A method for calculating seismic earth pressure of soil mass behind pile-slab wall considering time-history effect

Abstract

The application discloses a kind of pile board wall back soil mass seismic earth pressure calculation method considering time course effect, it is characterized in that, including the following steps: S10, according to the soil mass curve sliding surface behind pile board wall to establish calculation model;S20, considering the stress of sliding soil wedge differential unit body changes under the influence of slope surface and curve sliding surface, according to calculation model is divided into 0≤z≤H and H≤z≤H+L these two sections to calculate the seismic inertia force of sliding soil wedge body, gravity;S30, based on energy dissipation principle to calculate the work done by sliding soil wedge body external force and the internal energy dissipation of sliding soil wedge body;S40, according to the work done by sliding soil wedge body external force and internal energy dissipation to establish balance equation;S50, according to balance equation to calculate the seismic earth pressure time course;S60, according to seismic earth pressure time course to draw time course curve.The application can explore the dissipation, transmission mode of energy in the reinforced slope of pile board wall, make up the problem that traditional calculation method cannot accurately consider dynamic process in earthquake process.

Description

TECHNICAL FIELD

[0001] The present application relates to the civil engineering field, in particular to a pile-slab wall back soil seismic earth pressure calculation method considering time history effect. BACKGROUND

[0002] The pile-slab wall has been widely applied to various types of slopes due to its good anti-sliding capacity, flexible pile position, convenient construction and strong anti-seismic performance. The embedded part of the pile-slab wall in the soil is the embedded segment, and the part above the ground is the cantilever segment. The pile-slab wall mainly relies on the embedded segment to maintain stability under the action of soil pressure by utilizing the strong bending resistance of the pile body. However, the current anti-seismic design of the structure is too simple, the structural characteristics of the pile-slab wall are not considered during the design, and the seismic action is mostly considered as inertia force. The specific research on how the soil pressure of the pile-slab wall changes with time under the action of continuous earthquakes is still blank. Therefore, it is necessary to study the time history of the seismic soil pressure of the pile-slab wall.

[0003] The existing calculation methods for the soil pressure of the pile-slab retaining wall under the action of earthquakes include the pseudo-static method and the Newmark method. However, the existing methods do not accurately consider the dynamic process during the earthquake, but consider the seismic force as a static force to calculate the dynamic problem, which is quite different from the actual engineering. SUMMARY

[0004] Therefore, it is necessary to provide a pile-slab wall back soil seismic earth pressure calculation method considering time history effect. The calculation method can reveal the dissipation and transmission mode of energy in the pile-slab wall reinforced slope, make up for the problem that the traditional calculation method cannot accurately consider the dynamic process during the earthquake, and has sufficient theoretical conditions, reasonable calculation, and conforms to the actual engineering situation, which can more accurately serve the design of the pile-slab structure reinforced slope in high intensity areas.

[0005] To achieve the purpose of the present application, the following technical solutions are adopted:

[0006] A pile-slab wall back soil seismic earth pressure calculation method considering time history effect, comprising the following steps:

[0007] S10, a calculation model is established according to the curve sliding surface of the soil body behind the pile-slab wall: the curve sliding surface at the junction of the soil body and the bedrock is simplified as a cycloid, a two-dimensional coordinate system X0Y is established with the highest point of the cycloid as the origin, and the expression of the tangent slope tanω of the cycloid in the calculation model is obtained through the stress analysis of the differential unit body:

[0008]

[0009]

[0010] Wherein, ω represents the included angle between the tangent line of a point on the cycloid and the horizontal direction, x and y both represent the equation of the curve slip surface, θ represents the radian of the radius of the circle generating the cycloid, R represents the counterforce of the soil acting on the curve slip surface;

[0011] S20, a pile-slab wall theory analysis model is used to set the curved slip surface of the backfill soil after the pile-slab wall, the stress of the differential unit of the sliding soil wedge is changed under the influence of the slope surface and the curved slip surface, the seismic inertia force and the gravity of the sliding soil wedge are calculated according to the calculation model in two sections of 0≤z≤H and H≤z≤H+L, z represents the depth of an arbitrary point on the curved slip surface, H is the vertical distance from the top of the pile-slab wall to the origin, L represents the vertical length of the pile-slab wall, and h represents the vertical length of the cantilever section of the pile-slab wall;

[0012] S30, the work done by the external force of the sliding soil wedge is calculated based on the energy dissipation principle according to the seismic inertia force, the gravity and the supporting resistance of the pile-slab wall to the sliding soil wedge, and the internal energy dissipation of the sliding soil wedge is calculated based on the energy dissipation principle using the cohesion and the internal friction angle of the soil, wherein the work done by the external force of the sliding soil wedge and the internal energy dissipation of the sliding soil wedge are both calculated in two sections of 0≤z≤H and H≤z≤H+L;

[0013] 1) when 0≤z≤H, the work done by the external force of the sliding soil wedge is calculated based on the energy dissipation,

[0014]

[0015]

[0016]

[0017]

[0018] At this time, the work done by the external force of the sliding soil wedge is:

[0019]

[0020] When H≤z≤H+L,

[0021]

[0022]

[0023]

[0024]

