Anchor segment length calculation method, pile foundation retaining structure design method and system

Abstract

The present application relates to the field of geotechnical engineering design, in particular to an anchoring segment length calculation method, a pile foundation retaining structure design method and system, the method comprising the following steps: S1, obtaining a length interval of the anchoring segment length, and selecting an anchoring segment length preset value from the length interval; S2, substituting the anchoring segment length preset value and other pile foundation retaining structure design parameters into a pre-established finite element model of a foundation rock mass and a pile foundation retaining structure, and solving the horizontal displacement of a spring element; S3, calculating the lateral compressive stress suffered by the spring element according to the horizontal displacement of the spring element; S4, selecting an anchoring length interval and re-determining the anchoring segment length preset value according to the size between the lateral compressive stress and the allowable stress; and S5, repeating steps S1-S4 until the anchoring length interval is less than a preset allowable value, and obtaining the optimal anchoring length. The method uses the finite element method and the dichotomy idea to solve the optimal length of the anchoring segment, and is not only widely applicable, but is particularly suitable for programmatic use.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering design, and in particular to methods for calculating the length of anchorage sections and methods and systems for designing pile foundation retaining structures. Background Technology

[0002] In slope engineering, commonly used pile foundation retaining structures include anti-slide piles, anchored piles, pile-slab walls, chair piles, and anchored chair piles. Their main characteristic is that they rely on the soil resistance of the anchorage section to bear the external loads on the pile body. In the design calculations of pile foundation retaining structures, the structure is usually divided into a load-bearing section and an anchorage section for separate calculations. The load-bearing section is calculated according to relevant structural mechanics theories, while the anchorage section is calculated using the subgrade coefficient method based on Winkler's "elastic foundation" theory.

[0003] Based on the variation law of the subgrade coefficient, two commonly used calculation methods are derived: the "K" method and the "m" method. The "K" method assumes that the subgrade coefficient of the anchorage section is constant, while the "m" method assumes that the subgrade coefficient varies triangularly from the anchorage point. In the calculation of pile internal forces, piles are further classified into elastic piles and rigid piles according to their stiffness. Based on the variation law of the subgrade coefficient and the stiffness type of the pile, analytical solutions for calculating the internal forces and deformations of the pile can be derived. For detailed derivation processes, please refer to relevant literature, such as "Rock and Soil Support and Anchorage Engineering".

[0004] In practical retaining structure design, the geometric dimensions and loads of the load-bearing section, and the subgrade coefficient of the anchorage section, can be obtained directly from geological data or calculated. The cross-sectional shape and dimensions of the structure can also be preliminarily determined. At this point, only the length of the anchorage section remains to be calculated. For a given anchorage length, if the lateral compressive stress at each point of the pile anchorage section does not exceed the allowable lateral bearing capacity of the foundation, then the anchorage length can be considered to meet the theoretical calculation requirements. In actual engineering, the anchorage length must not only meet the theoretical calculation requirements but also the economic requirements of the project, i.e., be economically optimal. Therefore, the core of pile foundation retaining structure design is the calculation of the optimal (shortest) value of the anchorage length.

[0005] The invention patent "A Calculation Method for the Minimum Length of the Anchorage Section of an Anti-slide Pile" (application number CN201410794788.8) discloses a method for calculating the minimum length of the anchorage section of an anti-slide pile. It divides the anchorage section into equal-pressure and non-equal-pressure sections for separate calculation. However, this method only applies to rigid anti-slide piles and struggles to provide analytical solutions for complex structures such as anchored piles and anchored chair piles, thus exhibiting significant limitations. The invention patent "A Calculation Method for the Length of the Anchorage Section of an Anti-slide Pile in an Inclined Slippage" (application number CN201910264025.5) divides the anti-slide pile anchorage section into ineffective and effective anchorage sections, calculates them separately, and then sums the results to obtain the anchorage section length. However, it does not address how to calculate the optimal anchorage section length, and similarly has significant limitations for complex pile foundation retaining structures.

[0006] The two methods described above are not only limited to the case where the anchorage section is a homogeneous single-layer stratum, but also to the case where the anchorage section has multiple strata, such as soil above and rock below, or multiple different soil (rock) layers. In these cases, the subgrade coefficient does not exhibit the common linear variation, making it difficult to calculate the optimal anchorage length analytically. Furthermore, these methods are limited to the case of a single anti-slide pile. For composite piles, such as anchor piles, chair piles, and anchor-chair piles, the structure is more complex, and even with homogeneous anchorage section strata, it is difficult to derive an analytical solution for the optimal anchorage length. In fact, most analytical methods suffer from these limitations.

