Optimization design method for net thrust and spacing of double-row anti-slide piles

Abstract

The present application relates to the double-row anti-slide pile net thrust and row spacing optimization design method. The double-row anti-slide pile design net thrust calculation lacks key design elements in the design stage. The method obtains the rear side thrust of the rear row pile and the front side resistance of the front row pile; the soil between the pile rows is assumed to be several pile row blocks, and the residual sliding force of the pile row blocks is calculated; the function of the front side resistance of the rear row pile with respect to the rear side thrust of the front row pile is obtained; the design principle is that the net thrust borne by the rear row pile is equal to the net thrust borne by the front row pile, and the front side resistance of the rear row pile and the rear side thrust of the front row pile are calculated; the thrust bearing ratio of the rear row pile and the front row pile is calculated, and the row spacing is determined and adjusted according to the principle that the sum of the two is minimum. Based on the double-row pile anti-slide mechanism, the present application proposes the optimization design principle that the rear and front row piles should bear the same net thrust and the sum of the thrust bearing ratio of the rear and front row piles should be minimum, and solves the reasonable value problem of the design stage anti-slide pile net thrust and row spacing.

Description

Technical Field

[0001] This invention relates to the field of landslide control technology in geotechnical engineering, specifically to a method for optimizing the net thrust and spacing of double-row anti-slide piles. Background Technology

[0002] Double-row anti-slide piles are increasingly being used in large-scale landslide control projects, such as... Figure 1 As shown, the basic reinforcement mechanism is as follows: the sliding mass at the rear edge, exhibiting a downward trend, transfers thrust to the rear piles through the soil arching effect. The piles themselves transfer part of the thrust to the stable strata at the bottom, while the remaining thrust is transferred to the soil between the rows of piles through the squeezing action between the rear piles and the front sliding mass, and then to the rear side of the front piles. Therefore, the thrust behind the front piles includes part of the thrust from the rear sliding mass and all the thrust from the soil between the rows. Similar to the rear piles, the front piles themselves bear part of the thrust, while the remaining thrust is balanced by the resistance of the soil at the front edge of the landslide through squeezing the soil.

[0003] The above analysis shows that both the rear and front rows of piles transfer part of the thrust to the front sliding body through their own deformation, while actually only bearing part of the thrust transmitted from the rear sliding body. Similar to single-row piles, the thrust borne by each row of piles is referred to as the net thrust of the rear and front rows of piles. Currently, there is limited research on the net thrust of the rear and front rows of piles. Xiao Shiguo et al. proposed an algorithm for the net thrust of the rear and front rows of piles based on the foundation coefficient "k" method and the transfer coefficient method. This method helps to deepen the understanding of the stress on double-row piles. However, the implementation of this method requires knowledge of key design elements such as pile location, pile stiffness, cross-sectional dimensions, pile spacing, and embedment depth. Furthermore, the mode that the lateral resistance coefficient of the sliding body remains constant along the depth also needs optimization. Undoubtedly, these key elements are undetermined during the design phase. However, determining the net thrust of the rear and front rows of piles on the landslide slope is a crucial aspect of the design of this type of structure. Therefore, an optimization design method is needed to calculate the net thrust of the double-row anti-slide piles when the key design elements are unknown during the design phase. Summary of the Invention

[0004] The purpose of this invention is to provide a method for optimizing the net thrust and spacing of double-row anti-slide piles, so as to solve the design calculation problem of double-row anti-slide piles when key design elements are lacking in the design stage.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for optimizing the net thrust and row spacing of double-row anti-slide piles, the method comprising:

[0007] Obtain the rear thrust of the rear piles and the front resistance of the front piles;

[0008] Assume the soil between the rear and front pile rows is a number of inter-pile strips, and calculate the remaining sliding force of the inter-pile strips;

[0009] Based on the remaining sliding force of the strip between the frontmost pile rows, the function of the thrust on the rear side of the front piles with respect to the resistance on the front side of the rear piles is obtained.

[0010] The design principle is that the net landslide thrust borne by the rear piles is equal to that borne by the front piles. The front resistance of the rear piles and the rear thrust of the front piles are calculated based on the rear thrust of the rear piles and the front resistance of the front piles.

[0011] Calculate the thrust bearing ratio of the rear row of piles and the front row of piles, and determine the row spacing based on the principle of minimizing the sum of the two, and make design adjustments accordingly.