[0025] At this time, the work done by the external force of the sliding soil wedge is:

[0026]

[0027] In the formula, v represents the strain rate of the differential unit at a certain point on the curved sliding surface; θ' represents the corresponding rotation angle of the arbitrary differential unit on the curved sliding surface; δ represents the back normal angle of the vertical pile-slab wall; q sh represents the horizontal seismic inertial force borne by the differential unit, z represents the depth of an arbitrary point on the curved sliding surface, dz represents the thickness of the differential unit at an arbitrary point on the curved sliding surface, R represents the reaction force of the soil acting on the curved sliding surface, γ s represents the specific weight of the sliding soil wedge, θ a represents the rotation angle of the cycloid passing through the wall toe, a0 represents the base acceleration amplitude of the input wave, f s represents the seismic acceleration amplification coefficient of the fill, f represents the supporting resistance of the pile-slab wall to the sliding soil wedge, h represents the vertical length of the cantilever section of the pile-slab wall;

[0028] 2) Internal energy dissipation calculation of the sliding soil wedge based on the energy dissipation principle

[0029] The calculation expression of the internal energy dissipation Q'' of the sliding soil wedge calculated based on the energy dissipation principle is as follows:

[0030]

[0031]

[0032]

[0033] wherein, Q c represents the internal energy dissipation caused by the friction of the soil, Q f represents the internal energy dissipation caused by the cohesion of the soil, m z g represents the gravity borne by the differential unit, v represents the strain rate of the differential unit at a certain point on the curved sliding surface, δ represents the back normal angle of the vertical pile-slab wall, represents the internal friction angle, θ' represents the corresponding rotation angle of the arbitrary differential unit on the curved sliding surface, f represents the supporting resistance of the pile-slab wall to the sliding soil wedge, q sh represents the horizontal seismic inertial force borne by the differential unit, c s represents the cohesion of the soil, R represents the reaction force of the soil acting on the curved sliding surface;

[0034] S40, establishing a balance equation according to the work done by the external force of the sliding soil wedge and the internal energy dissipation;

[0035] S50, calculating the time history of the seismic earth pressure according to the balance equation;

[0036] S60, drawing a time history curve according to the time history of the seismic earth pressure, and completing the calculation of the seismic earth pressure of the gravity pile sheet wall.

[0037] In one embodiment, in step S20, the gravity W of the sliding soil wedge is expressed as follows:

[0038] When 0≤z≤H, i.e. the differential unit at any depth z above the pile sheet wall, the gravity expression of the sliding soil wedge W(z) in this range is:

[0039]

[0040] When H≤z≤H+L, i.e. the differential unit corresponding to the top end of the pile sheet wall to the bottom end of the pile sheet wall, the gravity expression of the sliding soil wedge W(z) in this range is:

[0041]

[0042] wherein γ s represents the specific gravity of the sliding soil wedge, θ a represents the rotation angle of the cycloid through the wall toe, z represents the depth of any point on the curved slip surface, dz represents the thickness of the differential unit at any point on the curved slip surface, R represents the reaction force of the soil acting on the curved slip surface, θ' represents the corresponding rotation angle of the differential unit on the curved slip surface, and a represents the distance from the slope end point A to the coordinate origin O.

[0043] In one embodiment, in step S20, the calculation expression of the seismic inertia force q sh of the sliding soil wedge is as follows:

[0044] When 0≤z≤H,

[0045]

[0046] When H≤z≤H+L,

[0047]

[0048] wherein a0 represents the base acceleration amplitude of the input wave, g represents the gravitational acceleration, f s represents the seismic acceleration amplification coefficient of the fill, γ s represents the specific gravity of the sliding soil wedge, θ arepresents the rotation angle of cycloid through the toe of the wall, z represents the depth of any point on the curved slip surface, dz represents the thickness of the microelement at any point on the curved slip surface; R represents the reaction force of the soil acting on the curved slip surface, θ' represents the corresponding rotation angle of the selected differential element on the curved slip surface, a represents the distance from the end point A of the slope to the coordinate origin O, H is the vertical distance from the top end of the sheet pile wall to the coordinate origin O, and h represents the vertical length of the cantilever section of the sheet pile wall.

[0049] In one embodiment, in step S40, the power balance equation of the sheet pile wall reinforced slope under the action of earthquake is expressed as follows:

[0050] When 0≤z≤H,

[0051]

[0052] When H≤z≤H+L,

[0053]

[0054] wherein c s represents the cohesion of the soil, v represents the strain rate of the differential element at a point on the curved slip surface, R represents the reaction force of the soil acting on the curved slip surface, θ' represents the corresponding rotation angle of the selected differential element on the curved slip surface, m z g represents the gravity of the differential element, f represents the supporting resistance of the sheet pile wall to the sliding soil wedge, δ represents the back normal angle of the vertical sheet pile wall, q sh represents the horizontal seismic inertial force of the differential element, H is the vertical distance from the top end of the sheet pile wall to the coordinate origin O, h represents the vertical length of the cantilever section of the sheet pile wall, a represents the distance from the end point A of the slope to the coordinate origin O, z represents the depth of any point on the curved slip surface, dz represents the thickness of the microelement at any point on the curved slip surface, θ a represents the rotation angle of cycloid through the toe of the wall, represents the internal friction angle, γ s represents the unit weight of the sliding soil wedge.

