Method and system for acquiring internal force of double-row anti-slide piles

Abstract

The invention discloses a double-row anti-slide pile internal force obtaining method and system, and relates to the field of geotechnical engineering.The double-row anti-slide pile internal force obtaining method comprises the steps that indoor experiments are conducted on pile top displacement, pile periphery soil pressure distribution and pile body bending moment and shearing force distribution of a coupling-beam-free double-row anti-slide pile, and the stress characteristics and deformation characteristics of the coupling-beam-free double-row anti-slide pile are obtained; constructing a coupling-beam-free double-row anti-slide pile internal force calculation model; an anti-slide pile is simplified into an elastic foundation beam with a fixed range above a slide surface as a directional support, a pile structure is divided into a load-bearing section and a load-bearing section-built-in section from the directional support, and the internal force of the coupling-beam-free double-row anti-slide pile is determined; the stress and deformation characteristics of the coupling-beam-free double-row anti-slide pile are input into the coupling-beam-free double-row anti-slide pile internal force calculation model, and the internal force of the whole pile body of the coupling-beam-free double-row anti-slide pile is accurately obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of geotechnical engineering, and in particular to a method and system for obtaining internal forces of double-row anti-slide piles. Background Art

[0002] Double-row anti-slide piles refer to a retaining structure in which two rows of piles are set at different heights of the landslide body, with a small distance between the piles. The piles interact with each other to resist the deformation of the slope body

[13] . The pile tops are not connected or connected by connecting beams, caps, etc. According to the different structural forms, double-row anti-slide piles can be divided into two types: double-row piles with connecting beams and double-row piles without connecting beams. Double-row piles with connecting beams include gate-type double-row piles (i.e., piles with connecting beams at the top) and H-type anti-slide piles (with connecting beams in the middle). Double-row piles with connecting beams have the advantages of less space occupation, good integrity, high anti-lateral stiffness, and good synergy; double-row anti-slide piles without connecting beams have the advantages of simple construction, short construction period, economical and practical, and easy promotion. Both have been widely used in engineering.

[0003] At present, the research content of double-row anti-sliding piles mainly focuses on the study of soil arching effect, the study of internal force calculation model, and the influence of parameters such as pile spacing on the stress and deformation of double-row anti-sliding piles. The research methods mainly include theoretical research, numerical analysis and model test research. The three methods have their own advantages and disadvantages: theoretical research has problems such as unclear pile-soil interaction and the interaction mechanism between piles and soil, and it is difficult to select theoretical analysis models. It is necessary to conduct a deeper study on more accurate calculation models; although numerical analysis and simulation solve some problems by considering the interaction between piles and soil, in the simulation process, the selection of calculation parameters is often affected by experience, resulting in differences between different research results. Its advantages are saving research costs and facilitating comparative analysis of multiple groups of tests or repeated tests to explore regularity in depth; model tests are time-consuming, labor-intensive and costly. Due to the size effect, there are certain differences from the actual stress state of anti-sliding piles. In addition, similar experiments are difficult to conduct, which has certain limitations. However, model tests are simpler than on-site monitoring and more in line with actual conditions than numerical simulations.

[0004] Although double-row anti-slide piles have been widely used in engineering practice, there are still some problems in their research and design. The main problems include: in actual engineering, when determining the soil resistance in front of the piles, the internal force design calculation of double-row anti-slide piles often does not take into account the soil resistance in front of the piles, resulting in the failure to fully exert the anti-slide effect; in addition, there is a lack of unified standards for the distribution of landslide thrust, and the thrust distribution of the front and rear rows of anti-slide piles is also relatively complicated; in addition, when studying the internal force distribution and deformation of double-row anti-slide piles, most of them are based on numerical simulation, and the simulation results will be affected to a certain extent by the selected parameters, etc. The above factors will affect the accuracy of the internal force of the double-row anti-slide piles. Summary of the invention

[0005] The present invention provides a method and system for obtaining the internal forces of double-row anti-slide piles to solve the above problems existing in the prior art, that is, the problem of how to improve the accuracy of obtaining the internal forces of double-row anti-slide piles in the prior art. The present invention provides a method for obtaining the internal forces of double-row anti-slide piles, and the method includes:

[0006] Conduct indoor experiments on the pile top displacement, pile surrounding soil pressure distribution, pile body moment and shear force distribution of double-row anti-slide piles without connecting beams to obtain the force characteristics and deformation characteristics of double-row anti-slide piles without connecting beams;

[0007] Construct an internal force calculation model for double-row anti-slide piles without connecting beams; by simplifying the anti-slide piles into elastic foundation beams with a fixed range above the slip surface as directional supports, splitting the pile structure into two parts, namely the loaded section and the loaded section - embedded section, from the directional support, to determine the internal forces of double-row anti-slide piles without connecting beams;

[0008] Input the force and deformation characteristics of double-row anti-slide piles without connecting beams into the internal force calculation model of double-row anti-slide piles without connecting beams to obtain the internal forces of the entire pile body of double-row anti-slide piles without connecting beams.

[0009] Optionally, the splitting the pile structure into two parts, namely the loaded section and the loaded section - embedded section, from the directional support to determine the internal forces of double-row anti-slide piles without connecting beams specifically includes:

[0010] Split the pile structure into two parts, namely the loaded section and the loaded section - embedded section, from the directional support, and respectively obtain the internal forces of the loaded sections of the front and rear rows of anti-slide piles by using the cantilever pile method; wherein, the internal forces of the loaded section include the shear force of the loaded section and the moment of the loaded section;

[0011] Based on the finite difference method, respectively obtain the flexural differential equations of the internal forces of the loaded section - embedded section of the front and rear rows of anti-slide piles, and combine the boundary conditions of the pile top and pile bottom of the front and rear rows of piles to obtain the internal forces of the loaded section - embedded section of the front and rear rows of anti-slide piles:

[0012] According to the internal forces of the loaded sections of the front and rear rows of anti-slide piles and the internal forces of the loaded section - embedded section, obtain the internal forces of double-row anti-slide piles without connecting beams.

