Analytical method for settlement of pile foundation based on vertical average additional stress coefficient

Abstract

The present application relates to a kind of pile foundation settlement analytical method based on vertical average additional stress coefficient.It is suitable for geotechnical engineering technical field.The present application is integrated along the depth of soil to the vertical additional stress of soil around pile produced by the rectangular distribution side resistance of pile, triangular distribution side resistance and end resistance, and deduces pile foundation settlement analytical solution.Single pile or group pile settlement is solved using pile foundation settlement analytical solution, and the compression settlement of pile end soil layer is directly substituted into formula for solving, to avoid the settlement calculation error caused by the additional stress at 1 / 2 depth of soil layer instead of the stress of the soil layer in the application process of traditional layering summation method;Avoid the heavy calculation workload caused by too much soil layering.Formula transformation is carried out to the settlement analytical solution to obtain vertical average additional stress coefficient for pile foundation settlement calculation, and vertical average additional stress coefficient is made into table, and the vertical average additional stress coefficient table can be used to realize the solution of pile foundation settlement, to reduce calculation workload.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of pile foundation settlement analytical method based on vertical average additional stress coefficient.It is suitable for geotechnical engineering technical field. BACKGROUND

[0002] The calculation method of pile foundation settlement in " Code for Design of Building Foundation " GB50007-2011 and " Technical Code for Building Pile Foundation " JGJ94-2008 specification is: first, the Boussinesq solution and Mindlin solution of elastic half-space infinite body are determined under the plane of pile end vertical additional stress, then the layered summation method (LSM) is used to calculate the settlement of pile foundation.

[0003] The additional stress of soil under pile end calculated based on Boussinesq stress solution, the soil between piles of pile group foundation is regarded as equivalent pier foundation, which does not consider the influence of pile length, pile spacing and soil between piles, and does not consider the influence of reverse friction resistance of soil around equivalent pier foundation, which leads to the additional stress of soil being too large.

[0004] At present, the additional stress of soil under pile end calculated based on Boussinesq stress solution, or the vertical additional stress of soil around pile calculated based on Mindlin solution, whichever method is used to calculate the additional stress of soil around pile, the layered summation method (LSM) is used to calculate the compression settlement of soil.

[0005] The layered summation method subdivides the soil layer under the pile end, and then the stress of the midpoint of the subdivided soil layer is used to represent the stress of the entire soil layer, and then the compression settlement of the soil layer is calculated using the stress, and the compression settlements of each layer of soil are summed. The accuracy of the settlement calculation result of the layered summation method is greatly affected by the number of layers, and when the number of soil layer division is small, the calculation result error is large, and when the number of soil layer division is large, the result accuracy is high, but the calculation workload is large, and it is difficult to calculate manually, even if the computer is used for calculation, it will also increase the memory overhead. SUMMARY

[0006] The technical problem to be solved by the present application is to provide a pile foundation settlement analytical method based on vertical average additional stress coefficient in view of the above problems.

[0007] The technical solution adopted by the present application is: a pile foundation settlement analytical method based on vertical average additional stress coefficient, characterized in that it comprises:

[0008] S1, the compression modulus E of the i-th layer of soil under the pile end is obtained si , the top depth z i-1 and the bottom depth z i of the i-th layer of soil under the pile end are obtained , i=1, 2, 3……;

[0009] S2, obtain the pile length L0, the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance Q of the pile at the settlement calculation point sr,0 st,0 p,0 , the pile length L j , the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance Q of the jth pile sr,j st,j p,j , j = 1, 2, 3, ….

[0010] S3, determine the vertical average additional stress coefficient of the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance of the jth pile at the settlement calculation point and within the range of the ith soil bottom from the pile top to the settlement calculation point based on the depth z i , the pile length L j of the jth pile, and the horizontal distance of the settlement calculation point from the center line of the pile itself

[0011] S4, determine the vertical average additional stress coefficient of the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance of the pile at the settlement calculation point and within the range of the ith soil bottom from the pile top to the settlement calculation point based on the depth z i , the pile length L0, and the diameter d0 of the pile at the settlement calculation point

[0012] S5, determine the vertical average additional stress coefficient of the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance of the pile at the settlement calculation point and within the range of the ith soil bottom from the pile top to the settlement calculation point based on the compression modulus E si , the top depth z i-1 , and the bottom depth z i of the ith soil sr,0 , the pile length L0, the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance Q of the pile at the settlement calculation point st,0 p,0 , the pile length L j , the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance Q of the jth pile sr,j st,j p,j , and the vertical average additional stress coefficient determine the soil compression settlement s sr s p ;

[0013] S6, determine the soil compression settlement s sr st p ​​​​​​​​​​​, determine the soil compression settlement amount of the jth pile.

