A safety assessment system and method for the substructure of a double-pile and double-column bridge in a slope section

Abstract

The present invention belongs to the technical field of bridge safety assessment, and relates to a safety assessment method for the substructure of a double-pile double-column bridge on a slope section, comprising the following steps: based on the natural geographical conditions and engineering geological conditions at the potential landslide location, analyzing the slope stability and determining the potential sliding surface; determining the residual sliding force of the rock and soil body on the pile side and the distribution law of the rock and soil body resistance according to the relative relationship between the bridge route and the slope, and the relative position relationship between the bridge substructure and the slope surface and the potential sliding surface; constructing a deflection curve differential equation based on the residual sliding force and resistance distribution law of the rock and soil body; considering the distribution conditions of the internal force and displacement of the front and rear piles by the cap beam and the tie beam, combining the deflection curve differential equation, determining the internal force and displacement of the double-pile double-column structure; and realizing the structural safety evaluation according to the bearing capacity limit state analysis method. The present invention solves the problems of inaccurate evaluation results of the substructure of the double-pile double-column bridge on the slope section.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge safety assessment, and relates to a system and method for safety assessment of the substructure of a double-pile and double-column bridge in a slope section. Background Art

[0002] Compared with the structure of a single pier column and pile foundation, the double-pile double-column structure is one of the most commonly used bridge substructure forms in mountain bridge projects. The double-pile double-column structure is composed of two pier columns, two pile foundations, a tie beam between the piles and columns, and a cap beam at the top of the pier. Compared with the single-pile single-column structure, when calculating the internal forces and displacements of the double-pile double-column structure, it is necessary to consider the influence of the tie beam and cap beam between the two pile columns on the forces of the two pile columns, establish the differential equations of the deflection curves of the front and rear piles, and then combine the boundary conditions, the continuity conditions of the internal forces and displacements between the pile segments, and the relationship between the cap beam, tie beam and the internal forces and displacements of the two pile columns to solve the power series solution of the structural displacement and internal forces.

[0003] Existing analyses of double-pile double-column structures usually do not consider the piers and cap beams above the pile foundations, but the piers and cap beams, the tie beams at the bottom, and the pile foundations actually work together as a whole. At the same time, existing studies usually only consider the transmission of axial forces by the tie beams. However, due to the large stiffness of the tie beams, their role in distributing the bending moment between the two piles cannot be ignored. In addition, in the process of constructing the power series solution of the internal forces and displacements of the double-pile double-column structure, the current solution method requires assumptions about the shear force at the top of the free section, and continuous iterative trial calculations are required to obtain the final result, and the solution process is relatively cumbersome. The assumptions and simplifications in the above solution process will lead to errors in the calculation of structural responses and displacements, which will lead to deviations between the evaluation results of the substructure of the double-pile double-column bridge on the slope section and the actual state, posing a potential threat to the safe operation of transportation infrastructure. Summary of the invention

[0004] The purpose of the present invention is to provide a system and method for safety assessment of the substructure of a double-pile double-column bridge on a slope section, which solves the problems of deviation between the assessment results of the substructure of a double-pile double-column bridge on a slope section and the actual state, inaccurate assessment results, etc.

[0005] The present invention is achieved through the following technical solutions:

[0006] A method for safety assessment of the substructure of a double-pile double-column bridge in a slope section comprises the following steps:

[0007] S1. Analyze slope stability and determine potential slip surfaces based on the natural geographical conditions and engineering geological conditions at the potential landslide location;

[0008] S2. According to the relative relationship between the bridge route and the slope, and the relative position relationship between the substructure of the double-pile double-column bridge and the slope surface and potential sliding surface, the bridge pile-column foundation is divided, and the residual sliding force of the rock and soil mass on the pile side and the distribution law of the rock and soil mass resistance are determined respectively;

[0009] S3. Based on the residual sliding force of the rock and soil mass on the pile side and the distribution law of the rock and soil mass resistance, the stress analysis of the bridge pile foundation is carried out and the corresponding deflection curve differential equation is constructed;

[0010] S4, based on the continuity conditions and structural boundary conditions of the displacement and internal force between each characteristic pile segment, and considering the distribution conditions of the internal force and displacement of the front pile and the rear pile by the cap beam and the tie beam, combined with the deflection curve differential equation established in S3, the equation group is simultaneously established and solved to determine the internal force and displacement of the double-pile double-column structure;

[0011] S5. According to the ultimate bearing capacity state analysis method, combined with the solved displacement and internal force of the double-pile double-column structure, the pile-column section strength and the pile-column top displacement are verified.