[0055] In one embodiment, step S50 specifically comprises the following steps:

[0056] S51, obtaining the expression of the supporting force P of the sheet pile wall to the sliding soil wedge under the action of earthquake according to the balance equation; a ;

[0057] S52, setting dP a / dθ a =0, and calculating the rotation angle θ a of cycloid through the toe of the wall by using Mathematica software;

[0058] S53. Based on the supporting force P of the pile-slab wall on the sliding soil wedge under seismic action. a and rotation angle θ a The supporting force P of the pile-slab wall on the sliding soil wedge under seismic loading was calculated. a The extreme values;

[0059] S54. Compare the supporting force P of the pile-slab wall on the sliding soil wedge under seismic loading. a The extreme value of the support force P a The maximum value;

[0060] S55. Calculate the supporting force P of the pile-slab wall on the sliding soil wedge under continuous seismic action. a The maximum value is the required earthquake earth pressure time history.

[0061] In one embodiment, in step S51, the supporting force P of the pile-slab wall on the sliding soil wedge under seismic action is... a The expression is as follows:

[0062] When 0≤z≤H

[0063]

[0064] in

[0065]

[0066] When H≤z≤H+L (from the top of the pile to the back of the slip surface):

[0067]

[0068] in

[0069]

[0070] In the above formula, ν represents the strain rate of the differential element at a point on the curved slip surface, R represents the reaction force of the soil acting on the curved slip surface, θ' represents the rotation angle of an arbitrarily chosen differential element on the curved slip surface, and m z g represents the gravity acting on the differential element, δ represents the angle of the back normal of the vertical pile-slab wall, and q sh Let θ represent the horizontal seismic inertial force acting on the differential element, H be the vertical distance from the top of the pile-slab wall to the origin O, h be the vertical length of the cantilever section of the pile-slab wall, a be the distance from the slope endpoint A to the origin O, z be the depth at any point on the curved slip surface, dz be the thickness of the differential element at any point on the curved slip surface, and θ be the depth of the differential element. a c represents the angle of rotation of the cycloid through the toe of the wall. s Indicates soil cohesion. γ represents the angle of internal friction. sThe gravity of the sliding soil wedge.

[0071] The method has the advantages that the external force power and internal energy dissipation are calculated according to the energy dissipation principle, the balance equation is established according to the energy conservation principle, and the time history of the seismic soil pressure of the pile-slab wall is calculated. The theoretical calculation result of the method is compared with the measured result through the shaking table test, and it is proved that the theoretical calculation result has high precision, and the applicability of the calculation method is verified. The calculation method can explore the dissipation and transmission mode of the energy in the pile-slab wall reinforced slope, makes up for the problem that the dynamic process in the seismic process cannot be accurately considered in the traditional calculation method, and has sufficient theoretical conditions, reasonable calculation and actual engineering conditions, and can more accurately serve the design of the pile-slab structure reinforced slope in the high intensity area. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 The method flow chart of the method;

[0073] Figure 2 The calculation model graph of the method;

[0074] Figure 3 The test simulation structure model graph;

[0075] Figure 4 The test simulation structure model measurement point cross section graph;

[0076] Figure 5 The comparison schematic graph of the test measured data and the calculation theoretical data of the method.

[0077] Markings in the graph: 110, soil body; 120, curved sliding crack surface; 130, bedrock; 140, pile-slab wall; 141, anchoring section; 142, cantilever section; 150, shaking table; 160, soil pressure gauge; 161, piezoelectric soil pressure gauge; 162, strain soil pressure gauge. DETAILED DESCRIPTION

[0078] In order to make the above-mentioned purposes, characteristics and advantages of the method more obvious and easy to understand, the specific embodiments of the method are described in detail below. In the following description, a large number of specific details are set forth in order to fully understand the method. However, the method can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the method, so the method is not limited by the specific embodiments disclosed below.

[0079] Please refer to Figure 1 The method provided by the method provides a pile-slab wall back soil body seismic soil pressure calculation method considering time history effect, which includes the following steps:

[0080] S10, according to the soil body 110 curve sliding surface 120 behind the pile-slab wall 140 to establish a calculation model: as shown, the curve sliding surface 120 at the junction of the soil body 110 and the bedrock 130 is simplified as a cycloid, a two-dimensional coordinate system X0Y is established with the highest point A of the cycloid as the origin, according to the stress analysis of the differential unit, the expression of the tangent slope tanω of the cycloid in the calculation model is obtained: Figure 2

[0081]

[0082]

[0083] Wherein, ω represents the included angle between the tangent line at a point on the cycloid and the horizontal direction, x and y represent the equation of the curve sliding surface 120, θ represents the radian through which the radius of the generated cycloid passes, R represents the counterforce of the soil body 110 acting on the curve sliding surface 120.