[0007] As for numerical methods, common methods such as the finite element method and the finite difference method can be used to calculate the internal forces of similar structures. However, purely numerical methods cannot calculate the optimal length of the anchorage segment, and no publicly available numerical calculation software has been found to have the function of calculating the optimal length of the anchorage segment.

[0008] Based on the theory of elastic foundations and the law of conservation of energy, the foundation soil and rock mass can be considered equivalent to a spring. Under otherwise constant conditions, the longer the anchorage section, the more foundation springs are in contact with the pile (the larger the bearing area of ​​the foundation). The deformation of these foundation springs under the same external load is smaller. When the anchorage section length reaches a certain value, the deformation of the foundation springs gradually stabilizes. That is, the anchorage section length and the deformation of the foundation springs are negatively correlated. Figure 1 As shown. The greater the deformation of the foundation spring, the greater the compressive stress it experiences. When the compressive stress is exactly equal to the allowable compressive stress, the deformation at this point is the maximum deformation that meets the theoretical calculation requirements, and the corresponding anchorage length is the optimal anchorage length (i.e., if it is less than this length, the compressive stress of the foundation soil exceeds the allowable value, which may lead to failure; if it is greater than this length, it meets the theoretical calculation requirements, but it is not economical).

[0009] Therefore, to address the limitations and difficulties of analytical methods in calculating the optimal anchorage length, and to compensate for the lack of corresponding pile foundation retaining structure design functions in numerical calculation software, a pile foundation retaining structure design and calculation method is proposed based on the aforementioned variation law. This method calculates the optimal value of the anchorage section of the pile foundation retaining structure, as well as the corresponding internal forces and deformations. Since the above law is only a qualitative description and cannot be specifically expressed by mathematical formulas, but the foundation deformation monotonically decreases with the anchorage section length during the variation process, the bisection method is used to solve for the anchorage section length when the foundation deformation is within the allowable deformation range. This method can be used to calculate the optimal anchorage length of pile foundation retaining structures in single-layer and multi-layer strata, the optimal anchorage length of retaining structures such as anti-slide piles, anchored piles, chair piles, and anchored chair piles, as well as calculations for combined cases. Summary of the Invention

[0010] This invention uses the finite element method to calculate the internal forces of the structure and the foundation stress of the anchorage section. It uses the bisection method to solve for the optimal length of the anchorage section and proposes a method for calculating the length of the anchorage section, a design method for pile foundation retaining structures, and a system.

[0011] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0012] A method for calculating the anchorage length of a pile foundation retaining structure includes the following steps:

[0013] S1, obtain the minimum and maximum values ​​of the anchorage segment length, the minimum and maximum values ​​constitute a length range, and select a preset value for the anchorage segment length between the minimum and maximum values;

[0014] S2, Substitute the preset value of the anchorage section length and other pile foundation retaining structure design parameters into the pre-established finite element model of the foundation soil and pile foundation retaining structure. In the finite element model, the foundation soil is equivalent to a spring element, and the pile foundation retaining structure is equivalent to several beam elements. The spring elements are fixed away from the pile side nodes. Apply load to the part of the pile foundation retaining structure outside the foundation soil and use numerical calculation method to solve the horizontal displacement of the spring elements.

[0015] S3, calculate the transverse compressive stress on the beam unit based on the horizontal displacement of the spring unit and the foundation coefficient of the stratum where the spring unit is located;

[0016] S4. If the lateral compressive stress is less than the allowable stress, select the length between the minimum value and the preset value of the anchorage section length as the length interval, replace the maximum value with the preset value of the anchorage section length, and return to step S1; if the lateral compressive stress is greater than or equal to the allowable stress, select the length between the preset value of the anchorage section length and the maximum value as the length interval, replace the minimum value with the preset value of the anchorage section length, and return to step S1.

[0017] S5, repeat steps S1 to S4 until the length interval is less than the preset allowable value, and obtain the anchorage length when the length interval is less than the preset allowable value, as the optimal anchorage length.

[0018] As a preferred embodiment, in step S5, when the length range is less than the preset allowable value, if the lateral compressive stress is less than the allowable stress, the optimal anchorage length is the maximum value of the current length range; if the lateral compressive stress is greater than or equal to the allowable stress, the optimal anchorage length is the value between the preset value and the maximum value of the anchorage segment length.

[0019] As a preferred embodiment, in step S5, when the length interval is less than the preset allowable value, if the transverse compressive stress is greater than or equal to the allowable stress, the method further includes selecting an adjustment intermediate value in the adjustment interval formed by the preset value and the maximum value of the anchorage segment length, obtaining a second length interval using the method of steps S1 to S4, repeating steps S1 to S4 until the second length interval is less than the preset allowable value, and taking the anchorage segment length obtained when the second length interval is less than the preset allowable value as the optimal anchorage length.