[0012] Furthermore, in S2, the pile foundation is divided into a longitudinal bridge foundation and a transverse bridge foundation according to the relative relationship between the bridge route and the corresponding slope;

[0013] According to the relative position relationship between the structure and the slope surface and the potential slip surface, the pile foundation is divided vertically into the first free section, the second free section, the load-bearing section and the embedded section which are connected in sequence from top to bottom;

[0014] The residual sliding force of the rock and soil in the loaded section is calculated by the residual thrust method in the extreme equilibrium method. If the pile foundation is a transverse pile foundation, the two piles bear the same rock and soil force. If the pile foundation is a longitudinal bridge foundation, the force distribution relationship between the front pile and the rear pile is determined by the ratio of the cross-sectional area of ​​the rock and soil between the piles to the cross-sectional area of ​​the sliding body, and the residual sliding force of the rock and soil on the front pile and the rear pile is obtained.

[0015] Furthermore, the resistance distribution law of the rock and soil mass on the pile side of the pile foundation is determined based on the elastic foundation reaction method.

[0016] Further, S3 is specifically:

[0017] Based on the residual sliding force of the rock and soil mass on the pile side and the distribution law of the rock and soil mass resistance, the first free section, the second free section, the loaded section and the embedded section are respectively taken for force analysis, and then the deflection curve differential equation is constructed. The deflection curve differential equations of the first free section, the second free section, the loaded section and the embedded section are shown in equations (1) to (4) respectively:

[0018]

[0019]

[0020]

[0021]

[0022] in,

[0023]

[0024]

[0025]

[0026] Among them, x represents the direction of the force acting on the rock and soil mass;

[0027] z indicates vertical direction;

[0028] N represents the axial force, and the subscripts 0, 1, 2, and 3 correspond to the first free section, the second free section, the loaded section, and the embedded section, respectively;

[0029] f represents the axial force growth coefficient, and the subscripts 0, 1, 2, and 3 correspond to the first free section, the second free section, the loaded section, and the embedded section, respectively;

[0030] E represents the elastic modulus;

[0031] I represents the moment of inertia of the section;

[0032] a, b, c represent the undetermined coefficients of the residual sliding force distribution function, and the subscripts 0, 1, 2, and 3 correspond to the first free section, the second free section, the loaded section, and the embedded section, respectively;

[0033] l2 represents the length of the pile body in the load-bearing section;

[0034] m represents the relevant parameters in the solution method, 2 and 3 correspond to the loaded section and the embedded section, respectively.

[0035] Furthermore, in S4, the piers, cap beams, pile foundations, and tie beams are considered as an integral frame structure for analysis during the establishment of the equation set;

[0036] In the process of establishing the equation group, the cap beam and tie beam are simplified as rigid arms, and the distribution of the axial force and bending moment between the two piles by the cap beam and tie beam is considered;

[0037] In solving the system of equations, it is assumed that the shear force at the top of the free segment is evenly distributed between the two pile columns;

[0038] After solving the equations, the matrix analysis method is used to determine the displacement and internal force of the double-pile double-column structure.

[0039] Furthermore, the set of equations includes a set of equations corresponding to the top of the first free section of the front pile and the rear pile, a set of equations corresponding to the connection between the first free section and the second free section, a set of equations corresponding to the connection between the second free section and the load section, a set of equations corresponding to the connection between the load section and the embedded section, and a set of equations corresponding to the boundary conditions at the bottom of the pile.

[0040] Furthermore, in S5, the cross-sectional strength of the pile column and the displacement of the top of the pile column are verified, and the following formula is used to determine |:

[0041] N now ≤N ud ;

[0042] M now ≤M ud ;

[0043] δ now ≤δ max ;

[0044] Among them, N now It represents the calculated value of the pile axial force at the unstable slope position;

[0045] M now It represents the calculated value of the bending moment of the pile at the unstable slope position;

[0046] δ now represents the calculated value of the displacement of the top of the pile at the unstable slope location;

[0047] N ud Indicates the compressive bearing capacity of the pile cross section;

[0048] M ud It indicates the bending bearing capacity of the pile cross section;

[0049] δ max represents the displacement limit of the pile top;

[0050] If the above three formulas are satisfied, the substructure of the double-pile double-column bridge is in a safe state under the action of an unstable slope; otherwise, there is a risk of damage.