[0013] Optionally, the based on the finite difference method, respectively obtaining the flexural differential equations of the internal forces of the loaded section - embedded section of the front and rear rows of anti-slide piles specifically includes:

[0014] Use the following formula to obtain the flexural differential control equation of the loaded section - embedded section of double-row anti-slide piles:

[0015]

[0016] Among them, EI represents the stiffness of the double-row anti-slide pile structure; B0 represents the calculated width of the pile; K(z) represents the foundation coefficient, and K(z) = mz; m represents the proportional coefficient of the foundation coefficient varying with depth; y represents the horizontal displacement of the pile body; z represents the distance from the pile top; q(z) represents the landslide thrust.

[0017] Optionally, the boundary conditions at the pile tops and pile bottoms of the front and rear rows of piles specifically include:

[0018] When subjected to the shear force and bending moment transmitted by the top beam of the pile, the boundary condition at the top of the front row of piles is:

[0019]

[0020] The boundary condition at the top of the rear row of piles is:

[0021]

[0022] When not subjected to the shear force and bending moment transmitted by the top beam of the pile, the boundary condition at the top of the front row of piles is:

[0023]

[0024] The boundary condition at the top of the rear row of piles is:

[0025]

[0026] Assuming the bottom of the elastic double-row pile is a free end, the bending moment and shear force at the pile bottom are zero, and the boundary condition at the bottom of the front row of piles is:

[0027]

[0028] The boundary condition at the bottom of the rear row of piles is:

[0029]

[0030] Among them, M b is the bending moment transmitted by the top beam at the top of the front row of piles, M a is the bending moment transmitted by the top beam at the top of the rear row of piles, Q b is the shear force transmitted by the top beam at the top of the front row of piles, Q a is the shear force transmitted by the top beam at the top of the rear row of piles, n is the node number, and y is the horizontal displacement of the pile body

[0031] The present invention provides a system for obtaining the internal forces of a double-row anti-slide pile, including:

[0032] An acquisition module, which is used to conduct indoor experiments on the pile top displacement, pile surrounding soil pressure distribution, pile body bending moment and shear force distribution of a double-row anti-slide pile without a top beam, and obtain the force characteristics and deformation characteristics of the double-row anti-slide pile without a top beam;

[0033] A building module for building an internal force calculation model of a double-row anti-slide pile without a connecting beam; by simplifying the anti-slide pile into an elastic foundation beam with a fixed range above the sliding surface as a directional support, the pile structure is split into a loaded section and a loaded section - embedded section from the directional support to determine the internal force of the double-row anti-slide pile without a connecting beam.

[0034] A determination module for inputting the force and deformation characteristics of the double-row anti-slide pile without a connecting beam into the internal force calculation model of the double-row anti-slide pile without a connecting beam to obtain the internal force of the entire pile body of the double-row anti-slide pile without a connecting beam.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention provides a method for obtaining the internal force of a double-row anti-slide pile. Through the indoor model test of the double-row anti-slide pile without a connecting beam, data such as the pile top displacement, the earth pressure before and behind the pile, and the pile body strain under the load of the anti-slide pile are obtained through real-time monitoring, and the force law and failure mode of the double-row anti-slide pile can be determined; on the basis of the test data and result analysis of the indoor experiment, by simplifying the anti-slide pile without a connecting beam into a two-section structure separated at the directional support, the internal force of the loaded section is obtained by using the cantilever pile method respectively, and the deflection differential equation of the internal force of the loaded section - embedded section is obtained by using the finite difference method respectively, and then the internal force of the double-row anti-slide pile without a connecting beam is obtained. Description of the Drawings

[0036] The drawings here are incorporated into the specification and form a part of this specification, showing the embodiments in line with the present invention, and are used together with the specification to explain the principles of the present invention.

[0037] Figure 1 It is a flowchart of a method for obtaining the internal force of a double-row anti-slide pile provided by an embodiment of the present invention;

[0038] Figure 2 It is the pile top displacement curve of the double-row anti-slide pile without a connecting beam provided by an embodiment of the present invention;

[0039] Figure 3 It is the distribution diagram of the earth pressure around the pile of the double-row anti-slide pile without a connecting beam provided by an embodiment of the present invention;

[0040] Figure 4 It is the thrust sharing ratio of the front and rear row piles of the double-row anti-slide pile without a connecting beam provided by an embodiment of the present invention;

[0041] Figure 5 It is the earth pressure behind - in front of the pile of the double-row anti-slide pile without a connecting beam provided by an embodiment of the present invention;

[0042] Figure 6 It is the force model of the double-row anti-slide pile with a connecting beam provided by an embodiment of the present invention;

[0043] Figure 7 It is the force decomposition schematic diagram of the double-row anti-slide pile with a connecting beam provided by an embodiment of the present invention;

[0044] Figure 8 It is the flexure of the pile body with coupling beams and its differential point diagram provided by the embodiment of the present invention;

[0045] Figure 9 It is the force diagram of the loaded section of the anti-slide pile without coupling beams provided by the embodiment of the present invention;

[0046] Figure 10 It is the force diagram of the loaded section - embedded section of the rear row pile without coupling beams provided by the embodiment of the present invention;

[0047] Figure 11 It is the differential point diagram of the loaded section - embedded section of the anti-slide pile without coupling beams provided by the embodiment of the present invention;

[0048] Figure 12 It is the bending moment comparison diagram of the double-row anti-slide piles provided by the embodiment of the present invention. Detailed implementation manners

[0049] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts shall fall within the protection scope of the present invention.

[0050] First, the terms related to the present invention are explained:

[0051] Double-row anti-slide piles: It refers to a retaining structure that sets two rows of piles at different heights of the landslide body, with a small pile spacing, and the piles in the rows interact with each other to jointly resist the deformation of the slope body. According to different structural forms, it can be divided into two forms: double-row piles with coupling beams and double-row piles without coupling beams. The double-row piles with coupling beams include portal double-row piles (with a coupling beam at the pile top) and H-shaped anti-slide piles (with a coupling beam in the middle), and the double-row piles without coupling beams have the advantages of simple construction, short construction period, economy and practicality.