[0014] The step S3 comprises:

[0015]

[0016] wherein, is the vertical additional stress σ of the soil generated by the rectangular distribution side resistance of the jth pile zsr.j is integrated along the soil depth; is the vertical additional stress σ of the soil generated by the triangular distribution side resistance of the jth pile zst.j is integrated along the soil depth; is the vertical additional stress σ of the soil generated by the tip resistance of the jth pile zst.j is integrated along the soil depth; m ji is the ratio of the bottom depth z of the ith layer of soil i to the pile length L of the jth pile. j

[0017] Further comprising:

[0018]

[0019] The step S4 comprises:

[0020]

[0021]

[0022] wherein, is the additional stress σ of the soil compression settlement of the pile rectangular distribution side resistance on the center line of the pile itself at the settlement calculation point zsr,0 is integrated along the soil depth; is the additional stress σ of the soil compression settlement of the pile rectangular distribution side resistance on the center line of the pile itself at the settlement calculation point zst,0 is integrated along the soil depth; is the additional stress σ of the soil compression settlement of the pile rectangular distribution side resistance on the center line of the pile itself at the settlement calculation point zp,0 is integrated along the soil depth; L0 is the pile length of the pile at the settlement calculation point; Q sr,0 , Q st,0 is the combined force of the rectangular distribution side resistance and the triangular distribution side resistance of the pile at the settlement calculation point; p,0 is the combined force of the uniform tip resistance of the pile at the settlement calculation point; m 0i is the ratio of the bottom depth z of the ith layer of soil i to the pile length.

[0023] Further comprising:

[0024] ​

[0025] The step S3 comprises:

[0026] based on the depth z of the i-th layer of soil bottom i , the pile length L of the j-th pile j and the horizontal distance p of the settlement calculation point from the center line of the pile itself, the vertical average additional stress coefficient of the rectangular distributed side resistance, the triangular distributed side resistance and the uniformly distributed end resistance of the j-th pile at the settlement calculation point and within the range of the i-th layer of soil bottom from the top of the j-th pile to the settlement calculation point is determined by referring to the preset Table 1, Table 2 and Table 3

[0027] Further comprising:

[0028] Table 1: vertical average additional stress coefficient of the rectangular distributed side resistance outside the center line of the pile without considering the influence of the pile diameter

[0029]

[0030] Table 2: vertical average additional stress coefficient of the triangular distributed side resistance outside the center line of the pile without considering the influence of the pile diameter

[0031]

[0032] Table 3: vertical average additional stress coefficient of the uniformly distributed end resistance outside the center line of the pile without considering the influence of the pile diameter

[0033]

[0034] The step S4 comprises:

[0035] based on the depth z of the i-th layer of soil bottom i , the pile length L0 and the diameter d0 of the pile at the settlement calculation point, the vertical average additional stress coefficient of the rectangular distributed side resistance, the triangular distributed side resistance and the uniformly distributed end resistance of the pile at the settlement calculation point and within the range of the i-th layer of soil bottom from the top of the pile to the settlement calculation point is determined by referring to the preset Table 4, Table 5 and Table 6

[0036] Further comprising:

[0037] Table 4: vertical average additional stress coefficient of the rectangular distributed side resistance on the center line of the pile with considering the influence of the pile diameter

[0038]

[0039] Table 5: vertical average additional stress coefficient of the triangular distributed side resistance on the center line of the pile with considering the influence of the pile diameter

[0040]

[0041] Table 6 considers the influence of pile diameter, and the vertical average additional stress coefficient of the uniformly distributed end resistance on the center line of the pile itself

[0042]

[0043]

[0044] The step S5 comprises:

[0045] The soil compression settlement s caused by the rectangular distribution side resistance, the triangular distribution side resistance and the uniformly distributed end resistance of the pile is determined by the following formula sr , s st , s p ;

[0046]

[0047] The beneficial effects of the present application are: the present application integrates the vertical additional stress of the soil around the pile caused by the rectangular distribution side resistance, the triangular distribution side resistance and the end resistance of the pile along the depth of the soil, and deduces the analytical solution of the pile foundation settlement. The analytical solution of the pile foundation settlement is used to solve the settlement of a single pile or a group of piles, and the soil layer compression settlement at the pile end is directly substituted into the formula to solve the soil layer compression settlement at the pile end, avoiding the settlement calculation error caused by replacing the stress of the soil layer with the additional stress at the depth of 1 / 2 of the soil layer in the application process of the traditional layering summation method; and avoiding the heavy calculation workload caused by excessive layering of the soil layer.