[0012] Furthermore, obtaining the rear thrust of the rear piles and the front resistance of the front piles includes:

[0013] Calculation of the rear thrust T of the rear pile using the transfer coefficient method b ;

[0014] Based on the assumption that the landslide thrust at the leading edge of the landslide body is zero, the resistance N at the front side of the front row of piles is calculated using the transfer coefficient method. f .

[0015] Furthermore, the soil between the rear and front rows of piles is assumed to be several inter-row blocks, and the residual sliding force of the inter-row blocks is calculated, including:

[0016] Assume that the soil between the pile rows and the pile front row consists of n pile rows, numbered sequentially from back to front as 1, 2...i...n;

[0017] The pile block numbered 1 is the last pile block. The formula for calculating the remaining sliding force E1 of the last pile block is:

[0018]

[0019] in:

[0020] W1 is the self-weight of the first row of piles;

[0021] θ1 is the inclination angle of the sliding surface of the first row of piles;

[0022] The internal friction angle of the first pile row interspersed blocks;

[0023] l1 is the sliding surface length of the strip block between the first pile row;

[0024] c1 is the sliding surface cohesion of the strips between the first pile row;

[0025] F s To design a safety factor;

[0026] N b For the front side resistance of the rear piles;

[0027] Calculate the residual sliding force transmission coefficient ψ between adjacent pile groups. i :

[0028]

[0029] in:

[0030] ψ i The residual sliding force transmission coefficient between the (i-1)th pile row inter-segment block and the ith pile row inter-segment block;

[0031] θ i Let be the sliding surface inclination angle of the strip block between the i-th pile row;

[0032] θ i-1 Let be the sliding surface inclination angle of the strip between the (i-1)th pile row;

[0033] Let be the internal friction angle between the blocks of the i-th pile row;

[0034] Based on E1, combined with ψ i The remaining sliding force E between each pile group is obtained. i The calculation formula:

[0035]

[0036] in:

[0037] E i Let be the remaining sliding force of the strip between the i-th pile row;

[0038] W i Let be the self-weight of the strip between the i-th pile rows;

[0039] l i Let be the length of the sliding surface of the strip between the i-th pile rows;

[0040] c i Let be the sliding surface cohesion of the strips between the i-th pile rows;

[0041] E i-1 The remaining sliding force of the inter-row blocks in the (i-1)th pile row.

[0042] Furthermore, based on the remaining sliding force of the blocks between the foremost pile rows, the function of the rear thrust of the front pile row with respect to the front resistance of the rear pile row is obtained, including:

[0043] According to E i The remaining sliding force E of the segment numbered n, i.e., the frontmost pile group, is obtained. n ;

[0044] Then the thrust T on the rear side of the front row of piles f for:

[0045] T f =E n cosθ n ;

[0046] in:

[0047] θ n The angle of inclination of the sliding surface of the strip between the foremost piles.

[0048] Furthermore, based on the design principle that the net landslide thrust borne by the rear piles is equal to that borne by the front piles, the front resistance of the rear piles and the rear thrust of the front piles are calculated based on the rear thrust of the rear piles and the front resistance of the front piles, including:

[0049] If the net landslide thrust borne by the rear piles is equal to the net landslide thrust borne by the front piles, then:

[0050] T b -N b =T f -N f

[0051] After calculation, the resistance N of the front side of the rear pile is obtained. b and the thrust T of the front row of piles f .

[0052] Furthermore, the thrust bearing ratio of the rear row of piles and the front row of piles is calculated, and the spacing between rows is determined based on the principle of minimizing the sum of the two, and design adjustments are made, including:

[0053] The net thrust of the landslide borne by the rear piles is R. b Calculate the thrust bearing ratio η of the rear piles. b :

[0054]

[0055] The net thrust of the landslide at the front row of piles is R. f Calculate the thrust bearing ratio η of the front row of piles. f :

[0056]

[0057] η b and η f The spacing between rows is determined by the principle that the sum of the two should be the minimum, and the design of the double-row piles is adjusted, including reducing the cross-sectional size and embedment depth, and adjusting the spacing between rows.