[0052] Next, the technical solutions of the present invention and how the technical solutions of the present invention solve the above technical problems are described in detail with specific embodiments. These several specific embodiments below can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. The embodiments of the present invention will be described below with reference to the accompanying drawings.

[0053] Figure 1 It is the technical roadmap of a method for obtaining the internal forces of double-row anti-slide piles provided by the embodiment of the present invention. As Figure 1 shown, a method for obtaining the internal forces of double-row anti-slide piles shown in this embodiment includes:

[0054] S1: Conduct indoor experiments on the pile top displacement, pile - surrounding soil pressure distribution, pile body moment and shear force distribution of a double - row anti - slide pile without a connecting beam to obtain the mechanical characteristics and deformation characteristics of the double - row anti - slide pile without a connecting beam.

[0055] S2: Construct an internal force calculation model for the double - row anti - slide pile without a connecting beam; by simplifying the anti - slide pile into an elastic foundation beam with a fixed range above the slip surface as a directional support, split the pile structure into a loaded section and a loaded - embedded section from the directional support to determine the internal force of the double - row anti - slide pile without a connecting beam.

[0056] S3: Input the mechanical and deformation characteristics of the double - row anti - slide pile without a connecting beam into the internal force calculation model of the double - row anti - slide pile without a connecting beam to obtain the internal force of the entire pile body of the double - row anti - slide pile without a connecting beam.

[0057] Exemplarily, measure data such as pile top displacement, pile body strain and pile - between soil pressure distribution through displacement gauges, earth pressure cells and strain gauges, and study the soil pressure distribution form of the double - row anti - slide pile and the thrust distribution of the front and rear row anti - slide piles under the action of landslide thrust; in this embodiment, the test results of the double - row anti - slide pile without a connecting beam are mainly analyzed.

[0058] As Figure 2 shown, it is the pile top displacement curve obtained from the test. By analyzing the pile top displacement data of the double - row anti - slide pile, it can be known that when the anti - slide pile plays its role in slope stabilization and retaining, it includes three deformation stages: elastic deformation, accelerated deformation and failure stage; by analyzing the pile - surrounding soil pressure of the anti - slide pile before pile body failure, the change trends of the landslide thrust behind the pile and the soil resistance in front of the pile on the front and rear row piles under different loads can be obtained. Figure 3 Shown is the pile - surrounding soil pressure change curve of the middle - group piles in this test. It can be seen that the pile - surrounding soil pressure distributions of the front and rear row piles are not exactly the same. Generally speaking, from the distribution of soil pressure in front of and behind the pile, the soil pressure behind the front and rear row piles is similar to a parabola - triangle distribution, and the soil pressure in front of the pile is slightly different for the two. The rear row pile is in a parabola - triangle distribution, and the front row pile is overall in a parabolic shape. Looking at the loaded section above the slip surface, the soil pressure in front of the rear row pile and behind the front row pile is in a parabolic shape, while the soil pressure behind the rear row pile and in front of the front row pile is in a triangular distribution. The thrust values behind the front and rear row piles differ greatly, and the ratio of the soil pressure behind the pile is about 1:0.6. The thrust ratio of the A and B row piles in the middle group is as follows Figure 4 shown. Then, in the design, the double - row anti - slide pile without a connecting beam is considered as two single - row piles, and it is safer when the thrust sharing ratio is between 1.4 - 1.9.

[0059] Exemplarily, according to the distribution of the pile - surrounding soil pressure of the double - row anti - slide pile, subtract the soil pressure in front of the pile from the soil pressure behind the pile to approximately obtain the change curve of the theoretically shear force of the pile body as Figure 5 shown. In this embodiment, the shear force value is used to replace the soil pressure behind the pile minus the soil pressure in front of the pile. Figure 5Figure (a) is the variation diagram of the earth pressure behind the rear row of piles - the earth pressure in front of the piles with the pile depth, Figure 5 Figure (b) is the variation diagram of the earth pressure behind the front row of piles - the earth pressure in front of the piles with the pile depth. The variation of the shear force of the front row of piles and the rear row of piles with the pile depth shows a positive - negative - positive - negative continuous parabolic distribution, and the maximum values of the shear forces of the front row of piles and the rear row of piles both appear near the slip surface of their pile bodies. When analyzing the earth pressure behind the piles - the earth pressure in front of the piles, it is found that the shear force is zero at a certain position above the slip surface. The shear force values of the pile body above this position fluctuate less, and the bending moment change is not obvious. Therefore, it is considered to be simplified as a directional support in the design calculation.

[0060] Exemplarily, an internal force calculation model of a double - row anti - slide pile with a connecting beam is constructed; by simplifying the double - row anti - slide pile structure with a connecting beam into two single - pile structures disconnected at the zero - moment point of the connecting beam on the pile top, based on the finite - difference method, the deflection differential equations of the front row of piles and the rear row of piles are constructed; according to the deflection differential equations of the front row of piles and the rear row of piles, the front row of piles and the rear row of piles are divided into several nodes, and the difference equations of each node of the front row of piles and the rear row of piles are established. According to the difference equations of each node of the front row of piles and the rear row of piles, combined with the boundary conditions of the pile top and the pile bottom of the front row of piles and the rear row of piles, the internal force distribution of each node of the front row of piles and the rear row of piles is obtained. According to the internal force distribution of each node of the front row of piles and the rear row of piles, the internal force of the front row of piles and the rear row of piles with a connecting beam is obtained; the force - bearing characteristics and deformation characteristics of the double - row anti - slide pile with a connecting beam are input into the internal force calculation model of the double - row anti - slide pile with a connecting beam to obtain the internal force of the pile body of the double - row anti - slide pile with a connecting beam.