[0051] The present invention also discloses a safety assessment system for the substructure of a double-pile double-column bridge in a slope section, comprising:

[0052] Slope stability analysis module, used to analyze slope stability and determine potential slip surfaces based on the natural geographical conditions and engineering geological conditions at the potential landslide location;

[0053] The foundation force characteristics analysis module is used to divide the bridge pile foundation according to the relative relationship between the bridge route and the corresponding slope, the relative position relationship between the structure and the slope surface, and the potential sliding surface, and to determine the residual sliding force of the rock and soil mass and the distribution law of the rock and soil mass resistance respectively;

[0054] The module for establishing the differential equation of deflection curve is used to analyze the stress of each part of the pile foundation and establish the corresponding differential equation of deflection curve according to the residual sliding force of the rock and soil mass and the distribution law of the resistance of the rock and soil mass;

[0055] The analytical module is used to determine the internal forces and displacements of the double-pile double-column structure based on the continuity conditions and structural boundary conditions of the displacements and internal forces between the characteristic pile segments, and considering the distribution conditions of the cap beam and tie beam on the internal forces and displacements of the front and rear piles, combined with the deflection curve differential equation, and to solve the equation system simultaneously;

[0056] The structural safety assessment module is used to verify the cross-sectional strength of the pile column and the displacement of the top of the pile column based on the displacement and internal force of the double-pile double-column structure according to the ultimate bearing capacity state analysis method.

[0057] Compared with the prior art, the present invention has the following beneficial technical effects:

[0058] The present invention discloses a safety assessment system and method for the substructure of a double-pile double-column bridge in a slope section, and proposes to analyze and calculate the pier, cap beam, pile foundation and tie beam as an integral frame structure. The analytical calculation method can simultaneously consider the distribution of the axial force and bending moment between the two piles by the cap beam and the tie beam, and improves the shortcomings of existing studies that require iterative trial calculations based on the assumption of free segment shear force and cannot directly calculate the axial force in the lateral connection. The calculation theory of this analysis method is more practical, and can achieve refined analysis of the displacement and internal force of the entire structure, and support the safety assessment of the foundation structure during the bridge operation stage based on more accurate analysis data of structural displacement and internal force, providing reliable data support for ensuring the safe operation of the bridge structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a general framework diagram of a safety assessment system and method for a double-pile double-column bridge substructure in a slope section of the present invention;

[0060] Figure 2 This is the force characteristic analysis diagram of the substructure of the double-pile double-column bridge on the slope section;

[0061] Among them, 1 is the cap beam, 2 is the tie beam, 3 is the front pile, 4 is the rear pile, 5 is the slope surface, and 6 is the potential slip surface;

[0062] A is the first free section, B is the second free section, C is the load-bearing section, and D is the embedded section. DETAILED DESCRIPTION

[0063] like Figure 1 As shown, the overall framework of the slope section double-pile double-column bridge substructure safety assessment system of the present invention includes the following parts:

[0064] 1) Slope stability analysis module: Based on the natural geographical conditions and engineering geological conditions at the potential landslide location, the slope stability is analyzed and the potential slip surface is determined6.

[0065] Specifically, when the slope is small and the geological conditions are simple, the transfer coefficient method is used to analyze the slope stability; when the geological conditions are complex, slope stability simulation software, such as GeoStudio, is used for simulation analysis.

[0066] 2) Foundation force characteristics analysis module: The relative relationship between the bridge route and the corresponding slope can be used to divide the pile foundation into a longitudinal bridge foundation where the route direction is perpendicular to the slope direction or has a large intersection angle with the slope, and a transverse bridge foundation where the route direction is parallel or nearly parallel to the slope direction.

[0067] The pile foundation of the longitudinal bridge foundation can be further divided into a front pile 3 and a rear pile 4. The front pile 3 is the side of the pile foundation close to the bottom of the slope, and the rear pile 4 is the side of the pile foundation close to the top of the slope.

[0068] According to the relative position relationship between the structure and the slope 5 and the potential slip surface 6, the pile foundation is divided vertically into the first free section A, the second free section B, the load section C and the embedded section D. The specific division method is as follows: Figure 2 shown.

[0069] The residual sliding force of the rock and soil mass on the pile foundation is calculated by the residual thrust method in the extreme equilibrium method. If the pile foundation is a transverse pile foundation, the two piles bear the same residual sliding force of the rock and soil mass. If the pile foundation is a longitudinal bridge foundation, the force distribution relationship between the front pile 3 and the rear pile 4 is first determined by the ratio of the cross-sectional area of ​​the rock and soil mass between the piles to the cross-sectional area of ​​the sliding mass, and then the residual sliding force of the rock and soil mass borne by the front pile 3 and the rear pile 4 is determined. The distribution law of the rock and soil mass resistance on the pile side of the pile foundation is determined according to the elastic foundation reaction method.