[0084] S20, using the theoretical analysis model of the pile-slab wall 140, setting that the curve sliding surface 120 is generated behind the pile-slab wall 140, considering that the stress of the sliding soil wedge differential unit is changed under the influence of the slope surface and the curve sliding surface 120, according to the calculation model, the seismic inertia force and the gravity of the sliding soil wedge are calculated in two sections of 0≤z≤H and H≤z≤H+L, wherein the pile-slab wall 140 has an anchoring section 141 and a cantilever section 142, z represents the depth of an arbitrary point on the curve sliding surface 120, H is the vertical distance from the top end of the pile-slab wall 140 to the coordinate origin O, L represents the vertical length of the pile-slab wall 140, and h represents the vertical length of the cantilever section 142 of the pile-slab wall 140.

[0085] 1) about the gravity W of the sliding soil wedge

[0086] Specifically, when 0≤z≤H, that is, the differential unit at any depth z above the pile-slab wall 140, the gravity expression of the sliding soil wedge in this range is:

[0087]

[0088] When H≤z≤H+L, that is, the differential unit corresponding to the top end of the pile-slab wall 140 to the bottom end of the pile-slab wall 140, the gravity expression of the sliding soil wedge in this range is:

[0089]

[0090] Wherein, γ s represents the specific gravity of the sliding soil wedge, θ a ​where z represents the depth of an arbitrary point on the curved slip surface 120, dz represents the thickness of the infinitesimal element at an arbitrary point on the curved slip surface 120, R represents the reaction force of the soil body 110 acting on the curved slip surface 120, θ' represents the corresponding rotation angle of the arbitrary differential element on the curved slip surface 120, and a represents the distance from the slope end point A to the coordinate origin O.

[0091] 2) Seismic inertia force q of the sliding soil wedge sh Calculation,

[0092] In this embodiment, the seismic inertia force calculation adopts the following basic assumptions:

[0093] (1) When the pile-slab wall 140 is in a critical overturning state, the soil body 110 behind the pile-slab wall 140 reaches limit equilibrium and forms a sliding soil wedge, and a curved slip surface 120 is formed inside the soil body 110 passing through the wall toe of the pile-slab wall 140;

[0094] (2) The pile-slab wall 140 is regarded as a rigid body, and the backfill soil of the pile-slab wall 140 is homogeneous and isotropic sand with a certain cohesion.

[0095] In this embodiment, under the action of the earthquake, when the pile-slab wall 140 is away from the backfill soil, the soil body 110 behind the pile-slab wall 140 slides downward along a certain cycloid surface to form a cycloid-shaped sliding soil wedge. As shown in the calculation model diagram, Figure 2 an arbitrary point P is taken on the curved slip surface 120, the depth of the point is z, and the corresponding rotation angle is θ'. The thickness of the infinitesimal element at the point is taken as the research object. In Figure 2 , the pile-slab wall 140 is upright, and the vertical length is L. The backfill soil of the pile-slab wall 140 is sand with a certain cohesion, the density is p s , the specific gravity of the sliding soil wedge is g s , the cohesion of the soil body 110 is c s , and the internal friction angle is The top surface of the backfill soil is horizontal, and the surface is not subjected to other loads. Under the action of the earthquake, the sliding soil wedge is subjected to the action of the horizontal seismic inertia force q sh .

[0096] The calculation expression of the seismic inertia force q sh of the sliding soil wedge is as follows:

[0097] When 0≤z≤H,

[0098]

[0099] When H≤z≤H+L,

[0100]

[0101] wherein a0 represents the base acceleration amplitude of the input wave, g represents the acceleration of gravity, f s represents the earthquake acceleration amplification factor of the fill, γ s represents the specific gravity of the sliding soil wedge, θ a represents the rotation angle of the cycloid through the wall toe, z represents the depth of an arbitrary point on the curved slip surface 120, dz represents the thickness of the microelement on the curved slip surface 120, R represents the reaction force of the soil body 110 acting on the curved slip surface 120, θ' represents the corresponding rotation angle of the arbitrary differential element on the curved slip surface 120, a represents the distance from the slope endpoint A to the coordinate origin O, H represents the vertical distance from the top of the sheet pile wall 140 to the coordinate origin O, and h represents the vertical length of the cantilever section 142 of the sheet pile wall 140.

[0102] S30, based on the seismic inertial force, the gravity, and the supporting resistance of the sheet pile wall 140 to the sliding soil wedge, the work done by the external force of the sliding soil wedge is calculated based on the energy dissipation principle, and the internal energy dissipation of the sliding soil wedge is calculated based on the energy dissipation principle using the cohesion and internal friction angle of the soil body 110, wherein the work done by the external force of the sliding soil wedge and the internal energy dissipation of the sliding soil wedge are both calculated in two sections of 0≤z≤H and H≤z≤H+L.

[0103] 1) Calculation of the work done by the external force based on energy dissipation

[0104] In this embodiment, the external forces acting on the differential element of the sliding soil wedge include the gravity m z g, the seismic inertial force q sh , and the supporting force p a of the sheet pile wall 140 to the differential element. When the soil body 110 is in a plastic flow state, it is assumed that the strain rate of the differential element at point P on the curved slip surface 120 is v, and the differential element is inclined downward along the tangent direction at point P. The force diagram of the differential element is shown in Figure 2 , from which it can be seen that the work done by the external force of the sliding soil wedge Q' = Q w + Q' f + Q sh + Q" f , wherein Q w represents the work done by the gravity, Q sh represents the work done by the horizontal seismic inertial force, Q' f represents the work done by the sheet pile wall 140 to the sliding soil wedge in the vertical direction, Q' f represents the work done by the sheet pile wall 140 to the sliding soil wedge in the horizontal direction, and Q" f represents the work done by the sheet pile wall 140 to the sliding soil wedge in the vertical direction.

