A method for predicting the settlement of a single pile in dry sand subjected to horizontal cyclic loading

Abstract

The present invention discloses a method for predicting the settlement of a single pile in dry sand under horizontal cyclic load. The method is based on MATLAB to calculate the settlement value of the pile under horizontal cyclic load in dry sand, and mainly includes: establishing a theoretical model of pile settlement movement; determining the basic parameters of the theoretical model and inputting them into MATLAB; using MATLAB to calculate the total settlement value of the pile until the end of the incremental step, including calculating the normal stress on the pile side, calculating the unbalanced force and vertical shear stiffness on the pile side, calculating the settlement of the pile body and distributing the unbalanced force on the pile side surface, until the total unbalanced force on the pile side is equal to zero, and the pile settlement obtained at this time is the total settlement of the pile body at this time; until the movement cycle reaches a specified number of times and outputs the final settlement value. The present invention realizes the automatic calculation of the settlement of the pile under horizontal cyclic load in dry sand, and provides an effective calculation tool for solving engineering problems of similar working conditions and scientific research problems in related fields.

Description

Technical Field

[0001] The invention relates to a method for analyzing the stress of a pile in infrastructure construction, and in particular to a method for predicting the settlement of a single pile in dry sand under horizontal cyclic load. Background Art

[0002] Pile foundations are widely used in the construction of various infrastructures, such as viaducts, high-rise buildings, and offshore structures. As the basic components supporting the superstructure, piles are inevitably subjected to horizontal cyclic loads during their service life (e.g., vehicle starting and braking forces acting on viaducts, seismic forces acting on high-rise buildings, wind or wave loads acting on the sea). Although there are a lot of literatures on the behavior of pile deformation and bearing capacity under horizontal loads, and the relevant industry standards are relatively complete, most of the literature and industry standards focus on the horizontal response (deformation and bearing capacity) of piles under horizontal loads, while there are few studies on the vertical settlement phenomenon of pile foundations under horizontal cyclic loads.

[0003] Regarding the settlement of piles under horizontal cyclic loading, a mainstream view is that the piles sink due to the failure of the soil due to vibration. The most typical case is soil liquefaction, which is considered to be the cause of excessive settlement of piles during earthquakes, but this view does not match the results of the 1985 Mexico earthquake. Another typical counterexample is that buildings with piles driven in clay also show obvious settlement due to cyclic horizontal loading, but clay is a typical non-liquefied soil. Therefore, soil liquefaction leading to a reduction in soil strength is not a reasonable explanation for the settlement of piles under horizontal cyclic loading.

[0004] A more reasonable view is that the main reason for the settlement of piles under cyclic horizontal loads is that the force at the pile-soil interface decreases under seismic loads. The force balance of the pile is destroyed, resulting in the settlement of the pile foundation. However, there are currently few studies on the settlement of piles under horizontal cyclic loads, and the relevant calculation theory is relatively scarce. There is a lack of effective calculation methods when solving engineering problems under similar working conditions and scientific research problems in related fields. Summary of the invention

[0005] In view of the above-mentioned prior art, the present invention provides a method for predicting the settlement of a single pile in dry sand under horizontal cyclic load, which is mainly based on MATLAB to calculate the settlement value of the pile under horizontal cyclic load in dry sand, including: establishing a theoretical model of pile settlement movement; determining the basic parameters of the above-mentioned theoretical model and inputting them into MATLAB; using MATLAB to calculate the total settlement value of the pile body at the end of the incremental step, until the movement cycle reaches a specified number of times and outputs the final settlement value.

[0006] Further, the method for predicting the settlement of a single pile in dry sand under horizontal cyclic loading according to the present invention comprises:

[0007] The theoretical model of pile settlement movement is as follows: the pile moves periodically under the action of horizontal cyclic load, and the total number of movement cycles is N; the movement process of the pile is decomposed into multiple small movements, each of which is called an incremental step and the horizontal movement distance of each incremental step is da; the stress and displacement relationship between the pile side surface and the soil is described by the load transfer method, and the pile side surface is divided into multiple units along the vertical and circumferential directions, and the number of vertical units of the pile is N. z , the number of units in the circumferential direction is N c ; Four subscript parameters i, j, p, and o are set respectively to represent the movement process of each unit surface and the pile, where i and j represent the circumferential and vertical numbers of the unit surface on the pile side, p represents the movement direction, and o represents the position of the pile body.