[0020] As a preferred embodiment, the construction of the finite element model of the foundation soil and pile foundation retaining structure in step S2 includes the following steps:

[0021] The anchorage section of the pile foundation retaining structure is divided into N length elements based on the length of the finite element elements, where N is an integer; the anchorage section of the pile foundation retaining structure is divided into beam elements according to the thickness of the stratum.

[0022] The anchorage section stratum is equivalently converted into spring elements, with each beam element corresponding to one spring element, and the spring element is perpendicular to the axis of the beam element.

[0023] As a preferred embodiment, if the anchoring section consists of multiple strata, then each stratum in the anchoring section is equivalently converted into a spring unit with different stiffness.

[0024] As a preferred solution, if the number of length elements obtained during the process of dividing the anchorage section of the pile foundation retaining structure into finite element elements is not an integer, the following processing is performed:

[0025] If the remaining length l i <0.5l e Then the length range l i With the last length unit l e After merging, it is divided into two equal parts with a length of 0.5 (l). e +l i (units);

[0026] If the remaining length l i ≥0.5l e Then the remaining length l i It is treated as a separate unit.

[0027] As a preferred option, the preset value of the anchorage section length selected in step S1 is half the length of the sum of the minimum and maximum values.

[0028] As a preferred option, if the pile foundation retaining structure is a multi-pile composite retaining structure, the following steps are also included: constructing the initial length range of each pile foundation respectively, and calculating the optimal anchorage length of each pile foundation anchorage segment according to the preset initial length range;

[0029] The method for constructing the initial length interval for each pile foundation includes: presetting the anchorage length, and setting the initial length interval based on the preset anchorage length. The initial length interval is [L]. fore -α·tol,L fore +α·tol], where L fore α is the preset anchorage length, α is the adjustment coefficient, and tol is the allowable length of the anchorage section.

[0030] Based on the same concept, a design calculation method for pile foundation retaining structures based on the bisection method is also proposed. The anchorage length of the pile foundation retaining structure is obtained by using any of the above-mentioned methods for calculating the anchorage length. The horizontal displacement curve, bending moment curve, and shear force curve of the pile foundation retaining structure are fitted according to the anchorage length. Then, the required design results are calculated by further interpolation based on the distributed horizontal displacement curve, bending moment curve, and shear force curve. The required design results include key point displacement, maximum shear force, maximum positive bending moment, and maximum negative bending moment.

[0031] Based on the same concept, a system for calculating the anchorage length of a pile foundation retaining structure is also proposed, including at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, which are executed by the at least one processor to enable the at least one processor to perform the method described above.

[0032] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0033] This method uses numerical calculation as its structural algorithm, equating the structure to beam elements and the anchorage section stratum to spring elements. Based on the relationship between the anchorage section length and foundation deformation, it employs a bisection method to determine the optimal anchorage section length, and unifies the calculation of a specified anchorage section length. It is applicable not only to pile foundation retaining structure calculations in single-layer and multi-layer strata, but also to the calculation of various types of retaining structures such as anti-slide piles, anchored piles, chair piles, and anchored chair piles, as well as structural calculations involving combinations thereof. This method unifies the design and calculation of pile foundation retaining structures under various strata and structural forms, offering broad applicability and avoiding the drawbacks of analytical methods that struggle to obtain analytical solutions. The calculation process is simple and clear, making it particularly suitable for procedural use. Attached image description:

[0034] Figure 1 This is a diagram illustrating the relationship between the anchorage length and the amount of foundation deformation in the background technology of this invention.

[0035] Figure 2 This is a common calculation profile of the anti-slide pile in Embodiment 2 of the present invention;

[0036] Figure 3 This is a simplified calculation model of the anti-slide pile in Embodiment 2 of the present invention;

[0037] Figure 4 This is the finite element model established in Embodiment 2 of the present invention;

[0038] Figure 5 This is a schematic diagram of the adjustment of the anchorage section length range in Embodiment 2 of the present invention;

[0039] Figure 6 This is a common calculation profile of the chair pile in Embodiment 2 of the present invention;

[0040] Figure 7 This is a fitted curve of the calculation results of the anti-slide pile in Embodiment 2 of the present invention. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to experimental examples and specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0042] Example 1

[0043] A method for calculating the anchorage length of a pile foundation retaining structure includes the following steps:

[0044] S1, obtain the minimum and maximum values ​​of the anchorage segment length, the minimum and maximum values ​​constitute a length range, and select a preset value for the anchorage segment length between the minimum and maximum values;

[0045] S2, Substitute the preset value of the anchorage section length and other pile foundation retaining structure design parameters into the pre-established finite element model of the foundation soil and pile foundation retaining structure. In the finite element model, the foundation soil is equivalent to a spring element, and the pile foundation retaining structure is equivalent to a beam element corresponding to the foundation soil. The spring element is fixed away from the pile side node. Apply load to the part of the pile foundation retaining structure outside the foundation soil and use numerical calculation method to solve the horizontal displacement of the spring element.