[0070] 3) Deflection curve differential equation establishment module: Based on the determined residual sliding force of rock and soil mass and the distribution law of rock and soil mass resistance, the force characteristics of the first free section A, the second free section B, the loaded section C and the embedded section D are analyzed, and the differential elements are taken for force analysis and the deflection curve differential equation is constructed. The deflection curve differential equations of the first free section A, the second free section B, the loaded section C and the embedded section D are shown in equations (1) to (4) respectively.

[0071]

[0072]

[0073]

[0074]

[0075] in,

[0076]

[0077]

[0078]

[0079] Wherein, N represents the axial force, and the subscripts 0, 1, 2, and 3 correspond to the first free section A, the second free section B, the loaded section C, and the embedded section D, respectively;

[0080] f represents the axial force growth coefficient, and the subscripts 0, 1, 2, and 3 correspond to the first free section A, the second free section B, the loaded section C, and the embedded section D, respectively;

[0081] E represents the elastic modulus;

[0082] I represents the moment of inertia of the section;

[0083] a, b, c represent the undetermined coefficients of the residual sliding force distribution function, and the subscripts 0, 1, 2, and 3 correspond to the first free section A, the second free section B, the loaded section C, and the embedded section D, respectively;

[0084] l2 represents the length of the pile body in the load-bearing section C;

[0085] m represents the relevant parameters in the solution method, and the subscripts 2 and 3 correspond to the loaded section C and the embedded section D, respectively.

[0086] 4) Analytical module (establishment and solution of control equations):

[0087] The continuity conditions of displacement and internal force between characteristic pile segments, structural boundary conditions, and the distribution conditions of internal force and displacement of front pile 3 and rear pile 4 by cap beam 1 and tie beam 2 are introduced. At the same time, the shear force of cap beam 1 and the cantilever sections at both ends of cap beam 1 are ignored in the analysis process, and tie beam 2 and cap beam 1 are simplified as rigid arm models. The load of the free section of the bridge pier along the height direction is assumed to be a distributed load. Taking the longitudinal double-pile double-column foundation with a consolidated pile bottom constraint as an example, the following set of equations can be established:

[0088] 4.1) Top of the first free section A of the front pile 3 and the rear pile 4

[0089] The displacement coordination conditions of the front pile 3 and the rear pile 4 are as follows:

[0090]

[0091] in,

[0092] x h0 | z＝0 represents the displacement of the top of the first free section A of the rear pile 4;

[0093] x q0 | z＝0 represents the displacement of the top of the first free section A of the front pile 3;

[0094] h0 represents the first free section A of the rear pile 4;

[0095] z = 0 means the position is the top of the pile (unless otherwise specified, z = 0 in the following descriptions will refer to the top of the studied section);

[0096] q0 represents the first free section A of the front pile 3;

[0097] N g represents the axial force of cap beam 1;

[0098] L g Indicates the length of cap beam 1;

[0099] E g represents the elastic modulus of the cap beam 1;

[0100] I g represents the section moment of inertia of the cap beam 1.

[0101] From the effect of tie beam 2 on shear force distribution, we can know that:

[0102]

[0103]

[0104] Q1 represents the shear force at the connection between the cap beam 1 and the first free section A of the rear pile 4;

[0105] Q2 represents the shear force at the connection between the cap beam 1 and the first free section A of the front pile 3;

[0106] represents the shear force transmitted to the tie beam 2 by the first free section A of the rear pile 4;

[0107] E0 represents the elastic modulus of the first free segment A;

[0108] I0 represents the section moment of inertia of the first free segment A;

[0109] x h0″′ | z＝0 represents the shear force caused by the displacement at the top of the first free section A of the rear pile 4;

[0110] Where N h0 E represents the axial force of the first free section A of the rear pile 4; h0 I represents the elastic modulus of the first free section A of the rear pile 4; h0 represents the moment of inertia of the first free section A of the rear pile 4;

[0111] represents the turning angle of the first free section A of the rear pile 4;

[0112] Q q0 , x q0″′ | z＝0 ,λ q0 , In the figure, q0 represents the first free section A of the front pile 3, and its specific meaning is the same as above.

[0113] From the distribution effect of tie beam 2 on bending moment, we can know that:

[0114]

[0115]

[0116] M1 represents the bending moment at the connection between the cap beam 1 and the first free section A of the rear pile 4;

[0117] M2 represents the bending moment at the connection between the cap beam 1 and the first free section A of the front pile 3;

[0118] M gh represents the bending moment at the rear end of the cap beam 1;

[0119] M gq represents the bending moment at the front end of the cap beam 1;

[0120] x h0″ | z＝0 represents the bending moment caused by the displacement of the top end of the first free section A of the rear pile 4;

[0121] x q0″ | z＝0 represents the bending moment caused by the displacement of the top end of the first free section A of the front pile 3;

[0122] i g Represents the linear stiffness of cap beam 1.