[0008] The basic parameters of the theoretical model include: pile related parameters and sand related parameters, where: pile related parameters include: pile burial depth L, pile diameter D, pile top vertical load F v , horizontal cyclic load displacement amplitude a and horizontal cyclic load eccentricity e L , the ratio of the initial pile end resistance to the total load R ini ; The relevant parameters of sand include: soil weight γ, internal friction angle Poisson's ratio υ, elastic modulus calculation parameter m, friction coefficient between pile and soil μ.

[0009] The calculation of the total settlement of the pile by MATLAB at the end of the incremental step includes: 1) calculating the normal stress on the pile side; 2) calculating the unbalanced force and vertical shear stiffness on the pile side; 3) calculating the settlement of the pile; 4) distributing the unbalanced force on the pile side surface; repeating the above process until the total unbalanced force on the pile side is equal to zero, at which point the obtained pile settlement is the total settlement of the pile by the end of the incremental step.

[0010] Further, the calculation of pile side normal stress includes:

[0011] 1-1) Calculate the initial slope k of the load transfer curve in the normal and tangential directions of the pile side surface respectively n,ini and k v,ini and the initial slope k of the normal load transfer curve at the pile end b,ini ;

[0012] 1-2) Calculate the maximum normal stress σ on the pile side surface respectively n,max , minimum normal stress σ n,min , static earth pressure σ0, and then according to the geometric relationship, the change in horizontal displacement of each unit surface along its external normal in one increment step is obtained. n,ijpo , according to the initial slope k of the load transfer curve normal to the pile side surface n,iniand the maximum normal stress σ on the pile side surface n,max Calculate the maximum horizontal displacement of the pile when the normal stress is maximum n,max Finally, the absolute value of the normal stress change σ of each front side and rear side in each incremental step is calculated according to the formula of the load transfer curve nc,ijpo , the front side surface is the unit surface moving toward the soil, and the rear side surface is the unit surface moving away from the soil;

[0013] 1-3) Calculate the normal stress of each unit surface on the pile side. First, determine whether the unit surface is the front side or the rear side. For the front side, add the static soil pressure σ0 plus the absolute value of the normal stress change σ nc,ijpo Get the normal stress σ of the unit surface n,ijpo ; For the rear side, use the static earth pressure σ0 minus the absolute value of the normal stress change σ nc,ijpo Get the normal stress σ of the unit surface n,ijpo .

[0014] Further, the method for calculating the unbalanced force and vertical shear stiffness on the pile side is as follows:

[0015] 2-1) Compare the vertical lateral friction τ on each unit surface v,ijpo With the limit friction, when the vertical lateral friction τ v,ijpo When the friction force is greater than the limit, an unbalanced force will be generated. The unbalanced force F on each unit surface is calculated separately. un,ijpo , and then the unbalanced force F on each unit surface un,ijpo The total unbalanced force F is obtained by summing un ;

[0016] 2-2) When calculating the vertical shear stiffness of the pile side, first update the vertical friction resistance τ of each unit surface v,ijpo , and the corresponding pile-soil vertical relative displacement ω is calculated based on the updated vertical friction and load transfer curve v,ijpo Then, according to the initial slope k of the load transfer curve tangential to the pile side surface v,ini and the pile-soil vertical relative displacement ω v,ijpo Calculate the vertical shear stiffness k of each element v,ijpo Finally, the vertical shear stiffness k of each unit is v,ijpo The vertical shear stiffness K of the pile side is obtained by summing v1 .