[0058] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0059] This invention, based on the anti-slide mechanism of double-row piles, proposes an optimized design principle that the front and rear rows of piles should bear the same net thrust, and the sum of the thrust-bearing ratios of the front and rear rows should be minimized. The same design safety factor is applied to all sliding bodies, and the problem of determining the reasonable value of the net thrust of the anti-slide piles during the design stage is solved using the residual sliding force curve. Based on the optimization principle of minimizing the sum of the thrust-bearing ratios of the front and rear rows of piles, the spacing between the double-row piles can be further optimized. Therefore, from a design perspective, by reducing the cross-sectional dimensions of the rear piles and adjusting the embedment depth of the rear piles, the problem of the front piles' resistance performance not being fully utilized in traditional anti-slide piles is solved.

[0060] This invention has significant practical implications for optimizing the design of net thrust and row spacing in double-row anti-slide piles, and will contribute to the further promotion and application of double-row piles. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other embodiments can be obtained from these drawings without creative effort.

[0062] Figure 1 This is a typical schematic diagram of double-row anti-slide piles used to reinforce landslides.

[0063] Figure 2 This is a curve of the remaining sliding force of the landslide after reinforcement with double-row anti-slide piles.

[0064] Figure 3 This is a schematic diagram of a case study of a landslide reinforced with double-row anti-slide piles on a zigzag-shaped slip surface.

[0065] Figure 4 This is a schematic diagram showing the design thrust calculation results on the front and rear rows of piles in Case 1.

[0066] Figure 5 This is a schematic diagram of Case 2: Reinforcement of a Straight-Line Landslide with Double-Row Anti-Slide Piles.

[0067] Figure 6 This is a cross-sectional view of a landslide along the Baoji-Chengdu Railway reinforced with embedded piles.

[0068] Figure 7 The graphs show the changes in net thrust of anti-slide piles with the design safety factor in Case 1 and Case 2.

[0069] Figure 8 These are curves showing the variation of the design thrust value of the anti-slide piles with the spacing between rows in Case 1 and Case 2.

[0070] Figure 9This is a curve showing the change in the thrust bearing ratio of the anti-slide piles in Case 1 as a function of the design safety factor.

[0071] Figure 10 This is a curve showing the change in the thrust bearing ratio of the anti-slide piles in Case 2 as a function of the design safety factor.

[0072] Figure 11 This is a curve showing the change in the thrust bearing ratio of the anti-slide piles in Case 1 with the spacing between rows.

[0073] Figure 12 This is a curve showing the change in the thrust bearing ratio of anti-slide piles with the spacing between rows in Case 2. Detailed Implementation

[0074] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0075] It should be noted that similar reference numerals and letters indicate similar items; therefore, once an item is defined in one embodiment, it does not need to be further defined and explained in subsequent embodiments. Furthermore, the terms "comprising" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or device that includes a series of steps or modules is not necessarily limited to those steps or modules explicitly listed, but may include other steps or modules not explicitly listed or inherent to such processes, methods, products, or devices.

[0076] Furthermore, the steps "S1", "S2", etc. involved in the embodiments of the present invention are only for the convenience of describing the technical solution and for understanding the specific steps and contents of the embodiments. They should not be construed as a limitation on the order of steps. Any change in the order of steps should be within the protection scope of the present invention.

[0077] This invention provides a method for optimizing the net thrust and row spacing of double-row anti-slide piles. The specific principle analysis is as follows:

[0078] Many scholars, based on the assumption that the sliding body is a segmented rigid-plastic body, have used limit equilibrium theory to obtain the residual thrust curve of the landslide, and then calculated the design net thrust of a single-row anti-slide pile. This method is simple and practical and can be extended to the design of double-row piles. Meanwhile, existing engineering practice has shown that for double-row pile retaining structures, due to the shielding effect, the rear pile is the main load-bearing body of the landslide thrust. In fact, by adjusting the row spacing, reducing the cross-sectional size of the rear pile, and adjusting the embedment depth of the rear pile, the difference in net thrust between the front and rear piles can be significantly reduced. From a design perspective, this provides a possibility for optimizing double-row anti-slide pile structures.

