An automatic pile layout method for reducing differential settlement of pile-raft foundation

Abstract

The present invention discloses an automatic pile layout method for reducing the differential settlement of a pile-raft foundation. This method uses variable pile spacing for pile layout, positions each pile at an appropriate location to specifically bear the differential settlement generated by the pile-raft foundation. An initial design of the pile-raft foundation is made according to the traditional design method and an initial model is established. The load analysis of the pile-raft foundation is simulated by a computer, and cyclic optimization is carried out in combination with the settlement projection integral of the raft plate, so as to optimize the positioning of the foundation piles. The present invention can finely optimize the pile spacing between any two piles. During the optimization process, the pile-soil interaction and the influence of the nonlinear characteristics of the soil body can be considered, and the optimization result is more accurate. The application of the optimization method and the final achieved optimization efficiency are less affected by the superstructure and the load form.

Description

Technical Field

[0001] The present invention belongs to the field of optimized design of pile-raft foundations. This method realizes the automatic positioning of the optimal positions of each foundation pile through calculation to reduce the differential settlement of the pile-raft foundation. Background Art

[0002] As the preferred foundation type for important buildings such as high-rise buildings, nuclear power plants, and high-rise wind turbines, the pile foundation benefits from its advantages in controlling differential settlement, total settlement, and improving the bearing capacity of the foundation. Larger design loads or complex superstructures will make the foundation design more complex, and at the same time increase the scale of the foundation, and a large amount of resources need to be allocated to the foundation design and construction to meet the safety requirements. Therefore, it is necessary to optimize the design of the building foundation to achieve certain cost benefits.

[0003] Research shows that after the pile-raft foundation is optimized by changing the pile length, pile diameter, and pile spacing, its differential settlement can be reduced, and the loads on the tops of the foundation piles are also redistributed. Therefore, it is effective to realize the optimized design of the pile-raft foundation by changing the physical properties of the pile group itself. However, there are still certain limitations in the practicality of the existing pile-raft foundation optimized design methods and the stability of the optimization efficiency.

[0004] The difference between the optimized design of variable pile spacing and the traditional uniform pile layout design is that the spacing between each foundation pile in the pile group is not constant. The common optimized design of variable pile spacing is mostly variable pile spacing in different regions, and the pile spacing between different regions is different, but the pile spacing within the same region is the same. However, affected by the pile-soil interaction and the type of load, the loads borne by each foundation pile are not the same, indicating that there is still room for improvement in the existing variable pile spacing optimized design method. Therefore, the method of using refined variable pile spacing to achieve higher optimization efficiency needs further research. Summary of the Invention

[0005] Aiming at the problem that the loads borne by each foundation pile are not the same, resulting in different pile spacings between the foundation piles and the need for refined variable pile spacing to achieve higher optimization efficiency, the present invention proposes an automatic pile layout method for reducing the differential settlement of the pile-raft foundation. This method uses variable pile spacing for pile layout, positions each pile in an appropriate position, and specifically supports the differential settlement generated by the pile-raft foundation.

[0006] The specific technical solution adopted by the present invention to solve its technical problems is as follows: An automatic pile layout method for reducing the differential settlement of the pile-raft foundation, comprising:

[0007] Step 1: Make an initial design of the pile-raft foundation according to the traditional design method. The initial setting method does not consider the forces on the pile-raft and external factors, and adopts an equal-stiffness uniform pile layout method with equal pile length, pile diameter, and pile spacing to determine the basic parameters such as the number of foundation piles, pile diameter, pile spacing, pile length, and raft thickness.