[0048] The present application transforms the settlement analytical solution to obtain the vertical average additional stress coefficient for the calculation of the pile foundation settlement, and the vertical average additional stress coefficient is made into a table. The vertical average additional stress coefficient table can be used to solve the pile foundation settlement, simplify the calculation process and reduce the calculation workload. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 It is a comparison chart of the vertical additional stress coefficients considering the influence of pile diameter and not considering the influence of pile diameter in the embodiment.

[0050] Figure 2 It is a schematic diagram of the rectangular distribution side resistance, the triangular distribution side resistance and the uniformly distributed end resistance not considering the influence of pile diameter in the embodiment.

[0051] Figure 3 It is a schematic diagram of the rectangular distribution side resistance, the triangular distribution side resistance and the uniformly distributed end resistance considering the influence of pile diameter in the embodiment.

[0052] Figure 4 It is a pile calculation diagram of case one in the embodiment.

[0053] Figure 5 The vertical average additional stress coefficient verification for the case one in the embodiment.

[0054] Figure 6 The settlement observation point arrangement and geological profile for the case two in the embodiment. DETAILED DESCRIPTION

[0055] Based on the Mindlin stress formula, the pile body rectangular distribution side resistance Q sr is integrated along the pile length L to obtain the vertical additional stress σ sr of the rectangular distribution side resistance in the soil at any point outside the pile center (below the pile end surface). sr The pile body rectangular distribution side resistance Q sr0 is twice integrated along the pile surface and the pile length to obtain the vertical additional stress σ st of the pile peripheral side resistance in the soil on the pile center line (below the pile end surface). st The pile body triangular distribution side resistance Q st is twice integrated along the pile surface and the pile length to obtain the vertical additional stress σ st of the pile peripheral side resistance in the soil on the pile center line (below the pile end surface). p The pile end resistance Q p is directly substituted into the Mindlin stress calculation formula to obtain the vertical additional stress σ p of the pile end resistance in the soil below the pile end (below the pile end surface). p0 .

[0056] After the vertical additional stresses σ sr , σ sr0 , σ st , σ st0 , σ p , σ p0 of the six kinds of pile peripheral soil are obtained, the six kinds of stresses are respectively integrated along the soil depth z to obtain the six kinds of soil compression settlement values

[0057] wherein are the compression settlement values of the soil on the pile midline caused by the pile rectangular distribution side resistance, the triangular distribution side resistance and the uniform end resistance, respectively; are the compression settlement values of the soil outside the pile midline caused by the pile rectangular distribution side resistance, the triangular distribution side resistance and the end resistance, respectively.

[0058] When the settlement of the soil at a certain pile is calculated, the following steps are taken The compression settlement values of the pile rectangular distribution side resistance, the triangular distribution side resistance and the end resistance of the soil at the midline of the pile are calculated; the compression settlement values of the soil at the settlement calculation point caused by other piles in the relevant range of the pile are calculated, and then the settlement values are added to obtain the compression settlement of the soil under the pile at the settlement calculation point under the action of all the pile loads in the relevant range.

[0059] The settlement of the pile foundation includes the compression deformation of the pile under the action of the load at the top of the pile and the compression settlement of the soil below the pile end at the settlement calculation point within the horizontal influence range of the pile. The compression deformation of the pile is calculated by using the formula in the Technical Code for Building Pile Foundation. The compression settlement of the soil below the pile end is mainly described.

[0060] The soil outside the center line of the pile: when the settlement caused by the side resistance is calculated, the double integrals of the Mindlin stress are taken (the first integral is along the pile length and the second integral is along the depth of the soil), and the analytical solution of the compression settlement of the soil under the action of the side resistance is derived; when the settlement caused by the end resistance is calculated, the integral of the Mindlin stress along the depth of the soil is directly taken to derive the analytical solution of the settlement under the action of the end resistance. The soil on the center line of the pile: when the settlement caused by the side resistance is calculated, the integrals of the Mindlin stress along the circumference of the pile and the length of the pile are taken to derive the analytical solution of the vertical additional stress of the soil on the center line of the pile under the action of the side resistance, and then the integral of the analytical solution stress along the depth of the soil is taken to derive the analytical solution of the compression settlement of the soil under the action of the side resistance; when the settlement caused by the end resistance is calculated, the integral of the Mindlin stress along the end surface of the pile is taken to obtain the analytical solution of the vertical additional stress of the soil on the center line of the pile under the action of the end resistance, and then the integral of the analytical solution stress along the depth of the soil is taken to derive the analytical solution of the compression settlement of the soil under the action of the end resistance.