[0061] As Figure 6 shown, in the present invention, by regarding the front row of piles and the rear row of piles as two single - pile structures disconnected at the zero - moment point of the connecting beam, the internal forces are calculated separately. M b and M a respectively represent the bending moment at the pile top of the front row of piles and the bending moment at the pile top of the rear row of piles, and Q b and Q a respectively represent the shear force at the pile top of the front row of piles and the shear force at the pile top of the rear row of piles. According to the static equilibrium condition, it can be known that:

[0062] Q a +Q b =0(2.1)

[0063] Assume that the bending moment is positive when the rear of the double - row piles is in tension, and the shear force is positive along the positive y - axis. The double - row piles with a connecting beam are simplified into two single - pile structures with bending moments and shear forces acting on the pile tops of the front row of piles and the rear row of piles for the full - pile difference calculation. The bending moment M j and the shear force Q j at the pile top are determined by the principle of superposition of forces, Figure 7 is the force decomposition diagram. According to the superposition principle of linear elastic bodies, the forces on the double - row anti - slide pile with a connecting beam are considered by superposing the landslide thrust and soil resistance acting on the elastic foundation beam, the shear force transmitted at the connecting beam on the pile top, and the bending moment at the pile top in three cases. The deflections at the pile top in the above three cases are respectively yj1 , y j2 , y j3 , with the corner angle being φ j1 , φ j2 and φ j3 (where j = a is the rear row of piles and j = b is the front row of piles).

[0064] The shear force Q b , Q a and the bending moment M b , M a When acting separately, the deflection and corner angle of the pile top are calculated according to the following formula:

[0065]

[0066] In the formula, EI is the stiffness of the double - row anti - slide pile structure; H is the length of the rear row of piles, m; y j2 and φ j2 are respectively the deflection and corner angle of the pile top when the shear force Q j acts alone; y j3 and φ j3 are respectively the deflection and corner angle of the pile top when the bending moment M j acts alone (where j = a is the rear row of piles and j = b is the front row of piles). The boundary conditions for the equal horizontal displacement and zero corner angle of the pile tops of the front and rear rows of piles are:

[0067]

[0068] Substitute Equation (2.2) into Equation (2.3) and combine with Equation (2.1) to obtain the bending moment and shear force transmitted at the pile top continuous beam:

[0069]

[0070]

[0071] Based on the Winkler elastic foundation beam theory, the differential control equations for the flexure of the loaded section and the embedded section of the double - row anti - slide piles can be expressed as:

[0072]

[0073] Among them, EI represents the stiffness of the double - row anti - slide pile structure; B0 represents the calculated width of the pile, m; K(z) represents the foundation coefficient; y represents the horizontal displacement of the pile body, m; z represents the distance from the pile top, m; q(z) represents the landslide thrust, kN / m.

[0074] Exemplarily, the commonly used "m - method" can be used for calculation, K(z)=mz; where m represents the proportional coefficient of the foundation coefficient varying with depth, kN / m 4 ; Taking the rear row of piles as an example, the pile body flexure and differential points are shown inFigure 8 According to the finite difference theory, the rear row of piles is evenly discretized into n segments, each segment having a length of h. The numbers from the top to the bottom of the rear row of piles are -2, -1, 0... n, n + 1, n + 2, a total of n + 5 nodes, where -2, -1, n + 1, n + 2 are virtual nodes; the top node of the pile is numbered 0, and the bottom of the pile is numbered n; the node number at the sliding surface is l. The front row of piles and the rear row of piles adopt the same equal-segmentation method, and the difference equations at any node of the front and rear rows of piles can be obtained as follows:

[0075] Front row of piles:

[0076]

[0077] Rear row of piles:

[0078]

[0079] For the double-row anti-slide piles with a connecting beam, due to the existence of the connecting beam, the bending moments and shear forces at the tops of the front and rear rows of piles are not zero. In the simplified model of the present invention, the connecting beam is simplified to the bending moments M b 、M a acting on the tops of the front and rear rows of piles and the shear forces Q b 、Q a . The boundary conditions at the tops of the anti-slide piles are as follows:

[0080] Front row of piles:

[0081]

[0082] Rear row of piles:

[0083]

[0084] In the formula, M b is the bending moment transmitted by the connecting beam at the top of the front row of piles; M a is the bending moment transmitted by the connecting beam at the top of the rear row of piles; Q b is the shear force transmitted by the connecting beam at the top of the front row of piles; Q a is the shear force transmitted by the connecting beam at the top of the rear row of piles.

[0085] When the anti-slide pile is force-decomposed as shown in Figure 2 and is not subjected to the shear force and bending moment transmitted by the pile-top connecting beam (i.e., the shear force and bending moment at the pile top are zero), the boundary conditions at the pile top are:

[0086] Front row of piles:

[0087]

[0088] Rear row of piles:

[0089]

[0090] Assume that the bottom of the elastic double-row piles is a free end, then the bending moment and shear force at the pile bottom are zero. The pile bottom boundary conditions are:

[0091] The front-row piles:

[0092]

[0093] The rear-row piles:

[0094]

[0095] According to the differential equations of the front-row and rear-row pile bodies and combined with the 4 boundary conditions at the pile top and pile end, the horizontal displacement y at each node of the pile body can be solved. i Let The full-pile matrix linear equations of the rear-row piles can be obtained:

[0096] [A i [Y i =[Q i (2.15)

[0097] In the formula, [A i is the coefficient matrix; [Y i is the pile body displacement matrix; [Q i is the load matrix; among them:

[0098]

[0099] [Y i =[y -1 y -2 y0 … y l … y n-1 y n y n+1 y n+2 T (2.17)

[0100]

[0101] When the shear force and bending moment at the pile top are zero, the load matrix is:

[0102]

[0103] Substitute equations (2.16), (2.17), and (2.18) into equation (2.15), so as to establish a unified linear equation for the deformation of the loaded section and the embedded section of the rear-row piles, and solve the displacement of the whole pile according to equation (2.19).