[0017] Further, the calculation of pile settlement includes:

[0018] 3-1) First, according to the initial slope k of the normal load transfer curve at the pile end b,ini Calculate the maximum reaction force σ at the pile end b,max , then according to the load transfer curve formula and the pile end normal stress σ of the previous increment stepb,(o-1) The settlement s before the unbalanced force on the pile side is calculated v,(o-1) , and the total stiffness K of the soil at the pile end is calculated based on this b ;

[0019] 3-2) Based on the vertical shear stiffness K of the pile side v1 The total stiffness K of the soil at the pile end b The unbalanced force F transmitted to the pile end is obtained by the ratio of un,b , the pile end normal stress σ at the previous increment b,(o-1) Add the unbalanced force distributed to the pile end to obtain the pile end normal stress σ in this increment. b,o Finally, the total settlement s of the pile body at the end of this incremental step is calculated according to the load transfer curve formula. v,o .

[0020] Further, the distribution of the unbalanced force on the pile side surface includes:

[0021] 4-1) First, according to the stiffness k of each unit on the pile side v,ijpo Total stiffness K of the pile side surface v1 The ratio of the total unbalanced force F on the pile side un Distribute to each unit surface and calculate the lateral friction τ of each unit surface after the unbalanced force is distributed v2,ijpo ;

[0022] 4-2) Then determine the lateral friction τ of each unit surface v2,ijpo Is it greater than the limit friction resistance, that is, whether there is a force overflow, and then calculate the total pile side unbalanced force F at this time unv2,po , and calculate the vertical shear stiffness k of each unit on the pile side at this time v3,ijpo ;

[0023] In the repeated cycle, the total pile side unbalanced force and the vertical shear stiffness of each unit on the pile side are iteratively updated until the total pile side unbalanced force is equal to zero.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] The present invention realizes the automatic calculation of the settlement of piles under horizontal cyclic load in dry sand. The calculation theory is reasonable and has been effectively verified by centrifuge model test, which fills the gap in related fields and provides an effective calculation tool for solving engineering problems in similar working conditions and scientific research problems in related fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1It is a schematic diagram of the theoretical model established in the method of the present invention, wherein the process shown in (a) is the initial 1 / 4 motion cycle; the processes shown in (b) and (c) are two groups of half motion cycles, which constitute the subsequent complete motion cycle.

[0027] Figure 2 It is a schematic diagram of the pile movement process in a single incremental step;

[0028] Figure 3 It is a schematic diagram of the total horizontal displacement of the pile side unit surface along the normal direction;

[0029] Figure 4 It is a schematic diagram of the front side and the rear side defined in the present invention;

[0030] Figure 5 is a flow chart of the method of the present invention;

[0031] Figure 6 These are the results of the centrifuge model test (CT) and the calculation results of the method of the present invention (TM). DETAILED DESCRIPTION

[0032] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention in any way.

[0033] The present invention proposes a method for predicting the settlement of a single pile in dry sand under horizontal cyclic load. The method is based on MATLAB to calculate the settlement value of the pile under horizontal cyclic load in dry sand. Figure 5 As shown, it mainly includes:

[0034] The first step is to establish a theoretical model of pile settlement movement;

[0035] Step 2: Determine the basic parameters of the theoretical model and input them into MATLAB;

[0036] Step 3: Use MATLAB to calculate the total settlement of the pile at the end of the incremental step, including

[0037] 1. Calculate the normal stress on the pile side;

[0038] 2. Calculate the unbalanced force and vertical shear stiffness on the pile side;

[0039] 3. Calculate pile settlement;

[0040] 4. Distribute the unbalanced force on the pile side surface;

[0041] Repeat step 4 above until the total unbalanced force on the pile side is equal to zero. The pile settlement obtained at this time is the total settlement of the pile up to the end of this incremental step.

[0042] Step 4: Repeat the process of step 3 above until the motion cycle reaches the specified number of times and outputs the final settlement value.

[0043] The contents of the above steps are as follows:

[0044] The first step is to develop a theoretical model for pile settlement motion in the present invention.