[0061] The soil on the center line of the pile: if the integral of the Mindlin stress along the length of the pile is directly taken for the soil on the center line of the pile, stress concentration will occur in the soil within a short distance from the pile end, but since the side resistance of the pile actually acts on the entire circumference of the pile and the end resistance acts on the entire end surface of the pile, there is actually no stress concentration phenomenon in the Mindlin stress solution and the Geddes stress solution, so the stress caused by the side resistance and the end resistance on the center line of the pile itself needs to be taken by the integral of the Mindlin stress along the circumference of the pile, the length of the pile and the end surface of the pile.

[0062] Strictly speaking, the stress integral of the soil outside the center line of the pile should also consider the influence of the pile diameter, but it is known from the Saint-Venant principle that the influence of the pile diameter is smaller when the distance between the stress calculation point and the center of the load pile is farther, and through the comparison between the numerical integral stress considering the influence of the pile diameter and the analytical solution stress not considering the influence of the pile diameter, it is found that when the distance between the settlement calculation point and the center of the load pile is greater than 3 times the diameter of the pile d, the influence of the pile diameter is very small and can be ignored, such as​Figure 1 The pile spacing of the pile foundation is generally greater than 3d, and the settlement of the pile is concerned in the pile foundation engineering. Therefore, the stress integral of the soil outside the pile centerline is solved by using the analytical solution without considering the influence of the pile diameter.

[0063] In the solution of the settlement of the pile foundation, the vertical additional stress generated by the rectangular distribution side resistance, the triangular distribution side resistance and the uniform end resistance of the pile in the soil around the pile is solved by using the Mindlin solution, and then the vertical additional stress of the soil along the depth of the soil is integrated to solve the compression settlement of the soil at the settlement calculation point of the single pile. Then, the compression settlement of the soil at the settlement calculation point generated by all the piles in the horizontal influence range of the settlement calculation point is superimposed to obtain the total compression settlement of the soil.

[0064] The compression settlement of the soil generated by the rectangular distribution side resistance, the triangular distribution side resistance and the end resistance of the pile in the soil around the pile is expressed as formula (1). In formula (1), s sr , s st , and s p are the compression settlements of the soil generated by the rectangular distribution side resistance, the triangular distribution side resistance and the uniform end resistance of the pile, respectively.

[0065]

[0066] The settlement is then expressed separately on the pile centerline and outside the centerline, and formula (1) becomes formula (2).

[0067]

[0068]

[0069] Six basic integral terms represent six related additional stress integral formulas for the compression settlement of the soil, which are as follows: (1) the additional stress integral formula of the compression settlement of the soil at the settlement calculation point generated by the rectangular distribution side resistance of all the piles in the horizontal influence range (generally 0.6 times the length of the pile at the settlement calculation point); (2) the additional stress integral formula of the compression settlement of the soil on the pile centerline itself at the settlement calculation point generated by the rectangular distribution side resistance of the pile; (3) the additional stress integral formula of the compression settlement of the soil at the settlement calculation point generated by the triangular distribution side resistance of all the piles in the horizontal influence range; (4) the additional stress integral formula of the compression settlement of the soil on the pile centerline itself at the settlement calculation point generated by the triangular distribution side resistance of the pile; (5) the additional stress integral formula of the compression settlement of the soil at the settlement calculation point generated by the uniform end resistance of all the piles in the horizontal influence range; and (6) the additional stress integral formula of the compression settlement of the soil on the pile centerline itself at the settlement calculation point generated by the uniform end resistance of the pile.

[0070] The compression settlement of the soil outside the pile centerline caused by the side resistance and the end resistance of the pile is solved by using the model without considering the influence of the pile diameter, and the calculation diagram is as follows: Figure 2As shown; the compressive settlement of the soil along its centerline due to pile side resistance and end resistance is calculated using a model that considers the influence of pile diameter, and the simplified calculation diagram is shown below. Figure 3 As shown.

[0071] Compressive settlement of the soil outside the pile centerline caused by rectangular distributed side resistance: Rectangular distributed side resistance Q of the pile sr The vertical additional stress σ generated at any point M in the soil outside the pile centerline zsr Solving the vertical stress σ using Mindlin z Equation (3) is obtained by integrating along the length of the pile.