[0008] Step 2: Perform 3D modeling on the pile-raft foundation according to the basic parameters in Step 1;

[0009] Step 3: Apply loads to the 3D model step by step for static analysis, and the applied loads are to simulate the stress conditions under the real situation of the pile-raft;

[0010] Step 4: Conduct finite element analysis on the 3D model with applied loads, and extract the settlement surface z(x, y) of the raft plate from the finite element analysis results;

[0011] Step 5: Project the settlement surface z onto the raft plate plane for integration to form the result V T , A raft is the area of the raft plate plane;

[0012]

[0013] Step 6: Divide V T into N equal parts along the horizontal plane according to the number of base piles (N), that is, the volume V i of each equal part is equal. Through the equal division formula

[0014]

[0015] Divide V T into equal parts according to the number of base piles, where i = 1, 2, 3,..., N; A i is the projected area of the i-th equal part V i on the raft plate plane; the centroid coordinates (x, y) of V i are the optimized positions of the i-th pile bearing this part of the settlement;

[0016] Step 7: Perform 3D modeling according to the positions of the base piles obtained in Step 6, and repeat Steps 3 to 6 until the optimization goal is achieved.

[0017] Based on the above method, in the present invention, the loads applied in Step 3 adopt the Duncan-Chang E-v constitutive model to consider the nonlinearity of the soil body, the non-uniform characteristics of the soil layer, and the pile-soil-raft interaction, and fully refer to the stress conditions of the pile-raft in actual applications.

[0018] In Step 5, a discrete function is selected to represent the raft plate settlement surface, and the discrete settlement surface is fully refined by the interpolation function. After refinement, the raft plate settlement surface finally forms a two-dimensional surface composed of N t nodes, and these nodes are evenly distributed along the raft plate plane.

[0019] At the same time, in the present invention, the central netting search method (CNSM) is adopted in Step 6, and the central netting search method is specifically used for V TEqual division is carried out, and the discrete function refines the raft settlement surface into N t nodes. The calculation process of the Central Net Search Method (CNSM) includes:

[0020] Step 1, select a point from the N t nodes as the fixed point (P fix );

[0021] Step 2, select the point whose projection of the connection line with P fix on the raft plane is the longest as the center point P i ;

[0022] Step 3, always select the point j (sub-point P i ) closest to P j ), and continuously superimpose the corresponding v j onto v i until v i +v1+v2+…+v j ≥V avg , where V avg represents the average value after dividing V T into N equal parts, and then stop superimposing;

[0023] Step 4, delete all the selected center points and sub-points;

[0024] Step 5, repeat Steps 2 - 4 until all nodes are deleted.

[0025] Advantages of the present invention: 1) It can be finely optimized to the pile spacing between any two piles; 2) The pile - soil interaction and the influence of the non - linear characteristics of the soil body can be considered during the optimization process, and the optimization result is more accurate; 3) The application of the optimization method and the final achieved optimization efficiency are less affected by the superstructure and the load form. Description of the Drawings

[0026] Figure 1 Schematic diagram of the Central Net Search Method (CNSM).

[0027] Figure 2 Load distribution diagram on the top surface of the raft. Detailed Embodiment

[0028] The present invention will be further described below in conjunction with the drawings and embodiments.

[0029] Embodiment 1: The purpose of the present invention is to propose an automatic pile layout method for reducing the uneven settlement of the pile - raft foundation. This method uses variable pile spacing for pile layout, positions each pile at an appropriate location, and specifically supports the uneven settlement generated by the pile - raft foundation. The specific technical solution is as follows:

[0030] The pile-raft foundation is initially designed according to the "Technical Code for Building Pile Foundations" using the traditional design method (equal pile diameter, pile spacing, and pile length). The initial design does not consider the stress state of the pile-raft, but only makes an equal distribution based on the number of pile-rafts. That is, when keeping the pile length, pile diameter, and pile spacing equal, the pile-raft steel is uniformly distributed according to the area of pile layout. Based on the initial setting scheme, basic parameters such as the number of foundation piles, pile diameter, pile spacing, pile length, and raft thickness are determined. The ANSYS finite element analysis software is used to perform 3D modeling on the pile-raft foundation according to the initial design scheme, and static analysis is carried out on the model by applying loads step by step. The settlement surface z(x,y) of the raft in the finite element analysis results of the initial design scheme is extracted, and integration is performed on the raft plane to form the result V T , as shown in Equation (1); for V T make a "suitable" equal division according to the number of foundation piles. Taking the total number of foundation piles N as an example, that is, V1 = V2… = V N , as shown in Equation (2); the centroid of each divided part of the volume V i is the position of the foundation pile responsible for the settlement of this part.