[0045] When the pile performs reciprocating cyclic motion under the action of horizontal cyclic load, the normal stress on the pile side surface moving away from the soil decreases, so the maximum side friction resistance that can be provided also decreases. At the same time, the side friction resistance that can be provided by the pile side surface moving towards the soil increases. Therefore, the reciprocating cyclic motion causes the limit value of the pile side friction resistance to change continuously, and the pile side surface cannot maintain a static equilibrium state, thus causing the pile to settle. In order to calculate the settlement of the pile under the action of horizontal cyclic load, the movement process of the pile is decomposed into multiple small movements, each of which is called an incremental step and the horizontal movement distance of each incremental step is da, such as Figure 2 As shown in Figure 1. The pile moves periodically under the horizontal cyclic load, and the total number of movement cycles is N. When describing the stress and displacement relationship between the pile side surface and the soil by the load transfer method, the pile side surface needs to be divided into multiple units along the vertical and circumferential directions. The number of vertical units of the pile body is N. z , the number of circumferential units is N c In addition, four subscript parameters i, j, p, and o need to be set to represent the movement process of each unit surface and pile, where i and j represent the numbers of the unit surface of the pile side along the circumferential and vertical directions, p represents the movement direction, and o represents the position of the pile body, such as Figure 1 shown.

[0046] The second step is to determine the basic parameters of the theoretical model and input them into MATLAB for calling.

[0047] The basic parameters of the theoretical model include pile-related parameters and sand-related parameters.

[0048] The relevant parameters of the pile include the pile depth L, the pile diameter D, the vertical load F at the top of the pile v , horizontal cyclic load displacement amplitude a and horizontal cyclic load eccentricity e L , the ratio of the initial pile end resistance to the total load R ini .

[0049] The parameters related to sand include soil weight γ, internal friction angle Poisson's ratio υ, elastic modulus calculation parameter m, friction coefficient between pile and soil μ.

[0050] The third step is to use MATLAB to calculate the total settlement of the pile at the end of the incremental step.

[0051] 1. Calculate the normal stress on the pile side;

[0052] (1) Calculate the initial slope k of the load transfer curve in the normal and tangential directions of the pile side surface respectively n,ini and k v,ini and the initial slope k of the normal load transfer curve at the pile end b,ini ; The specific calculation formula is as follows:

[0053]

[0054]

[0055]

[0056]

[0057] Among them, σ′ is the effective stress of soil; σ r is the reference stress, here it is 100kPa; G s,ini is the initial shear modulus of the soil; ζ is a dimensionless coefficient, which is taken as 4 here; z ij is the depth of the unit.

[0058] (2) First, calculate the maximum normal stress σ on the pile side surface n,max , minimum normal stress σ n,min , static earth pressure σ0, and then according to the geometric relationship, the change in horizontal displacement of each unit surface along its external normal in one increment is obtained. n, ijp o, based on the initial slope k of the load transfer curve normal to the pile side surface n,ini and the maximum normal stress σ on the pile side surface n,max Calculate the maximum horizontal displacement of the pile when the normal stress is maximum n,max , the horizontal displacement ω when the normal stress reaches the maximum value n,max Finally, the absolute value of the normal stress change σ of each front side and rear side in each incremental step is calculated according to the formula of the load transfer curve nc, ijp o, the front side surface is the unit surface moving toward the soil, and the rear side surface is the unit surface moving away from the soil. Figure 4 It should be noted that, with the cross section where the rotation center RC of the pile is located as the boundary, the distribution of the front side surface and the rear side surface is opposite in the upper and lower parts of the cross section, and will change with the reciprocating motion of the pile.

[0059] The movement of the pile is as follows Figure 1As shown, the process shown in (a) is the first 1 / 4 motion cycle, and the processes shown in (b) and (c) are two groups of half motion cycles, which constitute the subsequent complete motion cycle. In the first 1 / 4 motion cycle, the parameter o corresponding to the initial position of the pile is 0, and when it reaches the amplitude a, the parameter o is a / da; in the subsequent two groups of half motion cycles, the parameter o corresponding to the initial position of the pile is still 0, and at the final position it is 2a / da.