[0104] Similarly, substitute equations (2.16), (2.17), and (2.19) into equation (2.15) to obtain equation (2.21).​

[0105]

[0106] Where Ma and Qa are obtained through Equation (2.4), and finally the internal force of the rear row of piles is obtained through Equation (2.20).

[0107] And the internal force and rotation angle are solved by combining the difference formula (2.22).

[0108]

[0109] In this embodiment, mat lab can be used to solve the internal force and displacement of the entire pile of the double-row piles, which greatly improves the calculation efficiency; and through the structural model test of the double-row anti-slide piles with connecting beams, the accuracy of the calculation results of the method of the present invention is verified. The results show that the finite difference calculation results of the double-row piles are in good agreement with the test results as a whole.

[0110] Optionally, the pile structure is split into a loaded section and a loaded section - embedded section from the directional support to determine the internal force of the double-row anti-slide piles without connecting beams. Specifically, it includes splitting the pile structure into a loaded section and a loaded section - embedded section from the directional support, and respectively obtaining the internal forces of the loaded sections of the front and rear rows of anti-slide piles by using the cantilever pile method; wherein, the internal force of the loaded section includes the shear force of the loaded section and the bending moment of the loaded section; based on the finite difference method, the deflection differential equations of the internal forces of the loaded section - embedded section of the front and rear rows of anti-slide piles are respectively obtained, and combined with the boundary conditions at the top and bottom of the front and rear rows of piles, the internal forces of the loaded section - embedded section of the front and rear rows of anti-slide piles are obtained:

[0111] According to the internal forces of the loaded sections of the front and rear rows of anti-slide piles and the internal forces of the loaded section - embedded section, the internal force of the double-row anti-slide piles without connecting beams is obtained.

[0112] Exemplarily, taking the rear row of piles as an example, the internal force and displacement of the loaded section are calculated by using the cantilever pile method; the deflection differential equation of the internal force and displacement of the loaded section - embedded section is solved according to the finite difference method, and its initial parameters are obtained through the solution of the internal force and displacement of the loaded section; combined with the boundary conditions at the top and bottom of the pile, the internal force and displacement of the loaded section - embedded section are solved, and finally the approximate analytical solutions of the internal force and displacement of the rear row of piles and even the double-row anti-slide piles are obtained.

[0113] The method for obtaining the internal force of the front row of piles refers to the above data processing process of the rear row of piles. The post-thrust of the front row of piles and the post-thrust of the rear row of piles are determined according to the sharing ratio obtained from the test. The pre-resistance of the front row of piles is triangularly distributed in the loaded section, and the distribution form of the post-thrust is the same as that of the pre-resistance of the rear row of piles, both in a parabolic shape. Therefore, when analyzing the forces of the loaded section - embedded section, the internal force calculations of the front and rear rows of piles are basically the same, only slightly different in the calculation of the internal force and displacement of the loaded section.

[0114] Referring to the landslide thrust, soil resistance, and the positions of their respective resultant force action points in different distribution forms shown in Table 1, as well as the soil pressure distribution in the model test, as Figure 9 shown, the force diagrams of the front and rear row piles in the loaded section (AB section) are obtained. The resistance in front of the front row pile is triangularly distributed in the loaded section, and the distribution form of the thrust behind the pile is consistent with the resistance in front of the rear row pile, both being parabolic.

[0115] Table 1 Distribution functions of landslide thrust and soil resistance in front of the pile

[0116]

[0117] Then, the position of the resultant force action point of the landslide thrust behind the pile:

[0118]

[0119] where z0 is the position of the resultant force action point of the landslide thrust behind the pile, h1 is the pile length of the rear row pile in the loaded section, ξ, η, are constants.

[0120] Similarly, the position of the resultant force action point of the soil resistance in front of the pile can be obtained:

[0121]

[0122] where z0′ is the position of the resultant force action point of the soil resistance in front of the pile, h1 is the pile length of the rear row pile in the loaded section, ξ', η', are constants.

[0123] The positions of the action points of the thrust behind the rear row pile and the resistance in front of the pile are represented by z a and z a ′ respectively. The positions of the action points of the thrust behind the front row pile and the resistance in front of the pile are represented by z b and z b ′ respectively. The position of the resultant force action point of its thrust behind the pile is basically the same as that of the rear row pile. However, considering that the resistance in front of the front row pile is triangularly distributed, the position of the resultant force action point of its resistance in front of the pile is at, that is

[0124] Extending the full length of the loaded section to the pile body above the slip surface, the distribution forms of the landslide thrust and soil resistance can still be represented by the distribution functions in Table 1, but its pile length is extended from h1 to H1. The position of the directional support is determined by the shear force calculation formula for the pile body above the slip surface, and the point where the shear force is zero is the action point of the hinge support B. The calculation formula for the landslide thrust at any height z1 above the slip surface is:

[0125]

[0126] Rear row pile:

[0127]

[0128] Front row piles:

[0129]

[0130] In the formula, w represents the thrust sharing ratio of double-row anti-slide piles. Generally, it is on the safe side when the value of the thrust sharing ratio of double-row anti-slide piles is between 1.4 and 1.9. The calculation formula for the soil resistance at any height z1 is (0 < z1 ≤ H1):

[0131] Rear row piles:

[0132]

[0133] Front row piles:

[0134]

[0135] In the formula, Eb′ represents the soil resistance in front of the front row piles, in kN; R(z1) represents the soil resistance at any height z1 of the rear row piles; R′(z1) represents the soil resistance at any height z1 of the front row piles, and H′1 represents the pile length after the extension of the loaded section of the front row piles.

[0136] The calculation formula for the shear force at any height above the slip surface is (0 < z1 ≤ H1):

[0137] Rear row piles:

[0138]

[0139] Front row piles:

[0140]

[0141] Among them, Q(z) is the shear force of the loaded section of the rear row piles, and Q′(z) is the shear force of the loaded section of the front row piles.