[0046] S3, calculate the transverse compressive stress on the beam unit based on the horizontal displacement of the spring unit and the foundation coefficient of the stratum where the spring unit is located;

[0047] S4. If the lateral compressive stress is less than the allowable stress, select the length between the minimum value and the preset value of the anchorage section length as the length interval, replace the maximum value with the preset value of the anchorage section length, and return to step S1; if the lateral compressive stress is greater than or equal to the allowable stress, select the length between the preset value of the anchorage section length and the maximum value as the length interval, replace the minimum value with the preset value of the anchorage section length, and return to step S1.

[0048] S5, repeat steps S1 to S4 until the length interval is less than the preset allowable value, and obtain the anchorage length when the length interval is less than the preset allowable value, as the optimal anchorage length.

[0049] As a preferred embodiment, in step S5, when the length range is less than the preset allowable value, if the lateral compressive stress is less than the allowable stress, the optimal anchorage length is the maximum value of the current length range; if the lateral compressive stress is greater than or equal to the allowable stress, the optimal anchorage length is the value between the preset value and the maximum value of the anchorage segment length.

[0050] As a preferred embodiment, in step S5, when the length interval is less than the preset allowable value, if the transverse compressive stress is greater than or equal to the allowable stress, the method further includes selecting an adjustment intermediate value in the adjustment interval formed by the preset value and the maximum value of the anchorage segment length, obtaining a second length interval using the method of steps S1 to S4, repeating steps S1 to S4 until the second length interval is less than the preset allowable value, and obtaining the anchorage segment length obtained when the second length interval is less than the preset allowable value as the optimal anchorage length.

[0051] As a preferred embodiment, the construction of the finite element model of the foundation soil and pile foundation retaining structure in step S2 includes the following:

[0052] The anchorage section of the pile foundation retaining structure is divided into N length elements based on the length of the finite element elements, where N is an integer; the anchorage section of the pile foundation retaining structure is divided into beam elements according to the thickness of the stratum.

[0053] The anchorage section stratum is equivalently converted into spring elements, with each beam element corresponding to one spring element, and the spring element is perpendicular to the axis of the beam element.

[0054] As a preferred embodiment, if the anchoring section consists of multiple strata, then each stratum in the anchoring section is equivalently converted into a spring unit with different stiffness.

[0055] As a preferred embodiment, the finite element model of the foundation soil and the pile foundation retaining structure also includes a load-bearing section; the load-bearing section of the pile foundation retaining structure is divided into M length elements by the length of the finite element element, where M is an integer, and the force distribution of the load-bearing section is rectangular, triangular, or trapezoidal, and the force is calculated based on the force distribution.

[0056] As a preferred solution, if the number of length elements obtained during the process of dividing the anchorage section of the pile foundation retaining structure into finite element elements is not an integer, the following processing is performed:

[0057] If the remaining length l i <0.5l e Then the length range l i With the last length unit l eAfter merging, it is divided into two equal parts with a length of 0.5 (l). e +l i (units);

[0058] If the remaining length l i ≥0.5l e Then the remaining length l i It is treated as a separate unit.

[0059] As a preferred option, the preset value of the anchorage section length selected in step S1 is half the length of the sum of the minimum and maximum values.

[0060] Based on the same concept, a design calculation method for pile foundation retaining structures based on the bisection method is also proposed. The anchorage length of the pile foundation retaining structure is obtained by using the above-mentioned method for calculating the anchorage length of the pile foundation retaining structure. Based on the anchorage length, the horizontal displacement curve, bending moment curve and shear force curve of the pile foundation retaining structure are fitted. Then, the required design results are calculated by further subtracting the distributed horizontal displacement curve, bending moment curve and shear force curve. The required design results include key point displacement, maximum shear force, maximum positive bending moment and maximum negative bending moment.

[0061] Example 2

[0062] This invention relates to a design and calculation method for pile foundation retaining structures based on the bisection method. It employs the finite element method to calculate the internal forces of the structure and the ground stress of the anchorage section, and uses the bisection approach to solve for the optimal length of the anchorage section. The following explanation uses an anti-slide pile as an example.

[0063] 1. Simplify the calculation model

[0064] Based on the design data, representative cross-sections that need to be calculated can be obtained, such as... Figure 2 As shown, basic calculation data can be obtained: the length of the loaded section L1, the strength parameters of the anchoring strata (such as the subgrade coefficient of the soil layer, the subgrade coefficient of the rock layer, and the allowable lateral bearing capacity of each stratum), and the thickness of the strata.