[0105] When 0≤z≤H,

[0106]

[0107]

[0108]

[0109]

[0110] The work done by the external force of the sliding soil wedge at this time is:

[0111]

[0112] When H≤z≤H+L,

[0113]

[0114]

[0115]

[0116]

[0117] The work done by the external force of the sliding soil wedge at this time is:

[0118]

[0119] In the above formula, v represents the strain rate of a differential unit at a certain point on the curved slip surface 120; θ' represents the corresponding rotation angle of the arbitrary differential unit on the curved slip surface 120; δ represents the back normal angle of the vertical pile-slab wall 140; q sh represents the horizontal seismic inertial force borne by the differential unit, z represents the depth of an arbitrary point on the curved slip surface 120, dz represents the thickness of the differential unit at the arbitrary point on the curved slip surface 120, R represents the reaction force of the soil body 110 acting on the curved slip surface 120, γ s represents the specific weight of the sliding soil wedge, θ a represents the rotation angle of the cycloid through the toe of the wall, a0 represents the base acceleration amplitude of the input wave, f s represents the seismic acceleration amplification coefficient of the backfill, f represents the supporting resistance of the pile-slab wall 140 to the sliding soil wedge, h represents the vertical length of the cantilever section 142 of the pile-slab wall 140.

[0120] 2) Internal energy dissipation calculation of the sliding soil wedge based on the energy dissipation principle

[0121] In this embodiment, the internal energy dissipation of an arbitrary differential unit at point P is studied, and the energy consumed at any point on the curved slip surface 120 includes the work done by the cohesive force of the soil body 110 and the work done by the friction force.

[0122] The expression of the internal energy dissipation Q" of the sliding soil wedge is calculated based on the energy dissipation principle as follows:

[0123]

[0124]

[0125]

[0126] wherein Q c represents the internal energy dissipation caused by the friction of the soil body 110, Q f represents the internal energy dissipation caused by the cohesion of the soil body 110, m z g represents the gravity of the differential unit, v represents the strain rate of the differential unit at a point on the curved sliding surface, δ represents the back normal angle of the vertical pile-slab wall 140, represents the internal friction angle, θ' represents the corresponding rotation angle of the arbitrary differential unit on the curved sliding surface 120, f represents the supporting resistance of the pile-slab wall 140 to the sliding soil wedge, q sh represents the horizontal seismic inertia force of the differential unit, c s represents the cohesion of the soil body 110, and R represents the reaction force of the soil body 110 on the curved sliding surface 120.

[0127] S40, establishing a balance equation according to the work done by the external force of the sliding soil wedge and the internal energy dissipation;

[0128] Specifically, in step S40, the power balance equation of the pile-slab wall 140 reinforcing the slope under the action of the earthquake is expressed as follows:

[0129] When 0≤z≤H,

[0130]

[0131] When H≤z≤H+L,

[0132]

[0133] wherein c s represents the cohesion of the soil body 110, v represents the strain rate of the differential unit at a point on the curved sliding surface 120, R represents the reaction force of the soil body 110 on the curved sliding surface 120, θ' represents the corresponding rotation angle of the arbitrary differential unit on the curved sliding surface 120, m z g represents the gravity of the differential unit, f represents the supporting resistance of the pile-slab wall 140 to the sliding soil wedge, δ represents the back normal angle of the vertical pile-slab wall 140, q shLet H represent the horizontal seismic inertial force acting on the differential element, H be the vertical distance from the top of the pile-slab wall 140 to the origin O, h be the vertical length of the cantilever segment 142 of the pile-slab wall 140, a be the distance from the slope endpoint A to the origin O, z be the depth at any point on the curved slip surface 120, dz be the thickness of the differential element at any point on the curved slip surface 120, and θ be the depth of the differential element. a This indicates the angle of rotation of the cycloid through the toe of the wall. γ represents the angle of internal friction. s This indicates the unit weight of the sliding soil wedge.

[0134] S50. The earthquake earth pressure time history is calculated based on the equilibrium equation.