[0060] The pile is loaded and starts to move from a vertical position to one side. It first goes through 1 / 4 of the movement cycle, with a movement distance of a, and reaches the horizontal displacement amplitude. Then the pile begins to enter a complete movement cycle. The process of moving from the horizontal displacement amplitude on one side to the horizontal displacement amplitude on the other side is called a half movement cycle. Two half movement cycles constitute a complete movement cycle. In the first 1 / 4 movement cycle, the parameter o corresponding to the pile at the initial position is 0, and when it reaches the amplitude, the parameter o is a / da; in the next two groups of half movement cycles, the parameter o corresponding to the pile at the initial position is still 0, and at the final position it is 2a / da.

[0061] The specific calculation formula is as follows:

[0062] D RC =[-(0.567Z p +2.7e L )+(5.307L p 2 +7.29e L 2 +10.541e L L p ) 0.5 ] / 2.1996 (5)

[0063] σ n，max =K p 2 γz ij (6)

[0064] σ n，min =0 (7)

[0065]

[0066]

[0067]

[0068] ω n，ijpo =o·Δω n，ijpo (11)

[0069]

[0070] Among them, K p is the passive earth pressure coefficient, and its calculation formula is ω n，ijpo is the absolute value of the total horizontal displacement of each unit surface along its outer normal, such as Figure 3 As shown; D RC is the depth of the rotation center, such as Figure 2 As shown; L p The depth of the pile into the soil.

[0071] (3) Calculate the normal stress of each unit surface on the pile side. First, determine whether the unit surface is the front side or the rear side. For the front side, use the static soil pressure σ0 plus the absolute value of the normal stress change σ nc，ijpo Get the normal stress σ of the unit surface n，ijpo ; For the rear side, use the static earth pressure σ0 minus the absolute value of the normal stress change σ nc，ijpo Get the normal stress σ of the unit surface n，ijpo The specific calculation formula is as follows:

[0072] For the front side, if σ0+σ nc，ijpo ≥σ n，max or n，ijpo ≥ω n，wax

[0073] σ n，ijpo =σ n，max

[0074] If σ nc，ijp0 +σ nc，ijpo <σ n，max or n，ijpo <ω n，wax

[0075] σ n，ijpo =σ n，ijp0 +σ nc，ijpo

[0076] For the rear side, if σ nc，ijp0 -σ nc，ijpo ≤σ n，min or n，ijpo ≥ω n，wax

[0077] σ n，ijpo =σ n，min

[0078] If σ nc，ijp0 -σ nc，ijpo >σ n，min or n，iijpo <ω n，wax

[0079] σ n，ijpo =σ n，ijp0 -σnc，ijpo (13)

[0080] Among them, the normal stress σ of the unit surface at the initial position n，ijpo The initial value in the first incremental step calculation is σ0.

[0081] 2. Calculate the unbalanced force and vertical shear stiffness on the pile side.

[0082] (1) Comparison of the vertical lateral friction τ on each unit surface v，ijpo With the limit friction, when the vertical lateral friction τ v，ijpo When the friction force is greater than the limit, an unbalanced force will be generated. The unbalanced force F on each unit surface is calculated separately. un，ijpo , and then the unbalanced force F on each unit surface un，ijpo The total unbalanced force F is obtained by summing un ; The specific calculation formula is as follows:

[0083]

[0084]

[0085]

[0086] Among them, τ v,ijp(o-1) is the vertical friction of each unit surface on the pile side in the previous incremental step. The initial value for the first incremental step is τ v,ini .

[0087] (2) When calculating the vertical shear stiffness of the pile side, first update the vertical friction resistance τ of each unit surface v,ijpo , and the corresponding pile-soil vertical relative displacement ω is calculated based on the updated vertical friction and load transfer curve v,ijpo , and then calculate the vertical shear stiffness k of each unit v,ijpo Finally, the vertical shear stiffness k of each unit is v,ijpo The total shear stiffness K is obtained by summing v1 .