[0123] 4.2) The connection between the first free section A and the second free section B

[0124] Due to the existence of tie beam 2, the displacement coordination conditions of front pile 3 and rear pile 4 show that:

[0125]

[0126] x h1 | z＝0 represents the displacement of the top of the second free section B of the rear pile 4;

[0127] x q1 | z＝0 represents the displacement of the top of the second free section B of the front pile 3;

[0128] N x , L x, E x , I x are the axial force, length, elastic modulus, and section inertia moment of tie beam 2. The connection satisfies the displacement continuity condition:

[0129]

[0130]

[0131] represents the displacement of the bottom end of the first free section A of the rear pile 4;

[0132] Indicates the displacement of the bottom end of the first free section A of the front pile 3.

[0133] The connection satisfies the corner continuity condition:

[0134]

[0135]

[0136] represents the rotation angle caused by the displacement of the bottom end of the first free section A of the rear pile 4;

[0137] x h1′ | z＝0 represents the rotation angle caused by the displacement of the top end of the second free section B of the rear pile 4;

[0138] represents the rotation angle caused by the displacement of the bottom end of the first free section A of the front pile 3;

[0139] x q1′ | z＝0 It represents the rotation angle caused by the displacement of the top end of the second free section B of the front pile 3.

[0140] The connection satisfies the moment continuity condition, and considering the distribution effect of tie beam 2 on the moment, we can obtain:

[0141]

[0142]

[0143] represents the bending moment caused by the displacement of the bottom end of the first free section A of the rear pile 4;

[0144] x h1″ | z＝0 represents the bending moment caused by the displacement of the top end of the second free section B of the rear pile 4;

[0145] represents the bending moment caused by the displacement of the bottom end of the first free section A of the front pile 3;

[0146] xq1″ | z＝0 represents the bending moment caused by the displacement of the top end of the second free section B of the front pile 3;

[0147] E1 represents the elastic modulus of the second free section B;

[0148] I1 represents the section moment of inertia of the second free segment B;

[0149] i x represents the linear stiffness of tie beam 2;

[0150] represents the turning angle of the second free section B of the rear pile 4;

[0151] Indicates the turning angle of the second free section B of the front pile 3.

[0152] The connection satisfies the shear continuity condition, and considering the distribution effect of tie beam 2 on the bending moment, we can obtain:

[0153]

[0154]

[0155] represents the shear force caused by the displacement of the bottom end of the first free section A of the rear pile 4;

[0156] x h1″′ | z＝0 represents the shear force caused by the displacement of the top end of the second free section B of the rear pile 4;

[0157] represents the shear force caused by the displacement of the bottom end of the first free section A of the front pile 3;

[0158] x q1″′ | z＝0 represents the shear force caused by the displacement of the top end of the second free section B of the front pile 3;

[0159] Medium h1 , E h1 , I h1 are the axial force, elastic modulus and section inertia moment of the second free section B of the rear pile 4, q1 in the middle is the second free section B of the front pile 3, and its specific meaning is the same as above;

[0160] N x is the axial force of tie beam 2.

[0161] 4.3) The connection between the second free section B and the loaded section C

[0162] The connection between the upper and lower pile segments meets the displacement continuity condition:

[0163]

[0164]

[0165] represents the displacement of the bottom end of the second free section B of the rear pile 4;

[0166] x h2 | z＝0 represents the displacement of the top of the load-bearing section C of the rear pile 4;

[0167] represents the displacement of the bottom end of the second free section B of the front pile 3;

[0168] x q2 | z＝0 Indicates the displacement of the top of the load-bearing section C of the front pile 3.

[0169] The connection between the upper and lower pile segments meets the corner continuity condition:

[0170]

[0171]

[0172] represents the rotation angle caused by the displacement of the bottom end of the second free section B of the rear pile 4;

[0173] x h2′ | z＝0 It represents the rotation angle caused by the displacement of the top end of the load section C of the rear pile 4;

[0174] represents the rotation angle caused by the displacement of the bottom end of the second free section B of the front pile 3;

[0175] x q2′ | z＝0 It represents the rotation angle caused by the displacement of the top end of the load-bearing section C of the front pile 3.