[0065] In the design of anti-slide piles, the designer initially determines the pile cross-section type (e.g., rectangular cross-section), pile cross-section dimensions (e.g., 1.5m × 2.0m), pile spacing, and pile concrete strength. The load on the load-bearing section is mainly the earth pressure or landslide thrust of the rock and soil behind the pile, which can be calculated according to relevant theoretical formulas or software. Its distribution form is usually simplified to rectangle, triangle, or trapezoid. Here, it is uniformly simplified to a trapezoidal distribution, with the top load being q1 and the bottom load being q2, resulting in the following simplified calculation model. At this time, the anchorage length L2 is the only unknown in the design of the anti-slide pile structure.

[0066] 2. Construct the initial section of the anchorage segment

[0067] For the desired anchorage length L2 of the anti-slide pile, specify a range of values ​​covering all possible lengths in the engineering design [L]. left ,L right For example, the minimum possible length L of the anchorage section in the project. min Given a length of 1m, the maximum possible length L max If the value is not more than 50m, then the range of values ​​is [L]. left ,L right The initial value of ] is [1, 50]. The optimal value of the anchorage length L2 lies in the initial interval [L]. left ,L right Within [ ], the midpoint of the interval is L mid =(L left +L right ) / 2.

[0068] 3. Structural Calculation

[0069] Take the anchorage length L2 as the midpoint of the interval L mid At this point, all design parameters of the anti-slide pile structure are known. Based on the elastic foundation theory and the above calculation model, numerical calculation methods are used to calculate the internal forces and deformations of the calculation model. For simple pile foundation retaining structures, such as anti-slide piles, theoretical analytical solutions can be used. However, for complex retaining structures, it is difficult to derive theoretical analytical solutions. Therefore, numerical calculation methods with better applicability are used. There are many numerical methods that can be used, such as the finite element method and the finite difference method. Essentially, they all approximate the solution by discretizing the solution domain. In this invention, the finite element method is used to model the calculation model into a finite element model, as follows:

[0070] (1) Given the finite element mesh length l e For a given length, such as L1, if it is divided into exactly an integer number of lengths l... e Then directly divide into units; if the number of units is an integer l... e After the length unit, the remaining length l i Insufficient e If so, then adjustments will be made:

[0071] If the remaining length l i <0.5l e Then the length range l i With the last unit length l e After merging, it is divided into two equal parts with a length of 0.5 (l). e +l i (units);

[0072] If the remaining length l i ≥0.5l e Then the length range l iIt is treated as a separate unit.

[0073] (2) Anti-slide piles are elastic (or rigid) structures, which are simplified as beam elements. The cantilever segment L1 and the anchorage segment L2 are divided into separate elements. The anchorage segment is further divided according to the thickness range of the stratum, such as... Figure 3 The beam consists of three segments: D1, D2, and D3. The required elastic modulus E, cross-sectional area A, and moment of inertia I for the beam element can be calculated based on the strength of the pile concrete and the geometric dimensions of the pile cross-section.

[0074] (3) If the structure contains anchor cables, it is simplified to a rod element, with one rod element corresponding to each anchor cable hole. The required elastic modulus E, cross-sectional area A, and length L of the rod element can be determined based on the anchor cable material and length.

[0075] (4) Based on the theory of elastic foundations, each stratum in the anchorage section is equivalently converted into a spring element with different stiffness. For a certain stratum (thickness D)... i Within this range, the anti-slide pile segment has been divided into multiple beam elements. Each beam element node within this range corresponds to a horizontally placed spring element. The length of all spring elements within this range has little impact on the calculation and can be taken as 1m. Their spring stiffness K can be calculated based on the soil subgrade coefficient, the calculated width of the pile section, and the spacing between the spring elements. Therefore, all spring elements within this range can be considered equivalent to this soil layer.

[0076] (5) The spring unit must be fixed away from the pile side node.

[0077] (6) Apply load to the load-bearing section of the beam element.

[0078] (7) Calculation and Solution. After the finite element model is established, as follows: Figure 4 By summarizing all nodes, elements, loads, and constraints, establishing and solving the algebraic matrix equations, the displacement and rotation of each node, as well as the bending moment and shear force of each element, can be obtained.