[0031]

[0032]

[0033] In the formula, i = 1, 2, 3, …, N; A i is the projected area of the i-th divided block V i on the raft plane; the centroid coordinates (x, y) of V i are the optimized position of the i-th pile responsible for the settlement of this part; A raft is the area of the raft plane; A i is the projected area of V i on the raft plane; the coordinates of the centroid of V i on the raft plane are the position of pile i.

[0034] Solutions to several core problems of this scheme:

[0035] (1) Calculate V T

[0036] The x, y, and z corresponding to each node are represented by matrices [X], [Y], and [Z], where [X] and [Y] represent the x and y coordinates of the node, and [Z] represents the settlement z corresponding to this node. The raft settlement surface finally forms a two-dimensional surface composed of N t nodes, and these nodes are evenly distributed along the raft plane. Assuming that the raft area supported by each node is the same, which is represented by a0, then a0 = A raft / N t . Finally, V can be obtained according to the integral solution method of the discrete function T, such as Equation (3):

[0037]

[0038] V i = V avg = V T / N, i = 1, 2, 3...N (4)

[0039] In the formula, Z j is the settlement of node j in the matrix [Z]; v j represents the volume corresponding to the area of the raft supported by node j. Each part after dividing V T equally can be expressed as V i , as shown in Equation (4), V avg represents the average value after dividing V T equally into N parts.

[0040] (2) Divide V T

[0041] When dividing V T equally, three conditions need to be met: 1) There should be no overlap between the obtained centroids; 2) The distance between any two centroids should not be too small (meeting the requirement of the minimum pile spacing in the specification); 3) The dimensions of V i in the x-direction and y-direction should not differ too much.

[0042] (3) Determine the centroid coordinates of V i The V

[0043] corresponding to pile i is represented by a discrete function as follows: i In the formula, N

[0044]

[0045] is the sum of all sub-points included in V i corresponding to the center point P i ; Z i is the value corresponding to point j in the matrix [Z]. Then, according to the volume centroid solution formula, we can obtain: j In the formula, X

[0046]

[0047]

[0048] is the value corresponding to point j in the matrices [X] and [Y] respectively. The matrix forms of Equations (6) and (7) are: j and Y j

[0049]

[0050] ​

[0051] Finally, (x ic , y ic ) is the optimized coordinate of the i-th pile.

[0052] (4) Optimization iteration

[0053] Extract the new raft settlement surface obtained from the calculation and analysis of the optimization scheme, and discretize it using the same interpolation points as in the initial design. The node information [X], [Y] is the same as in the initial design, and only the settlement is different, which is represented as the matrix [Z]. m . [Z] m Subtract each element in [Z] m by the element with the minimum value to form a new matrix [Z] m '(differential settlement matrix). Add [Z] m ' to the previously extracted [Z]. The resulting new raft settlement surface is used for the next round of optimization design, as follows:

[0054] [Z] = [Z]′ m + [Z] (10)

[0055] Repeat this loop, accumulating the new [[Z] m ' obtained from each optimization design until the optimization goal is met.

[0056] (5) Objective function

[0057] The optimization goal of the optimization design method proposed in this paper is to minimize the differential settlement of the pile-raft foundation, that is:

[0058] Minimize ΔS = S max -S min (11)

[0059] where S max and S min are the maximum and minimum settlements of the raft respectively; ΔS is the differential settlement of the raft.