[0142] The directional support is assumed to act at the point where the shear force on the pile body is zero. Taking the rear row piles as an example, let Q(z) = 0 and solve for z = z * Then z * = h1. Therefore, it is obtained that the action point of the directional support of the rear row piles is located at z*, and the determination method of the directional support position of the front row piles is the same as that of the rear row piles.

[0143] When obtaining the internal forces of the loaded section, it includes obtaining the shear force of the loaded section and the bending moment of the loaded section.

[0144] (1) Shear force calculation of the loaded section

[0145] The calculation formula for the landslide thrust and soil resistance at any point z1 in the loaded section is (0 < z1 ≤ h1):

[0146]

[0147] Among them, T(z1) is the landslide thrust at any point z1 in the loaded section, and R(z1) is the soil resistance at any point z1 in the loaded section;

[0148] The shear force calculation formula for the loaded section of the rear row of piles is (0 < z ≤ h1):

[0149]

[0150] The shear force calculation formula for the loaded section of the front row of piles is (0 < z ≤ h1′):

[0151]

[0152] Among them, Q(z) is the shear force of the loaded section of the rear row of piles, Q′(z) is the shear force of the loaded section of the front row of piles, ξ, η, are constants, and their meanings are the same as the parameters ξ, η, 2 in the above landslide thrust distribution function q(z) = ξz + ηz + ψ; ξ', η', are constants, and their meanings are the same as the parameters ξ', η', 2 in the above soil resistance distribution function p(z) = ξ′z + η′z + ψ′.

[0153] (2) Bending moment calculation of the loaded section

[0154] The bending moment M T (z) generated by the landslide thrust T:

[0155] M T (z) = T(z - z a )(3.14)

[0156]

[0157] Similarly, the bending moment M R (z) generated by the soil resistance R in front of the pile:

[0158] M R (z) = R(z - z a ′)(3.16)

[0159]

[0160] Among them, ξ, η, are constants, and their meanings are the same as the parameters ξ, η, 2 in the above landslide thrust distribution function q(z) = ξz + ηz + ψ; ξ', η', is a constant, representing the same meaning as the parameters ξ', η', 2 +η′z+ψ′ in the above soil resistance distribution function p(z) = ξ′z which have the same expressed meaning.

[0161] In the formula, the position z of the acting point of the thrust behind the rear row of piles a and the position z a ' of the acting point of the resistance in front of the pile are calculated in the same way as the processing procedures of the position z0 of the resultant force of the landslide thrust behind the pile and the position z0' of the resultant force of the soil resistance in front of the pile above. Then, the bending moment calculation formula for the loaded section of the rear row of piles is (0 < z ≤ h1):

[0162]

[0163] The bending moment calculation formula for the loaded section of the front row of piles is (0 < z ≤ h1'):

[0164]

[0165] Therefore, the internal force calculation formula for the loaded section of the anti-slide pile of the rear row of piles is:

[0166]

[0167] The internal force calculation formula for the loaded section of the anti-slide pile of the front row of piles is:

[0168]

[0169] Among them, Q(z) is the shear force of the loaded section of the rear row of piles, M(z) is the bending moment of the loaded section of the rear row of piles, Q′(z) is the shear force of the loaded section of the front row of piles, M′(z) is the bending moment of the loaded section of the front row of piles, and Eb′ represents the soil resistance in front of the front row of piles.

[0170] Taking the rear row of piles as an example, Figure 9 in the shown AB section, the pile top is a free end, M A = 0, Q A = 0, and the B end is a fixed hinge support. The displacement at this point can be obtained by solving the deflection differential control equation of the BC section. The internal force formula at the hinge support is:

[0171]

[0172] Substitute the constraint conditions at the fixed support obtained from the above formula into the loaded section - embedded section to solve for the internal force and displacement of the BC section, and the internal force calculation results of the entire anti-slide pile can be obtained.

[0173] Exemplarily, the finite difference method is used to calculate the internal force and displacement of the pile body in the loaded section - fixed section. The force conditions of the front and rear row piles are basically the same. In this embodiment, the rear row pile is taken as an example to introduce the calculation process of the internal force and displacement of the rear row pile. The front row pile will not be elaborated here. Figure 10 Figure 2 is the force diagram of the loaded section - fixed section of the rear row pile. In the figure, the BC section is the loaded section - fixed section; for the anti - slide pile with double - row piles without connecting beams in the loaded section - fixed section (BC section), the internal force and displacement are calculated according to the elastic foundation beam theory. The specific calculation process refers to the difference method in Chapter 3. The distribution of differential points in the BC section is as Figure 11 shown.

[0174] For the BC section of the pile body of the double - row anti - slide pile, as can be seen from the above analysis and calculation of the internal force in the loaded section, the bending moment and shear force at the pile top B of the BC section are not zero. In the calculation model of the present invention, the bending moment M B and shear force Q B at the pile top B of the BC section are the bending moment and shear force at point B calculated by the cantilever pile method for the AB section pile. According to the structural assumption that the B end is a hinged end, the model test shows that the shear force at this place is nearly zero. Therefore, the force at point B is used as the boundary condition at the pile top of the difference method to calculate the internal force of the BC section of the double - row anti - slide pile. The boundary condition at the pile top of the BC section of the anti - slide pile is obtained as follows:

[0175]

[0176] where M B is the bending moment at point B.

[0177] The pile bottom C is considered as a free end. According to the differential equation of the pile body of the BC section of the anti - slide pile and combined with the 4 boundary conditions at points B and C, a unified linear equation set for the deformation of the loaded section - fixed section of the rear row pile BC section is established, so as to solve the horizontal displacement y i at each node of the pile body BC section.

[0178] The following formula (3.25) is the linear equation set. Combining with the difference formula (3.26), the solution of the internal force and displacement of the pile body can be realized:

[0179]

[0180]

[0181] Furthermore, the displacement calculation formula at the assumed hinged end B of the rear row pile can be obtained as follows:

[0182]

[0183] By substituting formula (3.27) into the formula for solving the internal force and displacement in the loaded section, the calculation formulas for the internal force and displacement of the whole pile of the rear row pile can be obtained. The method for obtaining the internal force and displacement of the whole pile of the front row pile refers to the obtaining process of the rear row pile.