[0072]

[0073] In formula (3): μ is the Poisson's ratio of the foundation soil (0.35 is recommended according to the pile foundation code); ρ is the horizontal distance from the settlement calculation point to the centerline of the pile itself; z is the settlement calculation depth from the top of the pile; L is the pile length; h is the distance from a certain section of the pile to the top of the pile.

[0074] The additional vertical stress σ in the soil generated by the rectangular lateral resistance. zsr Integrating along the soil depth, i.e., the Mindlin solution for the vertical stress σ z The double integral of the additional stress integral of the soil compression settlement within a range of horizontal distance ρ from the pile centerline and depth z from the pile top, representing the side resistance of a rectangular pile. Equation (4) is given.

[0075]

[0076] Based on the same principle, the other five vertical stress integral formulas for the compressive settlement of the pile and soil can be obtained, namely formula (5), formula (6), formula (7), formula (8) and formula (9).

[0077]

[0078]

[0079] Furthermore, the integral formula of the vertical additional stress required for pile settlement is transformed as follows and defined as the vertical average additional stress coefficient, as shown in equation (10).

[0080]

[0081] say The average vertical additional stress coefficient of the rectangular distributed side resistance, triangular distributed side resistance, and uniformly distributed end resistance of the j-th pile at the settlement calculation point, and within the range from the top of the j-th pile to the bottom of the i-th soil layer at the settlement calculation point; is called... The vertical average additional stress coefficient of the rectangular, triangular, and uniformly distributed side resistance of the pile at the settlement calculation point is the range from the pile top to the bottom of the i-th soil layer along its own centerline. The meanings of the other symbols are the same as those described above.

[0082] In the above formula, L j Lj is the length of the j-th pile (j = 1, 2, 3...); L0 is the pile length at the settlement calculation point; m is the ratio of the depth of the i-th soil layer at the settlement calculation point to the length of the j-th pile, m = zj i / L j Q sr,j Q st,j The resultant forces of the rectangular and triangular distributed side resistances of the j-th pile are respectively; Q p,j Q is the uniformly distributed end resistance force of the j-th pile; sr,0 Q st,0 Q represents the resultant force of the rectangular and triangular distributed side resistance of the pile at the settlement calculation point; p,0 This represents the uniformly distributed end bearing force of the pile at the settlement calculation point.

[0083] The formula for calculating pile settlement expressed by the vertical average additional stress coefficient is Equation (11).

[0084]

[0085] In this embodiment, the analytical formulas (4), (5), (6) for the compression settlement of the soil outside its centerline caused by the basic shape of the pile side resistance distribution—rectangular and equilateral triangular distributed side resistance and uniformly distributed end resistance—and the analytical formulas (10a) to (10c) for the average additional stress coefficient are functions with m = z / L and n = ρ / L as independent variables; the analytical formulas (7), (8), (9) for the compression settlement of the soil on its centerline caused by the basic shape distributed side resistance and uniformly distributed end resistance, and the analytical formulas (10d) to (10f) for the average additional stress coefficient are functions with m = z / L and n' = r / L as independent variables. For ease of calculation, the calculation results of the above formulas are compiled into tables, and some results are listed in Tables 1 to 6 above.

[0086] The following are the meanings of the symbols in the embodiments:

[0087] d—Pile diameter;

[0088] r—Pile radius, equal to d / 2;

[0089] h—the height of a certain section of the pile from the top of the pile;

[0090] i — Number of soil layers with different compression moduli;

[0091] j—Pile number within the area affected by pile settlement;

[0092] ρ —— the horizontal distance from the pile centerline to the calculation point;

[0093] m —— the ratio of the depth of the calculation point to the pile length, m = z / L;

[0094] n —— the ratio of the horizontal distance from the pile centerline to the calculation point to the pile length, n = p / L;

[0095] n' —— the ratio of the pile radius to the pile length, n' = p / L

[0096] z —— the vertical distance from the pile top to the calculation point;

[0097] z i — the distance from the bottom of the ith soil layer to the pile top;

[0098] A p — the cross-sectional area of the pile;

[0099] E si — the compression modulus of the ith soil layer;

[0100] E c — the elastic modulus of the concrete;

[0101] L —— the length of the pile;

[0102] Q —— the load on the pile top;

[0103] Q sr — the resistance of the rectangular side of the pile;

[0104] Q st — the resistance of the triangular side of the pile;

[0105] Q p — the resistance of the pile tip;

[0106] s e — the compression deformation of the pile;