[0088]

[0089]

[0090]

[0091]

[0092]

[0093] where τ v,max is the maximum shear stress of each unit surface, according to the formula τv,max =μσ n,ijpo Calculate; v,max is the vertical relative displacement of pile-soil corresponding to the maximum value of the unit surface shear stress.

[0094] 3. Calculate pile settlement.

[0095] (1) First, according to the initial slope k of the normal load transfer curve at the pile end b,ini Calculate the maximum reaction force σ at the pile end b,max , then according to the load transfer curve formula and the pile end normal stress σ of the previous increment step b,(o-1) The settlement s before the unbalanced force on the pile side is calculated v,(o-1) , and the total stiffness K of the soil at the pile end is calculated based on this b ; The calculation formula is as follows:

[0096]

[0097]

[0098]

[0099]

[0100] Where λ is the coefficient reflecting the influence of pile construction method on foundation bearing capacity, which is taken as 0.2 here; s v,max is the displacement corresponding to the maximum stress of the pile end pressure, according to s v,max =λD for calculation;σ b,(o-1) is the pile end stress of the previous incremental step. The initial value of the first incremental step is σ b,ini , and is calculated according to formula (27) in the subsequent increment steps.

[0101] (2) Based on the pile side stiffness and pile end stiffness K b The unbalanced force F transmitted to the pile end is obtained by the ratio of un,b , the pile end normal stress σ at the previous increment b,(o-1) Add the unbalanced force distributed to the pile end to obtain the pile end normal stress σ in this increment. b,o Finally, the total settlement s of the pile body at the end of this incremental step is calculated according to the load transfer curve formula. v,o The calculation formula is as follows:

[0102]

[0103]

[0104] 4. Distribute the unbalanced force on the pile side surface.

[0105] (1) First, according to the stiffness k of each unit on the pile side v,ijpo Total stiffness K of the pile side surface v1 The ratio of the total unbalanced force F on the pile side un Distribute to each unit surface and calculate the total friction force τ of each unit surface after distributing the unbalanced force v2,ijpo ; The specific calculation formula is as follows:

[0106]

[0107] τ v2，ijpo =τ v，ijpo +f unv，ijpo (30)

[0108] Among them, f unv,ijpo is the unbalanced force distributed to each unit on the pile side surface, τ v2,ijpo is the updated vertical lateral friction.

[0109] (2) Then determine the vertical lateral friction τ of each unit surface v2,ijpo Is it greater than the limit friction resistance, that is, whether there is a force overflow, and then calculate the total unbalanced force F on the pile side at this time unv2,po , and calculate the vertical shear stiffness k of each unit on the pile side at this time v3，ijpo After updating the vertical shear stiffness of the pile side, the total unbalanced force on the pile side is distributed according to step (1), and this process is repeated until the total unbalanced force on the pile side is equal to zero. The specific calculation formula is as follows:

[0110] If τ v2，ijpo ≥μσ n，ijpo

[0111] f over，ijpo =τ v2，ijpo -τ v，max (31)

[0112] τ v3，ijpo =μσ n，ijpo (32)

[0113] If τ v2，ijpo <μσ n，ijpo

[0114] f over，ijpo =0 (33)

[0115] τ v3，ijpo =τ v2，ijpo (34)

[0116] F unv2，po =∑f over，ijpo (35)

[0117]

[0118]

[0119] K v2 =∑k v3，ijpo (38)

[0120]

[0121] τ v4，iijpo =τ v3，ijpo +f unv3，ijpo (40)

[0122] Among them, f over，ijpo is the overflow force of each unit on the pile side surface, τ v3，ijpo and k v3，ijpo are the updated vertical friction and vertical shear stiffness, K v2 is the total vertical shear stiffness of the pile side after the vertical shear stiffness of each unit surface is updated, f unv3，ijpo is the unbalanced force distributed to each unit surface, τ v4，ijpo The vertical lateral friction after adding the distributed unbalanced force to each unit surface.