[0184] In this step, based on the test data and result analysis in step S1 and combined with the structural characteristics of the double-row anti-slide piles without coupling beams, the anti-slide piles are simplified into a two-segment structure separated at the directional supports for internal force calculation. Taking the rear row of piles as an example, the cantilever pile method is used to calculate the internal forces and displacements of the loaded section (AB section); the deflection differential equations of the internal forces and displacements of the loaded section - embedded section (BC section) are solved according to the finite difference method, and the initial parameters are obtained from the solutions of the internal forces and displacements of the loaded section; combined with the boundary conditions at the pile bottom, the internal forces and displacements of the loaded section - embedded section are solved, and finally an approximate analytical solution of the internal forces and displacements of the rear row of piles and even the double-row anti-slide piles is obtained. The internal force calculation of the front row of piles is also carried out with reference to the rear row of piles. The thrust behind the front row of piles and the thrust behind the rear row of piles are determined according to the sharing ratio obtained from the test. The resistance in front of the front row of piles is triangularly distributed in the loaded section, and the distribution form of the thrust behind the piles is the same as that of the resistance in front of the rear row of piles, both in a parabolic shape.

[0185] The preliminary analysis of the calculation results of the double-row anti-slide piles based on the test analysis shows that this method is the same as the deformation of the pile body obtained from the test. Comparing the traditional internal force calculation method of the double-row anti-slide piles by predecessors with the calculation method based on the test can better illustrate the advantages and disadvantages of the two. The calculation results are shown in Figure 11 , and it can be seen from Figure 11 that the overall change of the internal force calculation results of the double-row anti-slide piles based on the test shows an "S" shape distribution, with positive and negative changes occurring at the slip surface, and moment extremes appear both above and below the slip surface, which is consistent with the failure mode of double-hinge failure above and below the slip surface presented by the double-row anti-slide piles in the model test.

[0186] As shown in Table 2, it is the result comparison of the maximum moments of the front and rear rows of piles obtained by using the calculation method of the present invention and the traditional calculation method.

[0187] Table 2 Result comparison of different calculation methods

[0188]

[0189] From the analysis of the position and value of the maximum moment in Table 2, it can be seen that the maximum moments calculated by the two methods are both near the slip surface. However, compared with the moment value calculated by the traditional method, the maximum moment value calculated based on the test of the present invention is larger, which is safer in design calculation. And compared with the front row of piles, the rear row of piles is more suitable for this calculation method, with an error of only 2%.

[0190] Double-row anti-slide piles have been widely used in engineering practice, but a relatively mature design and calculation method has not yet been formed. At present, the research on the internal force distribution and deformation of double-row anti-slide piles is mostly based on numerical simulation. Although it provides an effective means to understand the laws of pile body deformation and internal force distribution, there are problems such as over-reliance on the selection of simulation parameters. Based on two groups of double-row anti-slide pile model tests with and without connecting beams, this invention deeply studies the mechanical characteristics and deformation failure mechanism of double-row anti-slide piles, explores an effective internal force calculation method for double-row anti-slide piles, and compares and verifies the calculation results respectively. The main research results and conclusions are as follows:

[0191] (1) An internal force calculation model for double-row anti-slide piles with connecting beams is established based on the difference method. The structure of the double-row anti-slide piles with connecting beams is simplified into two single-pile structures disconnected at the zero moment of the pile-top connecting beam. A full-pile analysis and solution model for the loaded section and the embedded section of the double-row anti-slide piles is established and compared with the measured internal force results of the model test. The results show that the pile-top displacement and the pile body moment value obtained by the established calculation model are in good agreement, and the position of the maximum moment calculated is closer to the actual pile body failure position, providing a fast and efficient internal force calculation method for double-row piles with connecting beams in practical engineering.

[0192] (2) The results of the indoor model test show that: the earth pressure behind the front and rear rows of piles approximately presents a parabola-triangle distribution; the earth pressure in front of the piles is slightly different. For the rear row of piles, it is a parabola-triangle distribution, and for the front row of piles, it is generally parabolic; the landslide thrust sharing ratio is between 1.4 and 1.9. When analyzing the test shear force value, it is found that there is a place where the shear force is zero above the slip surface. The shear force value on the pile body above it fluctuates less, and the moment value changes more slowly. When calculating the internal force, this place is simplified as a fixed support.

[0193] (3) In the test, the stress mode of the double-row anti-slide piles without connecting beams is the "S" - shaped bending and shearing mode, and the failure mode is double-hinge failure. The failure position is generally within a certain range above the slip surface, and the landslide thrust borne by the rear row of piles is significantly greater than that of the front row of piles, resulting in more failure points and greater failure degree for the rear row of piles than the front row of piles. Therefore, when carrying out design calculations, the stress of the rear row of piles needs to be considered key.

[0194] (4) Based on the model test data and result analysis, combined with the structural characteristics of the double-row anti-slide piles without connecting beams, an internal force calculation model for double-row anti-slide piles based on the test is proposed. The thrust of the front and rear rows of piles is distributed according to the thrust sharing ratio obtained from the test, and the distribution form of the earth pressure around the piles is also selected with reference to the test results. Combined with a loess landslide example, the internal force calculation results based on the test are compared with the results calculated by the traditional method. The results show that: its calculation results are consistent with the "S" - shaped double-hinge failure mode of the double-row anti-slide piles above and below the slip surface, and the moment value is slightly larger than that calculated by the traditional method, being more conservative.