[0107] s sr — the compression settlement of the soil under the pile tip caused by the resistance of the rectangular side of the pile;

[0108] s st — the compression settlement of the soil under the pile tip caused by the resistance of the triangular side of the pile;

[0109] s p — the compression settlement of the soil under the pile tip caused by the resistance of the pile tip;

[0110] σ zsr — the vertical additional stress of the soil around the pile caused by the resistance of the rectangular side of the pile outside the pile centerline; σ zst — the vertical additional stress of the soil around the pile caused by the resistance of the triangular side of the pile outside the pile centerline;

[0111] σ zp—The additional vertical stress in the soil around the pile caused by the pile tip being blocked outside the pile centerline;

[0112] σ zsr ,0——The vertical additional stress in the soil around the pile generated by the rectangular side resistance of the pile along the center line of the pile;

[0113] σ zst ,0——The vertical additional stress in the soil around the pile generated by the triangular side resistance of the pile along the center line of the pile;

[0114] σ zp,0 —The additional vertical stress in the soil around the pile generated outside the pile centerline by the rectangular side resistance of the pile;

[0115] α — Pile end resistance ratio;

[0116] μ—Poisson's ratio;

[0117] ξ e — Pile compression coefficient.

[0118] This embodiment presents an analytical method for pile foundation settlement based on the vertical average additional stress coefficient, specifically including the following steps:

[0119] S1. Obtain the compression modulus E of the i-th soil layer below the pile tip. si And the top depth z of the i-th soil layer below the pile tip. i-1 and bottom depth z i , i = 1, 2, 3...;

[0120] S2. Obtain the pile length L0, rectangular distributed side resistance, triangular distributed side resistance resultant force, and uniformly distributed end resistance resultant force Q at the settlement calculation point. sr,0 Q st,0 Q p,0 The length L of the j-th pile j 1. Resultant force of rectangular distributed side resistance, 2. Resultant force of triangular distributed side resistance, 3. Resultant force of uniformly distributed end resistance Q sr,j Q st,j Q p,j The uniformly distributed end resistance force Q of the j-th pile p,j j = 1, 2, 3...;

[0121] S3. Using equations (10a) to (10c), or referring to Tables 1 to 3, determine the average vertical additional stress coefficient of the rectangular distributed side resistance, triangular distributed side resistance, and uniformly distributed end resistance of the j-th pile at the settlement calculation point, and within the range of the i-th soil layer from the top of the j-th pile to the bottom of the settlement calculation point.

[0122] S4. Using equations (10d) to (10f), or referring to Tables 4 to 6, determine the average vertical additional stress coefficient of the rectangular distributed side resistance, triangular distributed side resistance, and uniformly distributed end resistance of the pile at the settlement calculation point within the range from the pile top to the bottom of the i-th soil layer along its own centerline.

[0123] S5. Determine the soil compression settlement s caused by the rectangular distributed side resistance, equilateral triangular distributed side resistance, and uniformly distributed end resistance of the pile within itself and other piles in its influence range using equation (11). sr s st s p ;

[0124] S6. Soil compression settlement s based on rectangular distributed side resistance, equilateral triangular distributed side resistance, and uniformly distributed end resistance of piles. sr s st s p Determine the amount of soil compression settlement at the pile tip at the first settlement calculation point.

[0125] The following two specific cases demonstrate the effectiveness of the method presented in this embodiment.

[0126] Case 1: For example Figure 4 As shown, A and B are two free-loaded piles, both with a diameter of 0.6m and lengths of 30m and 27m respectively, spaced 2.4m apart. Pile A has a top load of 2000kN, and pile B has a top load of 1800kN. The end resistance ratio α = 0.25, so the end resistance of pile A is 500kN and that of pile B is 450kN. The end resistance is uniformly distributed along the pile end face. Assuming the side resistance is distributed in a trapezoidal shape along the pile shaft, with a rectangular distribution and a side resistance ratio β = 0.6, the side resistance of piles A and B is 70kN / m at the bottom and 30kN / m at the top. Assuming Poisson's ratio μ = 0.35, a comparison of the settlement at the lower end faces of piles A and B can be found in [reference needed]. Figure 5 .