[0123] After repeated distribution of unbalanced force, when the total unbalanced force on the pile side is equal to zero, the total settlement s obtained by formula (28) is v，o It is the total settlement of the pile up to the end of this incremental step.

[0124] Step 4: Repeat step 3 until the motion cycle reaches the specified number of times and output the final settlement value.

[0125] The third step explains the method and formula for calculating pile settlement. Repeat this step, and after 4aN / da incremental steps and N movement cycles, the final settlement S is obtained and output.

[0126] Figure 6 The results of the centrifuge model test (CT) and the results obtained by the method of the present invention (TM) are shown, where s v is the pile settlement, D is the pile diameter, F v is the vertical load on the pile top. Figure 6 It can be seen that under different vertical loads F v Under the action of the centrifuge model test and the pile settlement s obtained by the present invention, as the number of cycles N increases, v The trends are consistent.

[0127] Although the present invention has been described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can make many modifications without departing from the purpose of the present invention, all of which are within the protection of the present invention.

Claims

1. A method for predicting the settlement of a single pile in dry sand under horizontal cyclic loading, characterized in that: Calculate the settlement of piles under horizontal cyclic loads in dry sand based on MATLAB, including: establishing a theoretical model of pile settlement movement; determining the basic parameters of the theoretical model and inputting them into MATLAB; using MATLAB to calculate the total settlement of the pile until the end of the incremental step, until the movement cycle reaches a specified number of times and outputs the final settlement value; The theoretical model of pile settlement movement is as follows: the pile moves periodically under the action of horizontal cyclic load, and the total number of movement cycles is N; the movement process of the pile is decomposed into multiple small movements, each of which is called an incremental step and the horizontal movement distance of each incremental step is da; the stress and displacement relationship between the pile side surface and the soil is described by the load transfer method, and the pile side surface is divided into multiple units along the vertical and circumferential directions, and the number of vertical units of the pile is N. z , the number of units in the circumferential direction is N c ; Four subscript parameters i, j, p, and o are set to represent the movement process of each unit surface and the pile, where i and j represent the numbers of the unit surface of the pile side along the circumferential direction and the vertical direction, p represents the movement direction, and o represents the position of the pile body; Use MATLAB to calculate the total settlement of the pile at the end of the incremental step, including: Step 1) Calculate the pile side normal stress; Step 2) Calculate the unbalanced force and vertical shear stiffness on the pile side; Step 3) calculating pile settlement; Step 4) distributing the unbalanced force on the pile side surface; Repeat the above step 4) until the total unbalanced force on the pile side is equal to zero. The pile settlement obtained at this time is the total settlement of the pile body up to the end of this incremental step. The calculation of pile side normal stress in step 1) includes: 1-1) Calculate the initial slope k of the load transfer curve in the normal and tangential directions of the pile side surface respectively n,ini and k v,ini and the initial slope k of the normal load transfer curve at the pile end b,ini ; 1-2) Calculate the maximum normal stress σ on the pile side surface respectively n,max , minimum normal stress σ n,min , static earth pressure σ0, and then according to the geometric relationship, the change in horizontal displacement of each unit surface along its external normal in one increment step is obtained. n,ijpo , according to the initial slope k of the load transfer curve normal to the pile side surface n,ini and the maximum normal stress σ on the pile side surface n,max Calculate the maximum horizontal displacement of the pile when the normal stress is maximum n,max Finally, the absolute value of the normal stress change σ of each front side and rear side in each incremental step is calculated according to the formula of the load transfer curve nc,ijpo , the front side surface is the unit surface moving toward the soil, and the rear side surface is the unit surface moving away from the soil; 1-3) Calculate the normal stress of each unit surface on the pile side. First, determine whether the unit surface is the front side or the rear side. For the front side, add the static soil pressure σ0 plus the absolute value of the normal stress change σ nc,ijpo Get the normal stress σ of the unit surface n,ijpo ; For the rear side, use the static earth pressure σ0 minus the absolute value of the normal stress change σ nc,ijpo Get the normal stress σ of the unit surface n,ijpo .