[0079] There are currently no standardized regulations regarding the distribution of net thrust in the design of double-row anti-slide piles, leading to highly unreasonable design calculations. Therefore, based on an in-depth analysis of the anti-slide mechanism of double-row piles, this invention proposes a novel design method for the net thrust of double-row piles. This method assumes that the net thrust values ​​of the rear and front rows of piles are the same. Thus, the same design safety factor is applied to the entire sliding body. The remaining thrust curve can then be used to easily calculate the rear thrust, front resistance, and design net thrust of each row of piles. Based on the principle that the sum of the thrust-bearing ratios of the rear and front rows of piles should be minimized, the design of the double-row piles is adjusted accordingly.

[0080] (1) Analysis of the rear piles

[0081] The transmission coefficient method can be used to obtain Figure 1 The thrust on the rear side of the rear pile shown is denoted as T. b Assume N b Let R be the net thrust of the landslide borne by the rear piles, representing the resistance on the front side of the rear piles. b Then we have:

[0082] R b =T b -N b (1)

[0083] Obviously, R b The smaller the force, the better the stress and economy of the anti-slide pile. If the net thrust of the rear and front rows of piles is relatively small, then the overall double-row pile structure is more reasonable.

[0084] Equivalent transformation of equation (1) yields:

[0085]

[0086] In equation (2), R b / T b This is called the thrust-bearing ratio, denoted by η, where N... b / T b This is called the thrust transmission ratio. It is easy to see that the smaller η is, the greater the thrust transmitted forward by the anti-slide pile. Similarly, under the premise of meeting the design requirements, the smaller the sum of the thrust-bearing ratios of the rear and front rows of piles, the greater the thrust borne by the entire row and the leading edge of the front row of piles. In other words, the anti-slide effect of these two parts of the sliding body can be more fully utilized.

[0087] From equations (1) and (2), it can be seen that, given the selection of the front row of piles, T b It is closely related to the position of the rear piles, that is, the net thrust value and the thrust bearing ratio η are related to the row spacing.

[0088] (2) Analysis of sliding bodies between rows

[0089] Assuming there are n blocks between the pile rows, numbered 1, 2…i…n from back to front, then:

[0090]

[0091]

[0092]

[0093] In the formula, E i E i-1 With θ i θ i-1 The remaining sliding force and sliding surface inclination angle of the i-th and i-1-th blocks are respectively; W i l i c i , Let ψ be the weight of the i-th strip, the length of the sliding surface, the cohesion of the sliding surface, and the angle of internal friction; i F is the residual sliding force transfer coefficient between the (i-1)th and i-th blocks. s To design a safety factor.

[0094] (3) Analysis of the front row of piles

[0095] Record the front resistance N of the rear pile. b The horizontal thrust transmitted to the front row of piles is ΔE b Then we have:

[0096]

[0097] Specifically, when n=1 (the sliding surface between rows is a straight line), we have:

[0098]

[0099] Let the thrust behind the front row of piles be T. f Then we have:

[0100] T f =E n cosθ n (8)

[0101] As can be seen from equation (8), T f For the front resistance N of the rear pile b The function.

[0102] The design resistance value of the front side of the front row of piles can be solved using the transfer coefficient method, based on the same design safety factor as the rear side of the rear row of piles and the sliding body between the two rows of piles. This value is denoted as N. f Meanwhile, let R be the net thrust of the landslide borne by the front row of piles. f Then we have:

[0103] R f =E n cosθn -N f (9)

[0104] Based on the principle that the net thrust of the rear and front rows of piles is equal, we have:

[0105] T b -N b =T f -N f (10)

[0106] In equation (10), T b N f Both are constants, so N can be easily solved. b value.

[0107] Based on the above calculations, the landslide thrust curve for double-row anti-slide piles can be obtained as follows: Figure 2 As shown, CD and EF are the design net thrust values ​​on the front and rear rows of piles.

[0108] Based on the above principle analysis, the present invention provides a method for optimizing the net thrust and row spacing of double-row anti-slide piles. The method includes the following steps:

[0109] S1: Obtain the rear thrust of the rear piles and the front resistance of the front piles, including:

[0110] Calculation of the rear thrust T of the rear pile using the transfer coefficient method b ;

[0111] Based on the assumption that the landslide thrust at the leading edge of the landslide body is zero, the resistance N at the front side of the front row of piles is calculated using the transfer coefficient method. f .