[0079] 4. Adjust the interval range

[0080] Based on the above calculation results, the horizontal displacement of all spring elements is extracted, and the transverse compressive stress σ is calculated according to the subgrade coefficient of the corresponding stratum. c The lateral compressive stress σ on the foundation c Rather than the allowable transverse compressive stress σ r Comparison:

[0081] If any spring element in the anchorage section experiences the compressive stress σ, c ≥ Allowable stress σ r If the calculated foundation deformation exceeds the allowable deformation, the anchorage length is too short and does not meet the engineering requirements, and the optimal anchorage length is greater than the current value. Figure 5 (a) At this point, the range of the anchorage section length is adjusted to [L]. mid ,L right If ], then the midpoint of the interval is (L mid +L right ) / 2;

[0082] If all spring units within the anchorage section experience compressive stress σ c <Allowable stress σ r If the calculated foundation deformation is lower than the allowable deformation, the calculated anchorage length meets the engineering requirements, and the optimal anchorage length is less than or equal to the current value. Figure 5 (b) At this point, the range of the anchorage section length is adjusted to [L]. left ,L mid If ], then the midpoint of the interval is (L left +L mid ) / 2.

[0083] 5. Termination Condition

[0084] Based on the adjusted anchorage length range, repeat the above calculation process 3-4 cyclically until the interval length R of the anchorage length range is reached. len Less than a specified allowable value tol, such as the interval length R len ≤0.1. At this point, the calculation of the optimal value of the anchorage segment length is complete. Then, a result validity assessment is performed: if the final obtained maximum value of the anchorage segment interval is equal to the initial maximum value L... max If the length is within the specified range, it indicates that there is a problem with the selection of calculation parameters such as the foundation coefficient or pile cross-section size. All length values ​​within the range cannot meet the project requirements, and the calculation parameters or scheme need to be adjusted. Otherwise, the maximum value in the range is taken as the optimal value for the final anchorage section length.

[0085] For a certain interval [L] in the calculation lefti ,L righti The calculated anchorage length used is the midpoint L of the interval. midi =(L lefti +L righti If the interval length satisfies: tol / 2, <R len If the value of the anchorage segment length is less than 2·tol, then after completing the calculation of the anchorage segment length, the interval can be adjusted according to the calculation results to meet the termination condition, thus completing the process of calculating the optimal value of the anchorage segment length. If the midpoint of the interval in this calculation is L... midi If it fails, the adjusted interval is [L]. midi ,L righti The optimal length of the anchorage section is L. righti The structural calculation result is the anchorage section length L. midicorresponding calculation result does not correspond to the optimal value of the anchorage section length; if the current calculation passes, the adjusted interval is [L lefti , L midi , and the optimal value of the anchorage section length is L midi , which corresponds to the structural calculation result.

[0086] Therefore, to ensure that the final structural calculation result corresponds to the optimal value of the anchorage section length, based on the finally obtained anchorage section length L final , that is, L righti or L midi , re-construct the anchorage section length interval [L final -α·tol, L final +α·tol], where α needs to satisfy the condition: 0.5<α<1.0, then perform another cycle of calculation processes 3 to 4, and the finally obtained optimal value of the anchorage section length is L final , which corresponds to the final structural calculation result.

[0087] 6. Specified Anchorage Interval

[0088] For the case of a specified structural anchorage section length L c , its calculation process can be normalized so that the same method can be used to solve and calculate according to the above calculation processes 3 to 5, with the following processing performed:

[0089] According to the allowable length value tol of the anchorage section interval, construct an initial anchorage section length interval [L c -α·tol, L c +α·tol], where α needs to satisfy the condition: 0.5<α<1.0.

[0090] According to the aforementioned calculation processes 3 to 5, taking the midpoint of the interval can obtain the anchorage section length L2 = L c , and performing one calculation can meet the end condition, that is, the interval length R len =2α·tol<tol, and then proceed to the result rationality judgment: if the obtained interval is [L c , L c +α·tol], and the maximum value of the obtained interval is the maximum value of the initial interval, it indicates that the specified anchorage length L c cannot meet the engineering requirements, and the calculation parameters or scheme need to be adjusted; if the obtained interval is [L c -α·tol, L c , then the maximum value L c of the interval is taken as the final optimal value of the anchorage section length (equal to the specified anchorage section length L c ).

[0091] 7. Calculation of Multi-pile Composite Retaining Structure

[0092] The above calculation process mainly describes single-pile retaining structures (anti-slide piles). In actual design, there are also multi-pile composite retaining structures, such as... Figure 6 For the central chair-type pile, the design of the entire retaining structure requires calculation of more than one anchorage section length.

[0093] For multi-pile composite retaining structures, the anchorage length and the amount of foundation deformation still meet the requirements. Figure 1 The variation pattern shown indicates that the optimal value of the structural anchorage length can also be calculated using the aforementioned bisection method. The main difference lies in the construction of the anchorage length interval and the determination of the interval range adjustment, as detailed below:

[0094] (1) Initial interval construction of anchorage section length

[0095] The characteristic of this type of retaining structure is that it is anchored by two foundation piles (front pile and rear pile). In design calculations, the anchorage length typically falls into three categories: ① The anchorage length for both piles is not specified, and the optimal value is determined through calculation; ② The anchorage length for both piles is specified; ③ The anchorage length for one pile is specified, while the other is not, and the optimal value is determined through calculation.