[0127] Case 2: Jin Mao Tower, 88 stories above ground and 3 stories below ground, with a main structure height of 420.5 meters, is a steel-concrete composite frame core tube structure. The structural plan is symmetrical octagonal, with the distance between the outer edges of the columns in the east-west and north-south directions both being 53.4 meters. Eight 1500×5000 steel-concrete composite columns are set in the central perimeter, and eight 1200×1200 steel columns are set in the corners. The foundation uses a 4-meter thick C50 raft foundation with a foundation depth of 23.45 meters. The total load of the tower above the raft foundation is approximately 2589×10³ kN, of which the axial force at the bottom of the outer frame columns is approximately 1199×10³ kN, and the axial force in the concrete core tube is 1390×10³ kN. Based on the projected area of ​​the outer mega-columns and corner columns (2659 m²), the pressure at the bottom of the raft foundation is 1075 kN / m². The tower piles consist of 429 steel pipe piles, each 914.4×20 mm in diameter and 61 meters long. The pile tip bearing layer is composed of 9-2 fine sand mixed with medium and coarse sand.

[0128] There are 13 settlement observation points N1-N13 in the project, i.e. Figure 6 The settlement observation was started from the completion of the bottom pouring, and the settlement value of the middle measuring point N3 in the core tube was about 83.5mm, and the settlement value of the upper measuring point N1 was 52.6mm when the settlement was stable.

[0129] Table 7 Calculated settlement and measured settlement of Jinmao Mansion

[0130]

Claims

1. A pile foundation settlement analytical method based on a vertical average additional stress coefficient, characterized by, Comprising: S1, obtain the compression modulus E of the i-th layer of soil under the pile tip si and the top depth z of the i-th layer of soil under the pile tip i-1 and the bottom depth z of the i-th layer of soil under the pile tip i i = 1, 2, 3, … S2, obtain the pile length L0 of the pile at the settlement calculation point, the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance Q sr,0 , Q st,0 , Q p,0 , the pile length L of the jth pile j , the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance Q sr,j , Q st,j , Q p,j , j=1, 2, 3, … S3, the depth of the i-th layer of soil z i , the length of the j-th pile L j and the horizontal distance between the settlement calculation point and the center line of the pile itself, determine the vertical average additional stress coefficient of the rectangular distributed side resistance, the triangular distributed side resistance and the uniformly distributed end resistance of the j-th pile within the range from the top of the j-th pile to the bottom of the i-th layer of soil at the settlement calculation point 、 、 ; S4, based on the depth of the i-th layer of soil z i , the pile length L0 and the diameter d0 of the pile at the settlement calculation point, the vertical average additional stress coefficient of the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance of the pile at the settlement calculation point within the range from the top of the pile to the bottom of the i-th layer of soil on its own center line 、 、 ; S5, compression modulus E of the i-th layer of soil si , top depth z of the i-th layer of soil i-1 and bottom depth z i , pile length L0 of the pile at the settlement calculation point, rectangular distribution side resistance, triangular distribution side resistance, uniformly distributed end resistance Q sr,0 , Q st,0 , Q p,0 , pile length L of the j-th pile j , rectangular distribution side resistance, triangular distribution side resistance, uniformly distributed end resistance Q sr,j , Q st,j , Q p,j , and vertical average additional stress coefficient , , , , , , determine the soil compression settlement s generated by the rectangular distribution side resistance, the triangular distribution side resistance, and the uniformly distributed end resistance of the pile sr , s st , s p ; S6, the soil compression settlement s generated based on the pile rectangular distribution side resistance, the equilateral triangle distribution side resistance, and the uniformly distributed end resistance sr st p determining the soil compression settlement amount of the jth pile;​​ Said step S3 comprises: ； ； ； wherein, is the vertical additional stress in the soil due to the jth pile with rectangular distribution of side resistance zsr.j is integrated along the depth of the soil; is the vertical additional stress in the soil due to the jth pile with triangular distribution of side resistance zst.j is integrated along the depth of the soil; is the vertical additional stress in the soil due to the jth pile with tip resistance is integrated along the depth of the soil; m ji is the depth of the bottom of the ith layer of soil z i is the ratio of the length of the jth pile L j to the length of the jth pile L Said step S4 comprises: ； ； ； wherein, is the additional stress of the rectangular distributed side resistance of the pile at the settlement calculation point on the compression settlement of the soil body on the center line of the pile itself is integrated along the depth of the soil body; is the additional stress of the rectangular distributed side resistance of the pile at the settlement calculation point on the compression settlement of the soil body on the center line of the pile itself is integrated along the depth of the soil body; is the additional stress of the rectangular distributed side resistance of the pile at the settlement calculation point on the compression settlement of the soil body on the center line of the pile itself is integrated along the depth of the soil body; L0is the pile length of the pile at the settlement calculation point; Q sr,0 , Q st,0 is the combined force of the rectangular distributed side resistance and the triangular distributed side resistance of the pile at the settlement calculation point; Q p,0 is the combined force of the uniform end resistance of the pile at the settlement calculation point; m 0i is the bottom depth z i of the i-th layer of soil and the ratio of the pile length.