[0060] (6) Constraint conditions

[0061] 1) The minimum pile spacing is not less than 2 times the pile diameter, otherwise stop the optimization.

[0062] 2) The maximum load on the pile top (P max ) does not exceed the ultimate bearing capacity of a single pile (P u ), otherwise increase the number of piles N and recalculate this iteration until P max ≤P u .

[0063] 3) When the increment of the differential settlement (ΔS) optimization rate FF is less than 5%, the optimization result tends to be stable and the optimization stops. The calculation method of FF is as follows:

[0064]

[0065] In the formula, R and R' respectively represent the calculation results in the initial design and the optimized design models, and here they represent the differential settlement.

[0066] As Figure 2 shown, for the rectangular pile-raft foundation, uniform loads (P1 = P2) and non-uniform loads (P1 ≠ P2) act on the top respectively.

[0067] (1) Conduct initial designs for two schemes with different loads. The pile diameter is d, the pile length is L, the pile spacing is 3d, and the number of foundation piles is N.

[0068] (2) Use ANSYS to establish a three-dimensional solid model of the pile-raft foundation.

[0069] (3) Divide the surface load on the raft into m steps. The first load step (i = 1) is the self-weight of the soil layer, and the remaining m - 1 load steps are the upper loads equally divided into m - 1 parts and applied gradually.

[0070] (4) Extract the information (x, y, and z) of all nodes on the top surface of the raft in the initial design result to EXCEL and import it into MATLB.

[0071] (5) Use MATLAB to discretize and refine the data (x, y, and z) of the two schemes to form new node information: [X], [Y], and [Z], where [X] and [Y] respectively represent the x and y coordinates of the discrete points, and [Z] represents the settlement of the discrete points.

[0072] (6) Use CNSM to obtain the optimized position of each pile, re-model and calculate according to the new pile layout scheme, and repeat (2) to (6) until the optimization ends.

[0073] (7) In Case 1, after 2 optimization cycles, the differential settlement of the raft decreases from 0.011 m to 0.0018 m, a decrease of 83%; in Case 2, after 2 optimization cycles, the differential settlement of the raft decreases from 0.024 m to 0.0022 m, a decrease of 91%.

[0074] (8) Finally, the variation range of the pile spacing obtained after optimization for Case 1 is 3.7 m to 5 m, and that for Case 2 is 3 m to 5.3 m.

[0075] Embodiment 2: On the basis of Embodiment 1, the present invention adopts the Duncan-Chang E-v constitutive model to consider the nonlinear characteristics of the soil mass and the uneven characteristics of the soil layer as well as the pile-soil-raft interaction. This model can fully realize the actual stress conditions of the raft and the foundation piles. Through detailed and sufficient load application, the actual stress conditions of the raft and the foundation piles are shown as much as possible, and the settlement of the raft and the foundation piles under the real environment is simulated.

[0076] Thus, a real settlement surface is obtained, providing effective data for the subsequent calculation of the foundation pile positions.

[0077] Embodiment 3: Further, considering that the settlement surface of the raft in the initial design result is difficult to be represented by a continuous function and thus difficult to achieve integration, this study chooses to represent the settlement surface of the raft with a discrete function and fully refine this discrete settlement surface with the interpolation function in MATLAB.

[0078] Embodiment 4: The present invention proposes a Central Net Search Method (CNSM) specifically used for T equally dividing, and the discrete function refines the settlement surface of the raft into N t nodes.

[0079] There are two key points in the CNSM method: one is the central point (P i ), and the other is the fixed point (P fix ). The usage steps of this method are as follows: Step 1, select a point from the N t nodes as the fixed point (P fix ).

[0080] Step 2, select the point whose projection of the connection line with P fix on the raft plane is the longest as the central point P i .

[0081] Step 3, always select the point j (sub-point P i ) closest to P j , and continuously superimpose the corresponding v j onto v i until v i +v1+v2+…+v j ≥V avg , where V avg represents the average value after equally dividing V T into N parts, and then stop the superposition.