[0096] Assume the optimal value of the anchorage length to be calculated is L. mao .

[0097] In scenario ①, where the anchorage length is not specified for either the front or rear piles, a certain pile is used as the calculation benchmark. For example, for the front pile, the anchorage length of the front pile is taken as L. mao The difference in anchorage length between the front and rear piles is δL (δL = 0 when the anchorage sections of the front and rear piles are of equal length; when the anchorage lengths of the front and rear piles are of unequal length, the value can be taken according to the design requirements), that is, the anchorage length of the rear pile is L. mao +δL, at which point the anchorage length interval is [L] left ,L right The midpoint of the interval is L. mid =(L left +L right ) / 2. Take the length of the anchorage section of the preceding pile as the midpoint of the interval L. mao =L mid If the lengths of the anchorage sections of the front and rear piles are known, the optimal values ​​of the anchorage sections of the front and rear piles can be obtained by solving the calculations according to the above calculation process 3 to 5.

[0098] For scenario ②, when both the front and rear piles have specified anchorage lengths, one of the piles is taken as the calculation benchmark. For example, the specified anchorage length of the front pile is L. fore Similar to process 6, an initial interval [L] for the length of the anchorage segment is constructed based on the allowable length tol of the anchorage segment interval. fore -α·tol,L fore+α·tol], where α must satisfy the condition: 0.5<α<1.0.

[0099] In scenario ③, when only the anchorage length of one pile is unknown, its anchorage length is L. mao The anchorage section range is [L] left ,L right The midpoint of the interval is L. mid =(L left +L right ) / 2. Take the length of its anchorage section as the midpoint of the interval L. mao =L mid The optimal value of the pile anchorage section can be obtained by solving the calculations according to the above calculation process 3 to 5.

[0100] (2) Judgment of interval range adjustment

[0101] Similar to the calculation process for anti-slide piles, the horizontal displacement of all spring elements of the front and rear piles is extracted, and the transverse compressive stress σ is calculated based on the subgrade coefficient of the corresponding stratum. c The lateral compressive stress σ on the foundation c Rather than the allowable transverse compressive stress σ r Comparison:

[0102] If any spring element in the anchorage section of the front or rear pile experiences the compressive stress σ, c ≥ Allowable stress σ r If the calculated foundation deformation exceeds the allowable deformation, the range of the anchorage length should be adjusted to [L]. mid ,L right ];

[0103] If all spring elements within the anchorage sections of the front and rear piles experience the compressive stress σ... c <Allowable stress σ r If the calculated foundation deformation is lower than the allowable deformation, then the range of the anchorage length should be adjusted to [L]. left ,L mid ].

[0104] 8. Result Fitting

[0105] When designing the cross-sectional dimensions of a pile foundation retaining structure, the displacements of certain key points in the structure are needed to evaluate the design dimensions. Similarly, when designing the reinforcement, the maximum shear force, maximum positive bending moment, and maximum negative bending moment are required for subsequent reinforcement calculations. However, since the numerical calculation method (finite element method) used is essentially a discrete approximation of the solution domain, the resulting calculations are also discrete data.

[0106] Therefore, based on the structural calculation results (displacement, rotation angle of each node, and bending moment and shear force of each element) corresponding to the optimal anchorage length, the horizontal displacement curve, bending moment curve, and shear force curve distributed along the structure are fitted, such as... Figure 7 Based on the fitted curve results, further interpolation is used to calculate the displacement, maximum shear force, maximum positive bending moment, and maximum negative bending moment of key points, as well as other design-required results.

[0107] This method uses numerical calculation as its structural algorithm, equating the structure to beam elements and the anchorage section stratum to spring elements. Based on the relationship between the anchorage section length and foundation deformation, it employs a bisection method to determine the optimal anchorage section length, and unifies the calculation of a specified anchorage section length. It is applicable not only to pile foundation retaining structure calculations in single-layer and multi-layer strata, but also to the calculation of various types of retaining structures such as anti-slide piles, anchored piles, chair piles, and anchored chair piles, as well as structural calculations involving combinations thereof. This method unifies the design and calculation of pile foundation retaining structures under various strata and structural forms, offering broad applicability and avoiding the drawbacks of analytical methods that struggle to obtain analytical solutions. The calculation process is simple and clear, making it particularly suitable for procedural use.