[0135] Furthermore, step S50 specifically includes the following steps:

[0136] S51. Based on the equilibrium equations, obtain the supporting force P of the pile-slab wall 140 against the sliding soil wedge under seismic loading. a The expression;

[0137] In step S51, the supporting force P of the pile-slab wall 140 on the sliding soil wedge under seismic action is... a The expression is as follows:

[0138] When 0≤z≤H

[0139]

[0140] in

[0141]

[0142] When H≤z≤H+L (from the top of the pile to the back of the slip surface):

[0143]

[0144] in

[0145]

[0146] In the above formula, ν represents the strain rate of the differential element at a point on the curved slip surface, R represents the reaction force of soil 110 acting on the curved slip surface 120, θ' represents the rotation angle of an arbitrarily chosen differential element on the curved slip surface 120, and m z g represents the gravity acting on the differential element, δ represents the 140° back normal angle of the vertical pile-slab wall, and q shrepresents the horizontal seismic inertial force on the differential element, H is the vertical distance from the top of the sheet pile wall 140 to the coordinate origin O, h represents the vertical length of the cantilever section 142 of the sheet pile wall 140, a represents the distance from the slope end point A to the coordinate origin O, z represents the depth of an arbitrary point on the curved slip surface 120, dz represents the thickness of the differential element at an arbitrary point on the curved slip surface 120, and θ represents the rotation angle of the cycloid passing through the wall toe. a represents the rotation angle of the cycloid passing through the wall toe, c s represents the cohesion of the soil body 110, represents the internal friction angle, and γ s represents the unit weight of the sliding soil wedge.

[0147] S52, dP a / dθ a = 0 is established, and the rotation angle θ of the cycloid passing through the wall toe is calculated by using the Mathematica software. a

[0148] S53, according to the retaining force P of the sheet pile wall 140 on the sliding soil wedge under the action of the earthquake and the rotation angle θ, the extreme value of the retaining force P of the sheet pile wall 140 on the sliding soil wedge under the action of the earthquake is calculated. a a

[0149] S54, the maximum value of the retaining force P of the sheet pile wall 140 on the sliding soil wedge under the action of the earthquake is obtained by comparing the extreme value of the retaining force P of the sheet pile wall 140 on the sliding soil wedge under the action of the earthquake. a a

[0150] S55, the maximum value of the retaining force P of the sheet pile wall 140 on the sliding soil wedge under the action of the earthquake, i.e., the required time history of the seismic earth pressure, is calculated. a a

[0151] S60, the time history curve is drawn according to the time history of the seismic earth pressure, and the calculation of the seismic earth pressure of the gravity type sheet pile wall 140 is completed.

[0152] In order to verify the accuracy of the theoretical calculation method of the present application, the Wenchuan earthquake investigation data is combined, and the large-scale shaking table 150 test is used as a research means to obtain the earth pressure resultant force distribution of the sheet pile wall 140 reinforced slope under the action of the earthquake, and the results are compared with the theoretical calculation results, and the research results verify the applicability of the theoretical calculation method.

[0153] The reliability of the model test results depends on whether the test model truly reproduces the actual working state of the prototype structure system. In this study, the distortion model and the dimension analysis method are used to design the similarity relationship of the model, and the similarity constants of the physical quantities are shown in Table 1.

[0154] Table 1​​​​​​​

[0155]

[0156]

[0157] As Figures 3 to 5 shown, the prototype of the test simulation structure model is the dynamic response characteristics of a pile-slab wall 140 with a height of 21 m, according to the geometric similarity ratio, the size of the anti-slide pile in the test simulation structure model is 100 cm*12 cm*9 cm, 3 mm steel plates are installed on both sides of the pile, the two sides mainly subjected to bending moment are made of 20 mm PVC plates, the embedded depth of the anti-slide pile in the test simulation structure model is 0.4 m, each test simulation structure model includes 5 anti-slide piles and 4 soil retaining plates, the soil retaining plates are 0.6 m high and are simulated by 25 mm thick wooden plates, the front area of the pile is 0.58 m wide and 0.50 m deep. The base rock 130 has a unit weight of 20.3 kN / m 3 , a water content of 3.2%, a cohesion of 6.92 kPa and an internal friction angle of 38.26°. The soil body 110 has a unit weight of 18.5 kN / m 3 , a water content of 4%, a cohesion of 3.46 kPa and an internal friction angle of 32.17°. The soil pressure value is tested by using a soil pressure gauge 160, and the soil pressure value includes a strain type soil pressure gauge 162 and a piezoelectric type soil pressure gauge, which are used to test the static value and dynamic value of the soil pressure, respectively. A channel steel is used to isolate the sand and the soil pressure gauge 160, so as to reduce the damage of the model preparation soil to the soil pressure gauge 160 and avoid the influence of "zero drift" on the test results. The soil pressure gauge 160 is arranged on the side of the pile-slab wall 140 in contact with the soil, and one is arranged every 160 mm along the wall height, a total of 6. After the soil pressure intensity at each geometric height is measured by the soil pressure gauge 160 on the back of the wall, the area surrounded by the distribution curve and the coordinate axis can obtain the seismic soil pressure resultant force. As Figure 3 shown, the actually measured results are compared with the theoretically calculated results, and the comparison results verify the applicability of the analysis method. By comparing the theoretically calculated results and the actually measured results of the present application through the shaking table 150 test, it is proved that the theoretically calculated results of the present application have high precision, and the applicability of the analysis method of the present application is verified.

[0158] The pile-slab wall back soil body seismic soil pressure calculation method considering time history effect of the present application can prove the dissipation and transmission mode of energy in the pile-slab wall 140 reinforced slope, the soil pressure is calculated based on this method, the problem that the traditional static method cannot accurately consider the dynamic process of the seismic traveling wave in the slope is solved, the theoretical condition is sufficient, the calculation is reasonable, and the actual engineering situation is met, so that the present application can more accurately serve the design of the pile-slab structure reinforced slope in the high intensity area, and has important theoretical value and practical role.

