of the pile spacing x on both sides to form a calculation unit, see Figure 2 The moment of inertia I of this calculation unit is calculated using the following formula:

[0066] I = I1 + I2;

[0067]

[0068] A1 = xh1;

[0069] A2 = lh2;

[0070]

[0071] In the formula, I1 and I2 are the moments of inertia of the equivalent diaphragm wall and the equivalent sheet pile about the centroid of the calculation unit, respectively; x and l are the lengths of the equivalent diaphragm wall and sheet pile in the calculation unit, respectively; h1 and h2 are the thicknesses of the equivalent diaphragm wall and sheet pile, respectively; A1 and A2 are the cross-sectional areas of the equivalent diaphragm wall and sheet pile in the calculation unit, respectively; y1 and y2 are the distances between the centers of the equivalent diaphragm wall and sheet pile and the centroid of the calculation unit, respectively; and y is the center-to-center distance between the equivalent diaphragm wall and sheet pile.

[0072] Since x, l, and y are known, and h1 and h2 are calculated in step (2), the moment of inertia I of the calculation unit can be calculated.

[0073] (4) Then, according to the equivalent bending stiffness method, the calculation unit in step (3) is equivalent to a diaphragm wall of thickness H; the calculation formula is:

[0074]

[0075] Right now

[0076] Since x is known and I is calculated in step (3), the thickness H of the underground continuous wall after the overall calculation unit is equivalent can be calculated.

[0077] (5) Select the displacement and internal force of the pile in step (3) based on the equivalent underground continuous wall calculation in step (4); specifically, the displacement and internal force of the pile are calculated using Tianhan Foundation Pit Software.

[0078] (6) Repeat steps (3) to (5) to calculate the displacement and internal force of other pile groups.

[0079] (7) Determine the safety and stability of the pile support structure based on the calculated displacement and internal force of the piles.

[0080] Specifically, according to JGJ120-2012 "Technical Specification for Foundation Pit Support" and DB42 / T 159-2024 "Technical Specification for Foundation Pit Engineering", in the design of foundation pit support, the safety level and environmental protection level of the foundation pit support structure must be determined according to the specifications. The specifications clearly stipulate the horizontal deformation control range value of the support structure corresponding to each level. The safety feasibility of the support structure is verified by calculating the displacement and internal force of the pile stack. If it is not feasible, the number and quantity of support piles, the pile diameter, pile spacing, stack spacing, and the center distance between the retaining piles and the support piles closest to the retaining piles in the pile stack are adjusted to optimize the support structure while ensuring safety.

[0081] Application examples

[0082] Taking one side of a foundation pit support project as an example, the project overview is as follows: the edge of the foundation is approximately 2.5m from the edge of the internal road, and the excavation depth is 6.0m. According to DB42 / T 159-2024 "Technical Specification for Foundation Pit Engineering", based on the excavation depth, surrounding environment, engineering geological and hydrogeological conditions, the safety level of this foundation pit support structure is determined to be Level II, and the environmental protection level of the foundation pit is Level I. A uniformly distributed load of 25kPa is set at 2.0m from the top opening line of the foundation pit. The physical and mechanical parameters of the soil layer are shown in the table below:

[0083]

[0084] In this application example, the total length of the support section is approximately 49.31m, the width of the pile cap is approximately 5.3m, and the spacing between the pile caps is between 8 and 8.6m. The edge of the foundation pit enclosed by the bored piles is approximately 0.4m from the pile cap and approximately 3.4m from the outer wall of the basement, and there is sufficient space inside the pit.

[0085] According to the calculation method of the present invention, the diameter of the first and second support piles in the pile stack support structure is first determined to be 0.8m, the pile spacing is 1.2m, and the pile length is 16m. The pile spacing x is considered to be 10.5d², and a total of 5 sets of pile stacks are set. Each set of pile stacks consists of a row of two second support piles. The second support piles in the pile stacks are all coaxial with the first support piles in the retaining piles. The center distance y between the retaining piles and the second support piles in the pile stacks closest to the retaining piles is considered to be 2d². The plan layout of the pile stack support structure is as follows. Figure 3As shown. Based on the equivalent bending stiffness method, the retaining piles are equivalent to a diaphragm wall of thickness h1, and each pile stack is equivalent to a sheet pile of thickness h2. The calculated values ​​are h1≈0.586m and h2≈0.622m. Then, a pile stack is selected as the calculation object. Taking the center of this pile stack as the center of symmetry, half the pile spacing x is selected on both sides to form a calculation unit. The moment of inertia of this calculation unit is calculated to be I≈2.723m. 4 Then, according to the equivalent bending stiffness method, the aforementioned calculation unit is equivalent to a diaphragm wall with a thickness of H, and the calculated value is H≈1.572m. Since the number of rows and piles in each pile group is the same in this application example, the calculation unit of each pile group is equivalent to a diaphragm wall with a thickness of approximately 1.572m.