[0112] S2: Assuming the soil between the rear and front rows of piles is represented as several inter-row blocks, calculate the residual sliding force of these inter-row blocks, including:

[0113] S201: Assume that the soil between the pile rows and the pile front row consists of n pile rows, numbered sequentially from back to front as 1, 2...i...n;

[0114] S202: The pile block numbered 1 is the last pile block. The formula for calculating the remaining sliding force E1 of the last pile block is:

[0115]

[0116] in:

[0117] W1 is the self-weight of the first row of piles;

[0118] θ1 is the inclination angle of the sliding surface of the first row of piles;

[0119] The internal friction angle of the first pile row interspersed blocks;

[0120] l1 is the sliding surface length of the strip block between the first pile row;

[0121] c1 is the sliding surface cohesion of the strips between the first pile row;

[0122] F s To design a safety factor;

[0123] N b For the front side resistance of the rear piles;

[0124] S203: Calculate the residual sliding force transfer coefficient ψ between adjacent pile banks. i :

[0125]

[0126] in:

[0127] ψ i The residual sliding force transmission coefficient between the (i-1)th pile row inter-segment block and the ith pile row inter-segment block;

[0128] θ i Let be the sliding surface inclination angle of the strip block between the i-th pile row;

[0129] θ i-1 Let be the sliding surface inclination angle of the strip between the (i-1)th pile row;

[0130] Let be the internal friction angle between the blocks of the i-th pile row;

[0131] S204: Based on E1, combined with ψ i The remaining sliding force E between each pile group is obtained. i The calculation formula:

[0132]

[0133] in:

[0134] E i Let be the remaining sliding force of the strip between the i-th pile row;

[0135] W i Let be the self-weight of the strip between the i-th pile rows;

[0136] l i Let be the length of the sliding surface of the strip between the i-th pile rows;

[0137] c i Let be the sliding surface cohesion of the strips between the i-th pile rows;

[0138] E i-1The remaining sliding force of the inter-row blocks in the (i-1)th pile row.

[0139] S3: Based on the remaining sliding force of the inter-slab blocks at the foremost pile row, obtain the function of the thrust on the rear side of the front pile row with respect to the resistance on the front side of the rear pile row, including:

[0140] S301: According to E i The remaining sliding force E of the segment numbered n, i.e., the frontmost pile group, is obtained. n ;

[0141] S302: The thrust T behind the front row of piles f for:

[0142] T f =E n cosθ n ;

[0143] in:

[0144] θ n The angle of inclination of the sliding surface of the strip between the foremost piles.

[0145] S4: The design principle is that the net landslide thrust borne by the rear piles is equal to that borne by the front piles. The calculation of the front resistance of the rear piles and the rear thrust of the front piles is based on the rear thrust of the rear piles and the front resistance of the front piles, including:

[0146] S401: If the net landslide thrust borne by the rear piles is equal to the net landslide thrust borne by the front piles, then:

[0147] T b -N b =T f -N f

[0148] S402: After calculation, the front resistance N of the rear piles is obtained. b and the thrust T of the front row of piles f .

[0149] S5: Calculate the thrust bearing ratio of the rear row of piles and the front row of piles, determine the spacing between rows based on the principle of minimizing the sum of the two, and make design adjustments, including:

[0150] S501: The net thrust of the landslide borne by the rear piles is R. b Calculate the thrust bearing ratio η of the rear piles. b :

[0151]

[0152] S502: The net thrust of the landslide at the front row of piles is R. f Calculate the thrust bearing ratio η of the front row of piles. f :

[0153]

[0154] S503: Set η b and η f The spacing between rows is determined by the principle that the sum of the two should be the minimum, and the design of the double-row piles is adjusted, including reducing the cross-sectional size and embedment depth, and adjusting the spacing between rows.

[0155] Case 1:

[0156] Figure 3 The figure shows a typical base-overburden landslide located along the Baoji-Chengdu Railway in Sichuan Province. The upper sliding mass is gravelly soil, and the lower sliding bed is marble. The base-overburden interface is a broken line, which is also the initial most dangerous sliding surface. Double-row piles are considered to reinforce the landslide, achieving a safety factor of 1.25 after reinforcement. The specific pile locations are marked on the figure, with a row spacing of 28m. As shown in the figure, the landslide is approximately 148.9m long, with an average sliding mass thickness of approximately 17.4m. The main physical and mechanical parameters of the slope are shown in Table 1.