[0195] The above is the method for obtaining the internal forces of double-row anti-slide piles provided by one or more embodiments of this specification. Based on the same idea, this specification also provides a corresponding system for obtaining the internal forces of double-row anti-slide piles, including:

[0196] An acquisition module, which is used to conduct indoor experiments on the pile top displacement, pile surrounding soil pressure distribution, pile body moment and shear force distribution of double-row anti-slide piles without a connecting beam, so as to obtain the force characteristics and deformation characteristics of double-row anti-slide piles without a connecting beam;

[0197] A construction module, which is used to construct an internal force calculation model for double-row anti-slide piles without a connecting beam; by simplifying the anti-slide pile into an elastic foundation beam with a fixed range above the sliding surface as a directional support, splitting the pile structure into a loaded section and a loaded section - embedded section from the directional support, and determining the internal forces of double-row anti-slide piles without a connecting beam;

[0198] A determination module, which is used to input the force and deformation characteristics of double-row anti-slide piles without a connecting beam into the internal force calculation model for double-row anti-slide piles without a connecting beam, so as to obtain the internal forces of the entire pile body of double-row anti-slide piles without a connecting beam.

[0199] For the specific limitations on the system for obtaining the internal forces of double-row anti-slide piles, reference can be made to the limitations on the method for obtaining the internal forces of double-row anti-slide piles in the above text, which will not be elaborated here. Each module in the above system for obtaining the internal forces of double-row anti-slide piles can be implemented in whole or in part through software, hardware and their combinations. The above-mentioned modules can be embedded in the processor of a computer device in the form of hardware or be independent of it, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above-mentioned modules.

[0200] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in the present invention.

Claims

1. A method for obtaining internal force of double-row anti-sliding piles, characterized in that: include: Indoor experiments were conducted on the pile top displacement, soil pressure distribution around the pile, bending moment and shear force distribution of the double-row anti-sliding piles without coupling beams to obtain the stress and deformation characteristics of the double-row anti-sliding piles without coupling beams. The internal force calculation model of double-row anti-sliding piles without coupling beams was constructed; the internal force of double-row anti-sliding piles without coupling beams was determined by simplifying the anti-sliding piles into elastic foundation beams with a fixed range above the sliding surface as a directional support, and splitting the pile structure into two parts: a load-bearing section and a load-bearing section-embedded section. By inputting the stress and deformation characteristics of the double-row anti-sliding piles without coupling beams into the internal force calculation model of the double-row anti-sliding piles without coupling beams, the internal force of the entire pile body of the double-row anti-sliding piles without coupling beams can be obtained.

2. The method for obtaining internal force of double-row anti-sliding piles according to claim 1, characterized in that: The method of dividing the pile structure into a load-bearing section and a load-bearing section-embedded section from the directional support to determine the internal force of the double-row anti-sliding piles without coupling beams specifically includes: The pile structure is divided into two parts, the load-bearing section and the load-bearing section-embedded section, from the directional support. The internal forces of the load-bearing sections of the front and rear rows of the anti-sliding piles are obtained by using the cantilever pile method. The internal forces of the load-bearing sections include the shear force of the load-bearing section and the bending moment of the load-bearing section. Based on the finite difference method, the flexural differential equations of the internal forces of the front and rear rows of anti-sliding piles in the load-bearing section and the embedded section are obtained respectively. Combined with the boundary conditions of the top and bottom of the front and rear rows of piles, the internal forces of the front and rear rows of anti-sliding piles in the load-bearing section and the embedded section are obtained: The internal forces of the double-row anti-sliding piles without coupling beams are obtained based on the internal forces of the loaded sections of the front and rear rows of anti-sliding piles and the internal forces of the loaded section-embedded section.

3. The method for obtaining internal force of double-row anti-sliding piles as claimed in claim 2, characterized in that: The flexural differential equations of the internal forces of the load section and the embedded section of the front and rear rows of anti-sliding piles are obtained based on the finite difference method, specifically including: The deflection differential control equation of the loaded section and embedded section of the double-row anti-slide piles is obtained by the following formula: Among them, EI represents the stiffness of the double-row anti-slide pile structure; B0 represents the calculated width of the pile; K(z) represents the foundation coefficient, K(z)=mz; m represents the proportional coefficient of the foundation coefficient changing with depth; y represents the horizontal displacement of the pile body; z represents the distance from the pile top; q(z) represents the landslide thrust.

4. The method for obtaining internal force of double-row anti-sliding piles as claimed in claim 2, characterized in that: The boundary conditions of the pile tops and bottoms of the front and rear rows of piles specifically include: When subjected to the shear force and bending moment transmitted by the pile top connecting beam, the boundary conditions at the top of the front row of piles are: The boundary conditions at the top of the rear row piles are: When there is no shear force and bending moment transmitted by the pile top connecting beam, the boundary condition at the top of the front row of piles is: The boundary conditions at the top of the rear row piles are: Assuming the bottom of the elastic double-row piles is a free end, the bending moment and shear force at the bottom of the piles are zero, and the boundary conditions at the bottom of the front row of piles are: The boundary conditions at the bottom of the rear piles are: Among them, M b is the bending moment transmitted by the coupling beam at the top of the front pile, M a is the bending moment transmitted by the coupling beam at the top of the rear pile, Q b is the shear force transmitted by the coupling beam at the top of the front row of piles, Q a is the shear force transmitted by the connecting beam at the top of the rear row of piles, n is the node number, and y is the horizontal displacement of the pile body.

5. A double-row anti-sliding pile internal force acquisition system, characterized in that: include: The acquisition module is used to conduct indoor experiments on the pile top displacement, soil pressure distribution around the pile, pile body bending moment and shear force distribution of double-row anti-sliding piles without coupling beams, and obtain the stress characteristics and deformation characteristics of the double-row anti-sliding piles without coupling beams; A construction module is used to construct an internal force calculation model for double-row anti-sliding piles without coupling beams; the internal force of double-row anti-sliding piles without coupling beams is determined by simplifying the anti-sliding piles into elastic foundation beams with a fixed range above the sliding surface as a directional support, and splitting the pile structure into a load-bearing section and a load-bearing section-embedded section from the directional support; The determination module is used to obtain the internal force of the whole pile body of the double-row anti-sliding pile without a connecting beam by inputting the stress and deformation characteristics of the double-row anti-sliding pile without a connecting beam into the internal force calculation model of the double-row anti-sliding pile without a connecting beam.

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