2. The method for predicting the settlement of a single pile in dry sand under horizontal cyclic loading according to claim 1, characterized in that: The basic parameters of the theoretical model include: pile related parameters and sand related parameters, where: pile related parameters include: pile burial depth L, pile diameter D, pile top vertical load F v , horizontal cyclic load displacement amplitude a and horizontal cyclic load eccentricity e L , the ratio of the initial pile end resistance to the total load R ini ; The relevant parameters of sand include: soil weight γ, internal friction angle Poisson's ratio υ, elastic modulus calculation parameter m, friction coefficient between pile and soil μ.

3. The method for predicting the settlement of a single pile in dry sand under horizontal cyclic loading according to claim 1, characterized in that: The method for calculating the unbalanced force and vertical shear stiffness on the pile side described in step 2) is as follows: 2-1) Compare the vertical lateral friction τ on each unit surface v,ijpo With the limit friction, when the vertical lateral friction τ v,ijpo When the friction force is greater than the limit, an unbalanced force will be generated. The unbalanced force F on each unit surface is calculated separately. un,ijpo , and then the unbalanced force F on each unit surface un,ijpo The total unbalanced force F is obtained by summing un ; 2-2) When calculating the vertical shear stiffness of the pile side, first update the vertical side friction resistance τ of each unit surface v,ijpo , and the corresponding pile-soil vertical relative displacement ω is calculated based on the updated vertical lateral friction and load transfer curve v,ijpo Then, according to the initial slope k of the load transfer curve tangential to the pile side surface v,ini and the pile-soil vertical relative displacement ω v,ijpo Calculate the vertical shear stiffness k of each element v,ijpo Finally, the vertical shear stiffness k of each unit is v,ijpo The vertical shear stiffness K of the pile side is obtained by summing v1 .

4. The method for predicting the settlement of a single pile in dry sand under horizontal cyclic loading according to claim 3, characterized in that: The calculation of pile settlement described in step 3) includes: 3-1) First, according to the initial slope k of the normal load transfer curve at the pile end b,ini Calculate the maximum reaction force σ at the pile end b,max , then according to the load transfer curve formula and the pile end normal stress σ of the previous increment step b,(o-1) The settlement s before the unbalanced force on the pile side is calculated v,(o-1) , and the total stiffness K of the soil at the pile end is calculated based on this b ; 3-2) Based on the vertical shear stiffness K of the pile side v1 The total stiffness K of the soil at the pile end b The unbalanced force F transmitted to the pile end is obtained by the ratio of un,b , the normal stress σ at the pile end in the previous increment b,(o-1) Add the unbalanced force distributed to the pile end to obtain the pile end normal stress σ in this increment. b,o Finally, the total settlement s of the pile body at the end of this incremental step is calculated according to the load transfer curve formula. v,o .

5. The method for predicting the settlement of a single pile in dry sand under horizontal cyclic loading according to claim 4, characterized in that: The step 4) of distributing the unbalanced force on the pile side surface comprises: 4-1) First, according to the stiffness k of each unit on the pile side v,ijpo Total stiffness K of the pile side surface v1 The ratio of the total unbalanced force F on the pile side un Distribute to each unit surface and calculate the vertical lateral friction τ of each unit surface after the unbalanced force is distributed v2,ijpo ; 4-2) Then determine the vertical lateral friction τ of each unit surface v2,ijpo Is it greater than the limit friction resistance, that is, whether there is a force overflow, and then calculate the total pile side unbalanced force F at this time unv2,po , and calculate the vertical shear stiffness k of each unit on the pile side at this time v3,ijpo ; In the repeated cycle, the total pile side unbalanced force and the vertical shear stiffness of each unit on the pile side are iteratively updated until the total pile side unbalanced force is equal to zero.

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