[0157] Table 1. Main physical and mechanical parameters of the slope in Case 1

[0158]

[0159] Using the transfer coefficient method proposed in the design calculation section, the design landslide thrust of the rear piles is 4417.8 kN / m. Based on the same design safety factor for the rear side of the rear piles and the sliding body between the two piles, the resistance value of the front side of the front piles is calculated to be 1590.5 kN / m using the transfer coefficient method. Assuming the resistance value of the front side of the rear piles is N... b1 The thrust value at the rear of the front row of piles can be expressed as N. b1 -485.5, based on the design principle that the rear and front rows of piles should bear the same net thrust, then:

[0160] 4417.8-N b1 =N b1 -485.5-1590.5

[0161] The front resistance of the rear piles is 3246.9 kN / m, and the rear thrust of the front piles is 2761.4 kN / m. The net design thrust of both piles is 1170.9 kN / m.

[0162] From this, the remaining thrust curve and resistance curve of the landslide can be plotted as follows: Figure 4 As shown, it is easy to see that the remaining landslide thrust increases nonlinearly at the rear edge of the rear piles, and first increases and then decreases between the rows; the remaining resistance on the front side of the front piles decreases nonlinearly to 0, indicating that the rear piles are located in the sliding section, while the front piles are located in the anti-slide section. Figure 4Further calculations show that the thrust-bearing ratios of the rear and front rows of piles are 0.265 and 0.424, respectively. It is evident that the thrust-bearing ratio of the rear rows of piles is significantly lower than that of the front rows. As mentioned in the introduction, during the design phase, the net thrust borne by the rear and front rows of piles can be equalized by reducing the cross-sectional dimensions and embedment depth of the rear rows of piles.

[0163] Case 2:

[0164] Figure 5 The image shows a potential landslide in Sichuan Province, consisting of a moderately weathered sandstone overlying gravelly soil deposit. On-site geological investigation indicates that this is a straight landslide with a length of approximately 149.6 m and an average thickness of approximately 15.8 m. Given the large scale of the landslide, double-row pile reinforcement is considered, with a spacing of 30 m between the front and rear rows. A design safety factor of 1.25 is used. The main physical and mechanical parameters of the slope are shown in Table 2.

[0165] Table 2 Main Physical and Mechanical Parameters of the Slope in Case 2

[0166]

[0167] The design calculation process for Case 2 is the same as that for Case 1. Using this method, the remaining thrust and resistance of the slope under the design safety factor can be calculated as follows: Figure 6 As shown, unlike the aforementioned broken-line case, the remaining landslide thrust increases non-linearly at the rear edge of the rear piles and between rows; the remaining resistance on the front side of the front piles first increases and then decreases non-linearly, indicating that both rows of piles are located in the sliding section. Simultaneously, the design landslide thrust and resistance of the rear and front rows of piles are 2546.2 kN / m and 1310.5 kN / m, and 2205.2 kN / m and 969.4 kN / m, respectively. At this point, the design net thrust of both rows of piles is 1235.7 kN / m. Further calculations show that the thrust-bearing ratios of the rear and front rows of piles are 0.49 and 0.56, respectively. It is evident that the thrust-bearing ratio of the rear rows of piles is slightly smaller than that of the front rows. Therefore, for this straight-line sliding surface case, similar measures to those in Case 1 can be adopted to ensure that the net thrust borne by the two rows of piles is equal.

[0168] Furthermore, within this design framework, the design calculation method section proposes an optimization design principle that the front and rear rows of piles should bear the same net thrust, and the sum of the thrust-bearing ratios of the front and rear rows of piles should be minimized. To obtain more general conclusions and clarify the significance of the above design principle for the selection of the spacing between double-row anti-slide piles, the following section further discusses the relationship between the design net thrust value and the net thrust ratio as a function of the design safety factor and the spacing between rows, using cases of broken-line and straight-line slip surfaces.

[0169] (1) Relationship between design net thrust and design safety factor

[0170] Figure 7The figure shows the variation of the design net thrust value of the anti-slide piles with the design safety factor for Case 1 and Case 2, obtained based on this method. It can be seen that as the design safety factor Fs increases, the design net thrust value of the anti-slide piles increases non-linearly, and the increasing trend slows down.