[0176] The connection between the upper and lower pile segments meets the moment continuity condition:

[0177]

[0178]

[0179] E2 represents the elastic modulus of the loaded section C;

[0180] I2 represents the section inertia moment of the loaded section C;

[0181] represents the bending moment caused by the displacement of the bottom end of the second free section B of the rear pile 4;

[0182] x h2″ | z＝0represents the bending moment caused by the displacement of the top end of the loaded section C of the rear pile 4;

[0183] represents the bending moment caused by the displacement of the bottom end of the second free section B of the front pile 3;

[0184] x q2″ | z＝0 represents the bending moment caused by the displacement of the top end of the loaded section C of the front pile 3;

[0185] The connection between the upper and lower pile segments satisfies the shear continuity condition, which can be obtained as follows:

[0186]

[0187]

[0188] represents the shear force caused by the displacement of the bottom end of the second free section B of the rear pile 4;

[0189] x h2″′ | z＝0 represents the shear force caused by the displacement of the top of the loaded section C of the rear pile 4;

[0190] Medium h2 , E h2 , I h2 They represent the axial force, elastic modulus and section inertia moment of the loaded section C of the rear pile 4, q2 in the middle represents the load-bearing section C of the front pile 3, and its specific meaning is the same as above;

[0191] Indicates the rotation angle of the load-bearing section C of the rear pile 4;

[0192] represents the shear force caused by the displacement of the bottom end of the second free section B of the front pile 3;

[0193] x q2″′ | z＝0 represents the shear force caused by the displacement of the top of the load section C of the front pile 3;

[0194] Indicates the rotation angle of the load-bearing section C of the front pile 3.

[0195] 4.4) Connection between load-bearing section C and embedded section D

[0196] The connection between the upper and lower pile segments satisfies the displacement continuity condition, which can be obtained:

[0197]

[0198]

[0199] represents the displacement of the bottom end of the load section C of the rear pile 4;

[0200] x h3 | z＝0 represents the displacement of the top of the embedded section D of the rear pile 4;

[0201] represents the displacement of the bottom end of the load section C of the front pile 3;

[0202] x q3 | z＝0 Indicates the displacement of the top of the embedded section D of the front pile 3.

[0203] The connection between the upper and lower pile segments satisfies the corner continuity condition, which can be obtained:

[0204]

[0205]

[0206] represents the rotation angle caused by the displacement of the bottom end of the load section C of the rear pile 4;

[0207] x h3′ | z＝0 represents the rotation angle caused by the displacement of the top end of the embedded section D of the rear pile 4;

[0208] represents the rotation angle caused by the displacement of the bottom end of the load section C of the front pile 3;

[0209] x q3′ | z＝0 It represents the rotation angle caused by the displacement of the top end of the embedded section D of the front pile 3.

[0210] The connection between the upper and lower pile segments meets the moment continuity condition:

[0211]

[0212]

[0213] E3 represents the elastic modulus of the embedded section D;

[0214] I3 represents the section inertia moment of the embedded section D;

[0215] represents the bending moment caused by the displacement of the bottom end of the loaded section C of the rear pile 4;

[0216] x h3″ | z＝0 represents the bending moment caused by the displacement of the top end of the embedded section D of the rear pile 4;

[0217] represents the bending moment caused by the displacement of the bottom end of the loaded section C of the front pile 3;

[0218] x q3″ | z＝0 It represents the bending moment caused by the displacement of the top end of the embedded section D of the front pile 3.

[0219] The connection between the upper and lower pile segments meets the shear continuity condition:

[0220]

[0221]

[0222] represents the shear force caused by the displacement of the bottom end of the loaded section C of the rear pile 4;

[0223] x h3″′ | z＝0 represents the shear force caused by the displacement of the top end of the embedded section D of the rear pile 4;

[0224] Medium h3 , E h3 , I h3 are the axial force, elastic modulus, and section inertia moment of the embedded section D of the rear pile 4, q3 in the middle represents the embedded section D of the front pile 3, and its specific meaning is the same as above;

[0225] represents the rotation angle of the embedded section D of the rear pile 4;

[0226] Indicates the shear force caused by the displacement of the bottom end of the load section C of the front pile 3

[0227] x q3″′ | z＝0 represents the shear force caused by the displacement of the top end of the embedded section D of the front pile 3;

[0228] Indicates the turning angle of the embedded section D of the front pile 3.

[0229] 4.5) Boundary conditions at the bottom of the pile (taking pile bottom embedment as an example)

[0230] From the zero horizontal displacement of the pile bottom, we know that:

[0231]

[0232]

[0233] represents the displacement of the bottom end of the embedded section D of the rear pile 4;

[0234] Indicates the displacement of the bottom end of the embedded section D of the front pile 3.