2. The method according to claim 1, wherein Further comprising: ； ； ； wherein Q sr is the rectangular side resistance force of the pile body; Q st is the triangular side resistance force of the pile body; Q p is the pile tip resistance; μ is the Poisson's ratio of soil; L is the pile length; m is the ratio of the calculation depth to the pile length, m = z / L; z is the vertical distance from the pile top to the calculation point; ρ is the horizontal distance from the calculation point to the pile center line; n is the ratio of the horizontal distance from the calculation point to the pile center line to the pile length, n = ρ / L; ; ; ; .

3. The method according to claim 1, wherein Further comprising: ； ； ； where Q sr is the rectangular side resistance force of the pile body; Q st is the triangular side resistance force of the pile body; Q p is the pile tip resistance; μ is the Poisson's ratio of soil; L is the pile length; m is the ratio of the calculation depth to the pile length, m=z / L; z is the vertical distance from the pile top to the calculation point; r is the pile radius; is the ratio of the pile radius to the pile length, =r / L; ; ; ; .

4. The method according to claim 1, wherein Said step S5 comprises: The soil compression settlement s generated by the pile rectangular distribution side resistance, the equilateral triangle distribution side resistance and the uniformly distributed end resistance is determined by the following formula sr , s st , s p ; ； ； ； wherein, : soil compression settlement due to pile rectangular distribution side resistance : compression settlement of soil under pile tip due to side resistance of pile triangle distribution : compression settlement of soil under pile tip due to uniform end resistance : total number of soil layers with different compression modulus under pile tip; : Compression modulus of the i-th soil layer (Ei) ); : total number of piles within the horizontal influence range of the settlement calculation point ); : rectangular distribution side resistance of jth pile : Triangular distribution side resistance force of jth pile : uniform end resistance of jth pile : pile length of the jth pile; : bottom depth of the ith layer of soil; : top depth of the i-th layer of soil; : vertical average additional stress coefficient of rectangular distribution side resistance of the jth pile at the settlement calculation point, in the range from the top of the jth pile to the bottom of the ith layer soil : vertical average additional stress coefficient of rectangular distribution side resistance of the jth pile at the settlement calculation point, in the range from the top of the jth pile to the bottom of the i-1th layer soil : vertical average additional stress coefficient of triangular distribution side resistance of the jth pile at the settlement calculation point, in the range from the top of the jth pile to the bottom of the ith layer soil : the vertical average additional stress coefficient of the triangular distribution side resistance of the jth pile at the settlement calculation point, in the range from the top of the jth pile to the bottom of the ith-1 layer soil : the average additional stress coefficient of the jth pile at the settlement calculation point, in the range from the top of the jth pile to the bottom of the ith soil layer; : the average additional stress coefficient of the jth pile at the settlement calculation point, in the range from the top of the jth pile to the bottom of the i-1th layer soil; : calculates the lateral resistance force of the pile at the settlement calculation point : calculates the trapezoidal distribution side resistance force of the pile at the settlement calculation point; : the uniform end resistance force of the pile at the settlement calculation point; : length of pile at settlement calculation point; : the vertical average additional stress coefficient of the rectangular distributed side resistance of the pile at the settlement calculation point, on the center line of the pile, in the range from the top of the pile to the bottom of the i-th layer of soil; : the vertical average additional stress coefficient of the rectangular distributed side resistance of the pile at the settlement calculation point, on the center line of the pile, in the range from the top of the pile to the bottom of the i-1 layer soil : the vertical average additional stress coefficient of the triangular distribution side resistance of the pile at the settlement calculation point, on the center line of the pile, in the range from the top of the pile to the bottom of the i-th layer of soil; : the vertical average additional stress coefficient of the triangular distribution side resistance of the pile at the settlement calculation point, on the center line of the pile, in the range from the top of the pile to the bottom of the i-1 layer soil; : the vertical average additional stress coefficient of the pile at the settlement calculation point, on the center line of the pile, in the range from the top of the pile to the bottom of the i-th layer of soil; : The average additional stress coefficient of the pile at the settlement calculation point in the vertical direction, with the uniform end resistance of the pile at the center line of the pile itself, and the range from the top of the pile to the bottom of the i-1 layer soil.

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