[0159] Any combination of the technical features in the above-described embodiments can be made, and for the sake of brevity, not all possible combinations are described, however, as long as the combination of the technical features does not exist in contradiction, it shall be considered within the scope of the present disclosure.

[0160] The above-described embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it shall not be understood as a limitation on the patent scope of the present application. It shall be pointed out that, for ordinary skilled persons in the art, several modifications and improvements can be made without departing from the concept of the present application, and these shall be within the protection scope of the present application. Therefore, the protection scope of the present application patent shall be subject to the appended claims.

Claims

1. A method for calculating seismic earth pressure of a pile-slab wall backfill considering time history effect, characterized by, Comprising the following steps: S10, a calculation model is established according to the curve sliding surface of the soil body behind the pile-slab wall: the curve sliding surface at the junction of the soil body and the bedrock is simplified as a cycloid, a two-dimensional coordinate system X0Y is established with the highest point of the cycloid as the origin, and the expression of the tangent slope tanω of the cycloid in the calculation model is obtained according to the stress analysis of the differential unit body, wherein ω represents the included angle between the tangent at a point on the cycloid and the horizontal direction, x and y represent the equation of the curve sliding surface, θ represents the radian passed by the radius of the generated cycloid, and R represents the counterforce of the soil body acting on the curve sliding surface; S20, the theoretical analysis model of the pile-slab wall is used to set that the fill soil behind the pile-slab wall generates a curve sliding surface, the stress condition of the differential unit body of the sliding soil wedge is changed under the influence of the slope surface and the curve sliding surface, the seismic inertia force and the gravity of the sliding soil wedge are calculated according to the calculation model in two sections of 0≤z≤H and H≤z≤H+L, wherein z represents the depth of an arbitrary point on the curve sliding surface, H is the vertical distance from the top end of the pile-slab wall to the coordinate origin, L represents the vertical length of the pile-slab wall, and h represents the vertical length of the cantilever section of the pile-slab wall; S30, the work done by the external force of the sliding soil wedge is calculated based on the energy dissipation principle according to the seismic inertia force, the gravity and the supporting resistance of the pile-slab wall to the sliding soil wedge, and the internal energy dissipation of the sliding soil wedge is calculated based on the energy dissipation principle using the cohesion and the internal friction angle of the soil body, wherein the work done by the external force of the sliding soil wedge and the internal energy dissipation of the sliding soil wedge are also calculated in two sections of 0≤z≤H and H≤z≤H+L; 1) Calculation of the work done by the external force based on the energy dissipation When 0≤z≤H, At this time, the work done by the external force of the sliding soil wedge is: When H≤z≤H+L, At this time, the work done by the external force of the sliding soil wedge is: 2) Calculation of the internal energy dissipation of the sliding soil wedge based on the energy dissipation principle In the above formula, v represents the strain rate of the differential element at a certain point on the curved slip surface; θ' represents the corresponding rotation angle of the arbitrary differential element on the curved slip surface; δ represents the back normal angle of the vertical pile-slab wall; q sh represents the horizontal seismic inertia force on the differential element, z represents the depth of an arbitrary point on the curved slip surface, dz represents the thickness of the differential element at an arbitrary point on the curved slip surface, R represents the reaction force of the soil acting on the curved slip surface, γ s represents the specific weight of the sliding soil wedge, θ a represents the rotation angle of the cycloid passing through the wall toe, a0 represents the base acceleration amplitude of the input wave, f s represents the seismic acceleration amplification coefficient of the fill, f represents the supporting resistance of the pile-slab wall to the sliding soil wedge, h represents the vertical length of the cantilever section of the pile-slab wall; The calculation expression of the internal energy dissipation Q of the sliding soil wedge based on the energy dissipation principle is as follows: S40, a balance equation is established according to the work done by the external force of the sliding soil wedge and the internal energy dissipation; where Q c represents the internal energy dissipation caused by the friction of the soil mass, Q f represents the internal energy dissipation caused by the cohesion of the soil mass, m z g represents the gravity force on the differential element, v represents the strain rate of the differential element at a point on the curved slip surface, δ represents the normal angle of the vertical pile-slab wall, represents the internal friction angle, θ' represents the corresponding rotation angle of the arbitrary differential element on the curved slip surface, f represents the support resistance of the pile-slab wall to the sliding soil wedge, q sh represents the horizontal seismic inertia force on the differential element, c s represents the cohesion of the soil mass, R represents the reaction force of the soil mass on the curved slip surface; S50, the time history of the seismic soil pressure is calculated according to the balance equation; S60, the time history curve is drawn according to the time history of the seismic soil pressure, and the calculation of the seismic soil pressure of the gravity type pile-slab wall is completed. In step S20, the expression of the gravity W of the sliding soil wedge is as follows:

2. The method for calculating the seismic earth pressure of the pile-slab wall backfill considering the time-history effect according to claim 1, characterized in that, When 0≤z≤H, that is, the differential unit body at any depth z above the pile-slab wall, the gravity expression of the sliding soil wedge W(z) in this range is: When H≤z≤H+L, that is, the differential unit corresponding to the top end of the pile-slab wall to the bottom end of the pile-slab wall, the gravity expression of the sliding soil wedge W(z) in this range is: When 0≤z≤H, where γ s represents the specific weight of the sliding soil wedge, θ a represents the rotation angle of the cycloid through the wall toe, z represents the depth of an arbitrary point on the curved slip surface, dz represents the thickness of the microelement at an arbitrary point on the curved slip surface, R represents the reaction force of the soil acting on the curved slip surface, θ' represents the corresponding rotation angle of the arbitrary differential element on the curved slip surface, and a represents the distance from the slope endpoint A to the coordinate origin O.