[0171] (2) Relationship between design net thrust and row spacing

[0172] Based on a design safety factor of 1.25, keeping the front row of piles in place and moving the rear row of piles, this method can be used to obtain the variation of the design net thrust value of the anti-slide piles with the row spacing in Cases 1 and 2, as shown below. Figure 8 As shown. Overall, based on the design principle that the net thrust of the rear and front rows of piles is equal, the spacing between rows has a relatively small impact on the design net thrust value. For Case 1, the design net thrust value first decreases with the spacing between rows, then slowly increases, and then decreases again. The design net thrust is minimized when the spacing is approximately 28m and 65m. Therefore, considering the principles of economy and construction convenience, the spacing between rows can be taken as 28m. For Case 2, the design net thrust value increases approximately linearly with the spacing between rows. Therefore, the spacing between rows should be taken as small as possible, taking into account the actual situation.

[0173] (3) Relationship between thrust bearing ratio and design safety factor

[0174] Figure 9 and Figure 10 The figures show the variation of the thrust-bearing ratio of the front and rear piles with the design safety factor in Case 1 and Case 2, respectively, using this design method, with the pile positions remaining unchanged. Overall, the thrust-bearing ratio of the front and rear piles increases non-linearly with the increase of the design safety factor Fs, and the increasing trend becomes increasingly gradual. The net thrust ratio of the front piles is consistently greater than that of the rear piles. When the design safety factors are 1.15 and 1.50, the difference in the thrust-bearing ratio between the front and rear piles in Case 1 and Case 2 reaches a minimum of 0.10 and 0.01, and a maximum of 0.24 and 0.17, respectively. It can be seen that, compared to the polygonal slip surface case, the thrust-bearing ratios of the front and rear piles are closer in the straight slip surface case.

[0175] (4) Relationship between thrust bearing ratio and row spacing

[0176] Based on a design safety factor of 1.25, and keeping the position of the front row of piles unchanged, the variation of the thrust-bearing ratio of the front and rear rows of piles with different row spacings is shown in the figure. Figure 11 and Figure 12As can be seen, with the increase in row spacing, the thrust-bearing ratio of the rear piles in Cases 1 and 2 increases significantly, from 0.28 and 0.42 to 0.43 and 0.92 respectively, with the latter showing a larger increase; while the thrust-bearing ratio of the front piles changes very little. When the row spacing is 64.0m and 37.5m respectively, the thrust-bearing ratios of the rear and front piles in Cases 1 and 2 are equal. Meanwhile, corresponding to Cases 1 and 2, when the row spacing is 25m and 20m respectively, the sum of the thrust-bearing ratios of the front and rear piles reaches its minimum value.

[0177] Comprehensive analysis shows that, with a design safety factor of 1.25, based on the principle that the sum of the thrust bearing ratios of the rear and front rows of piles should be minimized, the row spacing in Case 1 can be taken as 25m to 28m. For Case 2, considering the "shielding effect" of the rear rows of piles on the front rows of piles in actual engineering, the row spacing should be taken as about 20m.

[0178] The above cases demonstrate that, compared to landslides with a broken-line slip surface, the thrust-bearing ratios of the rear and front rows of piles are closer in a straight-line slip surface. Furthermore, the net thrust value of the rear and front rows of piles and their thrust-bearing ratio show a gradually decreasing non-linear increasing relationship with the design safety factor; the relationship curves between the thrust-bearing ratio of the rear and front rows of piles and the design safety factor are steeper in a straight-line slip surface. The thrust-bearing ratio of the rear and front rows of piles exhibits different patterns of change with row spacing; the former increases non-linearly with increasing row spacing, while the latter changes very little; there exists a specific row spacing that makes the thrust-bearing ratios of the rear and front rows of piles the same; the row spacing has a relatively small impact on the design net thrust value. Based on the combined relationship curves of design net thrust, thrust-bearing ratio, and row spacing, it can be concluded that for slip surfaces with a broken-line or straight-line slip surface, the row spacing can be taken as 25m–28m and 20m, respectively.

[0179] The above examples illustrate the present invention only to aid in understanding it and are not intended to limit the scope of the invention. Those skilled in the art can make various simple deductions, modifications, or substitutions based on the principles of this invention.