[0235] From the pile bottom rotation angle being zero, we know that:

[0236]

[0237]

[0238] Indicates the turning angle of the bottom end of the embedded section D of the rear pile 4;

[0239] Indicates the turning angle at the bottom end of the embedded section D of the front pile 3.

[0240] Equations (1) to (38) are combined and the matrix analysis method is used to determine the power series solutions of the displacements and internal forces of the first free segment A, the second free segment B, the loaded segment C and the embedded segment D respectively.

[0241] 5) Structural safety assessment module: The sliding of an unstable slope and the residual sliding force acting on the bridge pile foundation are abnormal situations with a low probability of occurrence and a short duration. Therefore, the bearing capacity limit state analysis method is adopted. Based on the "Highway Reinforced Concrete and Prestressed Concrete Bridge and Culvert Design Code" (hereinafter referred to as the "Code") and the obtained pile column displacement and internal force, the cross-sectional strength of the pile column and the displacement of the pile column top are verified, as shown in equations (39) to (41).

[0242] N now ≤N ud (39)

[0243] M now ≤M ud (40)

[0244] δ now ≤δ max (41)

[0245] Among them, N now It represents the calculated value of the pile axial force at the unstable slope position;

[0246] M now It represents the calculated value of the bending moment of the pile at the unstable slope position;

[0247] δ now represents the calculated value of the displacement of the top of the pile at the unstable slope location;

[0248] N ud Indicates the compressive bearing capacity of the pile cross section, which is determined according to the Code and the design parameters of the pile column;

[0249] M ud It indicates the bending bearing capacity of the pile cross section, which is determined according to the Code and the design parameters of the pile column;

[0250] δ maxIndicates the displacement limit at the top of the pile, which is determined according to the Code.

[0251] If equations (39) to (41) are satisfied, the substructure of the double-pile double-column bridge is in a safe state under the action of an unstable slope; otherwise, the structure is at risk of damage, and engineering treatment of the unstable slope must be carried out.

Claims

1. A method for safety assessment of the substructure of a double-pile double-column bridge on a slope section, characterized in that: The following steps are involved: S1. Analyze slope stability and determine potential slip surfaces based on the natural geographical and engineering geological conditions at the potential landslide location (6); S2. Based on the relative relationship between the bridge route and the slope, and the relative positional relationship between the substructure of the double-pile double-column bridge and the slope surface (5) and the potential sliding surface (6), the bridge pile-column foundation is divided, and the residual sliding force of the rock and soil mass on the pile side and the distribution law of the rock and soil mass resistance are determined respectively; S3. Based on the residual sliding force of the rock and soil mass on the pile side and the distribution law of the rock and soil mass resistance, the stress analysis of the bridge pile foundation is carried out and the corresponding deflection curve differential equation is constructed; S4, based on the continuity conditions and structural boundary conditions of the displacement and internal force between the characteristic pile segments, and considering the distribution conditions of the internal force and displacement of the front pile (3) and the rear pile (4) by the cap beam (1) and the tie beam (2), combined with the deflection curve differential equation established in S3, the equation group is simultaneously established and solved to determine the internal force and displacement of the double-pile double-column structure; S5. According to the bearing capacity limit state analysis method, combined with the solved double-pile double-column structure displacement and internal force, the pile column section strength and pile column top displacement are verified; In S4, the piers, cap beams (1), pile foundations and tie beams (2) are considered as an integral frame structure for analysis during the establishment of the equation set; In the process of establishing the equation group, the cap beam (1) and the tie beam (2) are simplified as rigid arms, and the distribution of the axial force and bending moment between the two piles by the cap beam (1) and the tie beam (2) is considered; In solving the system of equations, it is assumed that the shear force at the top of the free segment is evenly distributed between the two pile columns; After solving the equations, the matrix analysis method is used to determine the displacement and internal force of the double-pile double-column structure.

2. The method for safety assessment of the substructure of a double-pile double-column bridge in a slope section according to claim 1 is characterized in that: In S2, the relative relationship between the bridge alignment and the corresponding slope divides the pile foundation into longitudinal bridge foundation and transverse bridge foundation; According to the relative positional relationship between the structure and the slope surface (5) and the potential slip surface (6), the pile foundation is divided vertically into a first free section A, a second free section B, a load-bearing section C and an embedded section D which are connected in sequence from top to bottom; The residual sliding force of the rock and soil mass in the loaded section C is calculated by the residual thrust method in the extreme equilibrium method. If the pile foundation is a transverse pile foundation, the two piles bear the same rock and soil mass force. If the pile foundation is a longitudinal bridge foundation, the force distribution relationship between the front pile (3) and the rear pile (4) is determined by the ratio of the cross-sectional area of ​​the rock and soil mass between the piles to the cross-sectional area of ​​the sliding mass, and the residual sliding force of the rock and soil mass on the front pile (3) and the rear pile (4) is obtained.