3. The method for calculating the seismic earth pressure of the pile-slab wall backfill considering the time-history effect according to claim 1, characterized in that, In step S20, the seismic inertia force q of the sliding soil wedge sh The calculation expression is as follows: When H≤z≤H+L, In step S40, the power balance equation expression of the pile-slab wall reinforced slope under the action of the earthquake is as follows: where a0 represents the base acceleration amplitude of the input wave, g represents the gravitational acceleration, f s represents the seismic acceleration amplification factor of the fill, γ s represents the specific gravity of the sliding soil wedge, θ a represents the rotation angle of the cycloid through the wall toe, z represents the depth of an arbitrary point on the curved slip surface, dz represents the thickness of the microelement at an arbitrary point on the curved slip surface; R represents the reaction force of the soil acting on the curved slip surface, θ' represents the corresponding rotation angle of the arbitrary differential element on the curved slip surface, a represents the distance from the slope endpoint A to the coordinate origin O, H is the vertical distance from the top of the sheet-pile wall to the coordinate origin O, and h represents the vertical length of the cantilever section of the sheet-pile wall.

4. The method for calculating the seismic earth pressure of the soil mass behind the pile-slab wall considering the time-history effect according to claim 1, characterized in that, When 0≤z≤H, When H≤z≤H+L, Step S50 specifically comprises the following steps: where c s represents the soil cohesion, v represents the strain rate of the differential element at a point on the curved slip surface, R represents the reaction force of the soil on the curved slip surface, θ' represents the corresponding rotation angle of the arbitrary differential element on the curved slip surface, m z g represents the gravity of the differential element, f represents the support resistance of the pile wall to the sliding soil wedge, δ represents the back normal angle of the vertical pile wall, q sh represents the horizontal seismic inertia force of the differential element, H represents the vertical distance from the top of the pile wall to the coordinate origin O, h represents the vertical length of the cantilever section of the pile wall, a represents the distance from the slope endpoint A to the coordinate origin O, z represents the depth of an arbitrary point on the curved slip surface, dz represents the thickness of the differential element at an arbitrary point on the curved slip surface, θ a represents the rotation angle of the cycloid through the toe of the wall, represents the internal friction angle, γ s represents the unit weight of the sliding soil wedge.

5. The method for calculating the seismic earth pressure of the soil mass behind the pile-slab wall considering the time-history effect according to claim 1, characterized in that, When 0≤z≤H, S51, get the retaining force P of the pile-slab wall to the sliding soil wedge under the earthquake action according to the balance equation a expression; S52, let dP a / dθ a = 0, and the cycloid through the wall toe rotation angle θ a ; S53、According to the retaining force P of the pile-slab wall to the sliding soil wedge under the action of earthquake a and the rotation angle θ a , the retaining force P of the pile-slab wall to the sliding soil wedge under the action of earthquake is calculated a The extreme value of the retaining force P S54, compare the retaining force P of the pile-slab wall to the sliding soil wedge under the action of earthquake a The extreme value of P a The maximum value of P S55, respectively calculate the corresponding pile-slab wall under the action of the earthquake sliding soil wedge support force P a The maximum value of the time history of the required seismic earth pressure.

6. The method for calculating the seismic earth pressure of the soil mass behind the pile-slab wall considering the time-history effect according to claim 5, characterized in that, In step S51, the retaining force P of the pile sheet wall against the sliding soil wedge under the action of the earthquake is calculated a The expression is as follows: When H≤z≤H+L (from the pile top to the pile back at the sliding surface): When H≤z≤H+L (from the pile top to the pile back at the sliding surface): ​ ​ In the above formula, v represents the strain rate of the differential element at a point on the curved slip surface, R represents the reaction force of the soil on the curved slip surface, θ' represents the corresponding rotation angle of the differential element on the curved slip surface, m z g represents the gravity of the differential element, δ represents the normal line angle of the vertical pile-slab wall, q sh represents the horizontal seismic inertia force of the differential element, H is the vertical distance from the top of the pile-slab wall to the coordinate origin O, h represents the vertical length of the cantilever section of the pile-slab wall, a represents the distance from the slope endpoint A to the coordinate origin O, z represents the depth of an arbitrary point on the curved slip surface, dz represents the thickness of the differential element at an arbitrary point on the curved slip surface, θ a represents the rotation angle of the cycloid through the toe of the wall, c s represents the cohesion of the soil, represents the internal friction angle, γ s represents the unit weight of the sliding soil wedge.

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