Claims

1. A method for optimizing the net thrust and row spacing of double-row anti-slide piles, characterized in that: The method includes: Obtain the rear thrust of the rear piles and the front resistance of the front piles; Assume the soil between the rear and front pile rows is a number of inter-pile strips, and calculate the remaining sliding force of the inter-pile strips; Based on the remaining sliding force of the strip between the frontmost pile rows, the function of the thrust on the rear side of the front piles with respect to the resistance on the front side of the rear piles is obtained. The design principle is that the net landslide thrust borne by the rear piles is equal to that borne by the front piles. The front resistance of the rear piles and the rear thrust of the front piles are calculated based on the rear thrust of the rear piles and the front resistance of the front piles. Calculate the thrust bearing ratio of the rear row of piles and the front row of piles, and determine the row spacing based on the principle of minimizing the sum of the two, and make design adjustments accordingly; in: Assuming the soil between the rear and front rows of piles is represented as several inter-row blocks, the residual sliding force of these inter-row blocks is calculated, including: Assume that the soil between the pile rows and the pile front row consists of n pile rows, numbered sequentially from back to front as 1, 2...i...n; The pile block numbered 1 is the last pile block. The formula for calculating the remaining sliding force E1 of the last pile block is: in: W1 is the self-weight of the first row of piles; θ1 is the inclination angle of the sliding surface of the first row of piles; φ1 is the internal friction angle of the strip between the first pile row; l1 is the sliding surface length of the strip block between the first pile row; c1 is the sliding surface cohesion of the strips between the first pile row; F s To design a safety factor; N b For the front side resistance of the rear piles; Calculate the residual sliding force transmission coefficient ψ between adjacent pile groups. i : in: ψ i The residual sliding force transmission coefficient between the (i-1)th pile row inter-segment block and the ith pile row inter-segment block; θ i Let be the sliding surface inclination angle of the strip block between the i-th pile row; θ i-1 Let be the sliding surface inclination angle of the strip between the (i-1)th pile row; φ i Let be the internal friction angle between the blocks of the i-th pile row; Based on E1, combined with ψ i The remaining sliding force E between each pile group is obtained. i The calculation formula: in: E i Let be the remaining sliding force of the strip between the i-th pile row; W i Let be the self-weight of the strip between the i-th pile rows; l i Let be the length of the sliding surface of the strip between the i-th pile rows; c i Let be the sliding surface cohesion of the strips between the i-th pile rows; E i-1 The remaining sliding force of the inter-row blocks in the (i-1)th pile row; Calculate the thrust bearing ratio of the rear and front rows of piles, determine the spacing between rows based on the principle of minimizing their sum, and make design adjustments, including: The net thrust of the landslide borne by the rear piles is R. b Calculate the thrust bearing ratio η of the rear piles. b : in: T b For the thrust on the rear side of the rear piles; The net thrust of the landslide at the front row of piles is R. f Calculate the thrust bearing ratio η of the front row of piles. f : in: T f This is the thrust from the rear of the front row of piles; N f For the front side resistance of the front row of piles; η b and η f The spacing between rows is determined by the principle that the sum of the two should be the minimum, and the design of the double-row piles is adjusted, including reducing the cross-sectional size and embedment depth, and adjusting the spacing between rows.

2. The method according to claim 1, characterized in that: Obtain the rear thrust of the rear piles and the front resistance of the front piles, including: Calculation of the rear thrust T of the rear pile using the transfer coefficient method b ; Based on the assumption that the landslide thrust at the leading edge of the landslide body is zero, the resistance N at the front side of the front row of piles is calculated using the transfer coefficient method. f .

3. The method according to claim 2, characterized in that: Based on the remaining sliding force of the inter-slab blocks at the foremost pile row, the function of the thrust on the rear side of the front pile row with respect to the resistance on the front side of the rear pile row is obtained, including: According to E i The remaining sliding force E of the segment numbered n, i.e., the frontmost pile group, is obtained. n ; Then the thrust T on the rear side of the front row of piles f for: ； in: θ n The angle of inclination of the sliding surface of the strip between the foremost piles.

4. The method according to claim 3, characterized in that: The design principle is that the net landslide thrust borne by the rear piles is equal to that borne by the front piles. Based on the rear thrust of the rear piles and the front resistance of the front piles, the front resistance of the rear piles and the rear thrust of the front piles are calculated, including: If the net landslide thrust borne by the rear piles is equal to the net landslide thrust borne by the front piles, then: After calculation, the resistance N of the front side of the rear pile is obtained. b and the thrust T of the front row of piles f .

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