[0086] The pile-supported structure of the diaphragm wall, which is equivalent to a diaphragm wall with a thickness of approximately 1.572m in this application, was calculated using Tianhan Foundation Pit Software. The internal forces and displacements of the diaphragm wall were obtained, and the results are as follows: Figures 5-8 As shown. The results show that the maximum displacement of the diaphragm wall is 38.8 mm, occurring at the pile top, which meets the specification requirement of no more than 50 mm; the maximum positive bending moment is 968 kN·m, occurring 10.5 m below ground level, and the maximum negative bending moment is -1 kN·m; the maximum positive shear force is 216 kN, occurring 7.1 m below ground level, and the maximum negative shear force is -282 kN, occurring 14 m below ground level; the minimum passive zone elastic resistance safety factor is 1.75. If it is necessary to strengthen the stiffness of the local support structure, it can be done according to... Figure 4 Indicates adjustment.

Claims

1. A simplified calculation method for the safety and stability of a pile-supported structure, characterized in that: The pile support structure includes a row of retaining piles arranged along the edge of the foundation pit and multiple sets of pile stacks arranged parallel to the retaining piles at equal intervals within the foundation pit. The retaining piles are composed of several first support piles arranged at equal intervals, and the tops of the first support piles are connected as one unit by a capping beam. Each set of pile stacks consists of 1 to 3 rows of piles, and each row of piles consists of 2 to 3 second support piles arranged at equal intervals. The tops of the retaining piles and the multiple sets of pile stacks are covered with cap plates, so that the retaining piles and the multiple sets of pile stacks are connected as a whole. The simplified calculation method for the safety and stability of the pile-support structure includes the following steps: (1) Based on the basic conditions of the foundation pit, determine the pile diameter d1 and pile spacing t1 of the first support pile, the pile diameter d2 and pile spacing t2 of the second support pile, the pile spacing x of two adjacent pile stacks, the center distance y between the retaining pile and the second support pile closest to the retaining pile in the pile stack, and the number of rows, quantity and row spacing c of the second support pile in each pile stack. (2) According to the equivalent bending stiffness method, the pile spacing t1 of the first support pile is taken as the calculation length, and the retaining pile is equivalent to a diaphragm wall with a thickness of h1; the actual width of the pile stack is taken as the calculation length, and each pile stack is equivalent to a sheet pile with a thickness of h2. The center distance between the equivalent diaphragm wall and the sheet pile is taken as the center distance y between the retaining pile and the second support pile closest to the retaining pile in the pile stack. The following assumptions must be made during the calculation: a) The elastic modulus of the first support pile and the equivalent diaphragm wall are equal; b) The elastic modulus of the second support pile and the equivalent sheet pile are equal. (3) Select a set of piles as the calculation object, and select half of the pile spacing x on both sides of the center of the piles as the center of symmetry to form a calculation unit, and calculate the moment of inertia of the calculation unit; (4) Then, according to the equivalent bending stiffness method, the calculation unit in step (3) is equivalent to a diaphragm wall with a thickness of H. (5) Based on the equivalent underground continuous wall calculation in step (4), select the displacement and internal force of the pile in step (3); (6) Repeat steps (3) to (5) to calculate the displacement and internal forces of the other pile groups; (7) Determine the safety of the pile support structure based on the calculated pile displacement and internal force.

2. The simplified calculation method for safety and stability based on pile-supported structures according to claim 1, characterized in that: The diameter d2 of the second support pile is not less than the diameter d1 of the first support pile.

3. The simplified calculation method for safety and stability based on pile-supported structures according to claim 1, characterized in that: When each pile group consists of three rows of piles, the row spacing c between adjacent rows of piles in each pile group is equal.

4. The simplified calculation method for safety and stability based on pile-supported structures according to claim 1, characterized in that: The center distance y between the retaining pile and the second support pile closest to the retaining pile in the pile stack is 1-2 times the pile diameter d2 of the second support pile.

5. The simplified calculation method for safety and stability based on pile-supported structures according to claim 1, characterized in that: The spacing x between two adjacent pile groups is 6-12 times the diameter d2 of the second support pile.

6. The simplified calculation method for safety and stability based on pile-supported structures according to claim 1, characterized in that: The spacing c between two adjacent rows of piles in the pile stack is 1-2 times the diameter d2 of the second support pile.

7. The simplified calculation method for the safety and stability of a pile-supported structure according to claim 1, characterized in that: The thickness of the cover plate is not less than the pile diameter d2 of the second support pile.

8. The simplified calculation method for safety and stability based on pile-supported structures according to claim 1, characterized in that: The number of pile rows in the middle pile stack of the foundation pit support structure shall not be less than the number of pile rows in the pile stacks on both sides of the foundation pit support structure; the number of support piles in each row of the pile stack in the middle pile stack of the foundation pit support structure shall not be less than the number of support piles in each row of the pile stacks on both sides of the foundation pit support structure.

9. The simplified calculation method for safety and stability based on pile-supported structures according to claim 1, characterized in that: In step (2) of the simplified calculation method for safety and stability based on pile stack support structure: when each row of piles in the pile stack consists of two second support piles, the actual width of the pile stack l=d2+t2 is equivalent to sheet piles; when each row of piles consists of three second support piles, the actual width of the pile stack l=d2+2t2 is equivalent to sheet piles.

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