3. The method for safety assessment of the substructure of a double-pile double-column bridge in a slope section according to claim 1 is characterized in that: The resistance distribution law of the rock and soil mass on the pile side of the pile foundation is determined based on the elastic foundation reaction method.

4. The method for safety assessment of the substructure of a double-pile double-column bridge in a slope section according to claim 1 is characterized in that: S3 is specifically: Based on the residual sliding force of the rock and soil mass on the pile side and the distribution law of the rock and soil resistance, the first free section A, the second free section B, the loaded section C and the embedded section D are respectively taken for force analysis, and then the deflection curve differential equation is constructed. The deflection curve differential equations of the first free section A, the second free section B, the loaded section C and the embedded section D are shown in equations (1) to (4) respectively: （1） （2） （3） （4） in, Among them, x represents the direction of the force acting on the rock and soil mass; z indicates vertical direction; N represents the axial force, and the subscripts 0, 1, 2, and 3 correspond to the first free section A, the second free section B, the loaded section C, and the embedded section D, respectively; f represents the axial force growth coefficient, with subscripts 0, 1, 2, and 3 corresponding to the first free section A, the second free section B, the loaded section C, and the embedded section D, respectively; E represents the elastic modulus; I represents the moment of inertia of the section; a , b , c represents the undetermined coefficient of the residual sliding force distribution function, and the subscripts 0, 1, 2, and 3 correspond to the first free section A, the second free section B, the loaded section C, and the embedded section D, respectively; l 2 represents the length of the pile body in the load-bearing section C; m Represents the relevant parameters in the solution method, 2 and 3 correspond to the loaded section C and the embedded section D respectively.

5. The method for safety assessment of the substructure of a double-pile double-column bridge in a slope section according to claim 1 is characterized in that: The equation group includes an equation group corresponding to the top of the first free section A of the front pile (3) and the rear pile (4), an equation group corresponding to the connection between the first free section A and the second free section B, an equation group corresponding to the connection between the second free section B and the load section C, an equation group corresponding to the connection between the load section C and the embedded section D, and an equation group corresponding to the boundary conditions at the bottom of the pile.

6. The method for safety assessment of the substructure of a double-pile double-column bridge in a slope section according to claim 1 is characterized in that: In S5, the cross-sectional strength of the pile column and the displacement of the top of the pile column are verified, and the following formula is used for judgment: ； ； ； in, It represents the calculated value of the pile axial force at the unstable slope position; It represents the calculated value of the bending moment of the pile at the unstable slope position; represents the calculated value of the displacement of the top of the pile at the unstable slope location; Indicates the compressive bearing capacity of the pile cross section; It indicates the bending bearing capacity of the pile cross section; represents the displacement limit of the pile top; If the above three formulas are satisfied, the substructure of the double-pile double-column bridge is in a safe state under the action of an unstable slope; otherwise, there is a risk of damage.

7. A system for safety assessment of the substructure of a double-pile double-column bridge on a slope section based on the method for safety assessment of the substructure of a double-pile double-column bridge on a slope section according to any one of claims 1 to 6, characterized in that: include: Slope stability analysis module, used to analyze slope stability and determine potential slip surfaces based on the natural geographical conditions and engineering geological conditions at the potential landslide location (6); The foundation force characteristic analysis module is used to divide the bridge pile foundation according to the relative relationship between the bridge route and the corresponding slope, the relative position relationship between the structure and the slope surface (5), and the potential sliding surface (6), and to determine the residual sliding force of the rock and soil mass and the distribution law of the rock and soil mass resistance respectively; The module for establishing the differential equation of deflection curve is used to analyze the stress of each part of the pile foundation and establish the corresponding differential equation of deflection curve according to the residual sliding force of the rock and soil mass and the distribution law of the resistance of the rock and soil mass; An analytical module is used to determine the internal force and displacement of the double-pile double-column structure based on the continuity conditions and structural boundary conditions of the displacement and internal force between each characteristic pile segment, and considering the distribution conditions of the internal force and displacement of the front pile (3) and the rear pile (4) by the cap beam (1) and the tie beam (2), combined with the deflection curve differential equation, and to solve the equation group simultaneously; The structural safety assessment module is used to verify the cross-sectional strength of the pile column and the displacement of the top of the pile column based on the displacement and internal force of the double-pile double-column structure according to the ultimate bearing capacity state analysis method.

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