[0082] Step 4, delete all the selected central points and sub-points. Step 5, repeat Steps 2 - 4 until all nodes are deleted, as Figure 1 shown.

[0083]

[0084] If there is more than one sub - point with an equal distance to P i then the point with a smaller parameter H ij (such as in formula (5)) is preferentially selected for superposition. If there is H ij = H ik , then the point with a smaller x is preferentially selected for superposition, where j and k are any points in [Z] other than i.

[0085] P fix should be as far as possible from less - core positions such as the corners or edges of the raft. For example, positions close to the center of the raft or the maximum settlement of the raft (provided that this position is not close to the edge or corner of the raft).

[0086] It should be understood that the above - mentioned specific embodiments of the present invention are only used for exemplary illustration or explanation of the principle of the present invention, and do not constitute a limitation to the present invention. Therefore, any modifications, equivalent replacements, improvements, etc. made without departing from the spirit and scope of the present invention shall be included within the protection scope of the present invention. In addition, the appended claims of the present invention are intended to cover all changes and modification examples falling within the scope and boundaries of the appended claims, or equivalent forms of such scope and boundaries.

Claims

1. An automatic pile layout method for reducing differential settlement of pile-raft foundations, characterized in that, It includes Step 1: making an initial design of the pile-raft foundation according to the traditional design method to determine the basic parameters of the number of foundation piles, pile diameter, pile spacing, pile length and raft thickness; Step 2: performing 3D modeling on the pile-raft foundation according to the basic parameters in Step 1; Step 3: applying loads to the 3D model step by step and performing static analysis. The surface load on the raft is divided into m steps. The first load step i = 1 is the self-weight of the soil layer, and the remaining m - 1 load steps are the upper loads equally divided into m - 1 parts and applied gradually; Step 4: performing finite element analysis on the 3D model with loads applied, and extracting the settlement surface z(x, y) of the raft from the finite element analysis results; Step 5: Project the settlement surface z onto the raft plane for integration to form the result V T , A raft is the area of the raft plane ； using a discrete function to represent the raft settlement surface instead of a continuous function, and fully refining the discrete settlement surface with an interpolation function; Step Six: Divide V according to the number of foundation piles N T into N equal parts along the horizontal plane, that is, the volume V of each equal part i is equal. Among them, the Central Net Search Method (CNSM) is used specifically for dividing V T into equal parts. The discrete function refines the raft settlement surface into N t nodes. The Central Net Search Method (CNSM) includes: Step 1, select a point from N t nodes as the fixed point P fix ; Step 2, select the point that has the longest projection of the connection line with P fix on the raft slab plane as the center point P i ; Step 3: Always select the sub-point P i closest to P j and the corresponding v j and continuously superimpose it on v i until v i + v1 + v2 + … + v j ≥ V avg , where V avg represents the average value after dividing V T into N equal parts, and stop superimposing; In Step 4, all the selected center points and sub-points are deleted; In Step 5, repeat Steps 2 - 4 until all nodes are deleted; The equal division formula is as follows, ； where \(i = 1, 2, 3, \cdots, N\); \(A\) i is the projected area of the \(i\)-th equal division block \(V\) i on the raft slab plane; the centroid coordinates \((x, y)\) of \(V\) i are the optimized positions of the \(i\)-th pile that bears the settlement of this part. Step 7: re-performing 3D modeling according to the pile positions obtained in Step 6, and repeating Steps 3 to 6 to continuously optimize the pile positions until the optimization goal is met.

2. The automatic pile layout method for reducing the differential settlement of a pile-raft foundation according to claim 1, wherein In Step 3, the Duncan-Chang E-v constitutive model is used to apply loads, considering the nonlinearity of the soil body, the uneven characteristics of the soil layer and the pile-soil-raft interaction.

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