[0108] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the anchorage length of a pile foundation retaining structure, characterized in that, Includes the following steps: S1, obtain the minimum and maximum values ​​of the anchorage segment length, the minimum and maximum values ​​constitute a length range, and select a preset value for the anchorage segment length between the minimum and maximum values; S2, Substitute the preset value of the anchorage section length and other pile foundation retaining structure design parameters into the pre-established finite element model of the foundation soil and pile foundation retaining structure. In the finite element model, the foundation soil is equivalent to a spring element, and the pile foundation retaining structure is equivalent to several beam elements. The spring elements are fixed away from the pile side nodes. Apply load to the part of the pile foundation retaining structure outside the foundation soil and use numerical calculation method to solve the horizontal displacement of the spring elements. S3, calculate the transverse compressive stress on the beam unit based on the horizontal displacement of the spring unit and the foundation coefficient of the stratum where the spring unit is located; S4. If the lateral compressive stress is less than the allowable stress, select the length between the minimum value and the preset value of the anchorage section length as the length interval, replace the maximum value with the preset value of the anchorage section length, and return to step S1; if the lateral compressive stress is greater than or equal to the allowable stress, select the length between the preset value of the anchorage section length and the maximum value as the length interval, replace the minimum value with the preset value of the anchorage section length, and return to step S1. S5, repeat steps S1 to S4 until the length interval is less than the preset allowable value, and obtain the anchorage length when the length interval is less than the preset allowable value, as the optimal anchorage length.

2. The method for calculating the anchorage length of a pile foundation retaining structure as described in claim 1, characterized in that, In step S5, if the length interval is less than the preset allowable value, and the lateral compressive stress is less than the allowable stress, then the optimal anchorage length is the maximum value of the current length interval; if the lateral compressive stress is greater than or equal to the allowable stress, then the optimal anchorage length is the value between the preset value and the maximum value of the anchorage segment length.

3. The method for calculating the anchorage length of a pile foundation retaining structure as described in claim 2, characterized in that, In step S5, if the length interval is less than the preset allowable value and the lateral compressive stress is greater than or equal to the allowable stress, the method further includes selecting an adjustment intermediate value in the adjustment interval formed by the preset value and the maximum value of the anchorage segment length, obtaining a second length interval using the method of steps S1 to S4, repeating steps S1 to S4 until the second length interval is less than the preset allowable value, and taking the anchorage segment length obtained when the second length interval is less than the preset allowable value as the optimal anchorage length.

4. The method for calculating the anchorage length of a pile foundation retaining structure as described in claim 1, characterized in that, The construction of the finite element model of the foundation soil and pile foundation retaining structure in step S2 includes the following steps: The anchorage section of the pile foundation retaining structure is divided into N length elements based on the length of the finite element elements, where N is an integer; the anchorage section of the pile foundation retaining structure is divided into beam elements according to the thickness of the stratum. The anchorage section stratum is equivalently converted into spring elements, with each beam element corresponding to one spring element, and the spring element is perpendicular to the axis of the beam element.

5. The method for calculating the anchorage length of a pile foundation retaining structure as described in claim 4, characterized in that, If the anchoring section consists of multiple strata, then each stratum in the anchoring section is equivalently converted into a spring element with different stiffness.

6. The method for calculating the anchorage length of a pile foundation retaining structure as described in claim 4, characterized in that, If the number of length elements obtained during the process of dividing the anchorage section of the pile foundation retaining structure into finite element lengths is not an integer, the following processing is performed: If the remaining length Then the length range With the last length unit After merging, it is divided into two equal parts with lengths of Units; If the remaining length Then the remaining length It is treated as a separate unit.

7. A method for calculating the anchorage length of a pile foundation retaining structure as described in any one of claims 1-6, characterized in that, The preset value for the anchorage length selected in step S1 is half the length of the sum of the minimum and maximum values.

8. The method for calculating the anchorage length of a pile foundation retaining structure as described in claim 1, characterized in that, If the pile foundation retaining structure is a multi-pile composite retaining structure, the following steps are also included; Construct initial length intervals for each pile foundation separately, and calculate the optimal anchorage length of each pile foundation anchorage segment based on the preset initial length intervals; The method for constructing the initial length interval for each pile foundation includes: presetting the anchorage length, and setting the initial length interval based on the preset anchorage length. The initial length interval is... ,in, It is the preset anchorage length. It is the adjustment factor, and tol is the allowable length of the anchorage section.

9. A design and calculation method for pile foundation retaining structures based on the bisection method, characterized in that, The anchorage length of the pile foundation retaining structure is obtained by using the method described in any one of claims 1-8. Based on the anchorage length, the horizontal displacement curve, bending moment curve, and shear force curve of the pile foundation retaining structure are fitted. Then, based on the distributed horizontal displacement curve, bending moment curve, and shear force curve, the required design results are further calculated by interpolation. The required design results include key point displacement, maximum shear force, maximum positive bending moment, and maximum negative bending moment.

10. A system for calculating the anchorage length of a pile foundation retaining structure, characterized in that, It includes at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1 to 8.

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