Pile anchor foundation vertical bearing performance calculation method considering loading anchor point position

Abstract

The invention discloses a piled anchor foundation vertical bearing performance calculation method considering loading anchor point positions, which comprises the following steps: dividing a piled anchor into an upper section and a lower section according to the anchor point positions, enabling the upper section to be subjected to upward supporting force (bearing axial pressure), enabling the lower section to be subjected to upward pulling force (bearing axial pulling force), and calculating the vertical bearing performance of the piled anchor foundation by assuming a vertical load and a load distribution coefficient. The side friction of the pile body is calculated by combining a tau-s curve model, a load distribution coefficient is iteratively solved by adopting a dichotomy method to meet force balance and displacement coordination conditions, and finally the load distribution coefficient, the bearing capacity of the upper pile section and the bearing capacity of the lower pile section and the deformation value are obtained. The method can accurately reflect the axial force distribution of the pile body, the exertion of the side friction resistance and the change rule of the bearing performance along with the anchor point position and the load angle, establishes the relationship between the load distribution coefficient at the loading point and the total uplift load for the first time, and is suitable for complex working conditions such as different anchor point depths and slant angles. And more comprehensive theoretical support is provided for design of floating platform pile anchor foundations of floating photovoltaic, floating wind power, floating bridges and the like.

Description

Technical Field

[0001] This invention belongs to the field of marine and deep-water engineering technology, and relates to a method for calculating the vertical bearing capacity of pile-anchor foundations, specifically a method for calculating the vertical bearing capacity of pile-anchor foundations considering the location of the loading anchor point. Background Technology

[0002] Pile-anchor foundations transfer loads through the synergistic effect of pile embedding into the ocean and deep-water bed, and the oblique tension of the anchor chain. As the core anchoring structure of a floating platform, its load-bearing capacity directly affects the stability and safety of the platform. Therefore, the analysis and research of the vertical bearing capacity of pile-anchor foundations under anchor tension loads is crucial. However, traditional studies on pull-out bearing capacity often focus on the pure axial tension case at the pile top. In reality, the anchor chain of a pile-anchor foundation does not necessarily act at the pile top; more often, it acts at a point along the pile shaft. Existing methods for calculating the vertical bearing capacity of pile-anchor foundations cannot predetermine the load distribution between the upper and lower pile sections at the anchor point, and cannot reflect the segmented axial force distribution characteristics of the pile shaft caused by anchor tension loads. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to address the shortcomings in current research on the vertical bearing capacity analysis of pile-anchor foundations under anchor loads by providing a method for calculating the vertical bearing capacity of pile-anchor foundations that considers the location of the loading anchor point.

[0004] Technical solution: The present invention provides a method for calculating the vertical bearing capacity of pile-anchor foundations considering the location of loading anchor points, comprising:

[0005] S1. Based on the anchor point location, the pile anchor is divided into upper pile segment and lower pile segment. The upper pile segment and lower pile segment are each divided into n pile units. The upper pile units are ordered from bottom to top as 1, 2, ..., n, and the lower pile units are ordered from top to bottom as 1, 2, ..., n.

[0006] S2, Configure vertical load V AL V AL =F AL sinθ, F AL The anchor load is represented by θ, which represents the angle between the anchor load and the horizontal plane; the maximum value of the load distribution coefficient η is specified. max and the minimum value of the load distribution factor η min The initial values ​​of both;

[0007] S3, based on the vertical load V AL The load distribution coefficient η determines the vertical pull-out load V at the top of the first pile unit of the lower pile segment. pt1 Vertical upward load V at the pile tip of the first pile unit of the upper section pile u1 :

[0008]

[0009] S4. Solve for the uplift load V using the bisection method iteratively. pt1 The axial tensile deformation value s at the top of the first pile element of the lower pile segment that satisfies the load transfer convergence condition of the lower pile segment under the action. pt1 ;

[0010] S5. Solve the upper load V using the bisection method iteratively. u1 The axial compression deformation value s at the pile tip of the first pile element of the upper pile segment that satisfies the convergence condition of load transfer in the upper pile segment under the action. u1 ;

[0011] S6. Based on steps S3 to S5 and Δ = (s pt1 -s u1 )| η Obtain the maximum value η of the load distribution coefficient respectively. max The pile anchor deformation value Δ max and the minimum value of the load distribution factor η min The pile anchor deformation value Δ min ;

[0012] S7, Load distribution factor η is taken as η m =(η min +η max ) / 2, based on steps S3 to S5 and Δ=(s pt1 -s u1 )| η Obtain the corresponding pile-anchor deformation value Δ m ;

[0013] S8. Determine whether the load distribution coefficient η converges. The determination process is as follows:

[0014] When Δ m When ≤ε5, the convergence requirement is met, and the outputs η and V are obtained. pt1 V u1 s pt1 s u1 ε5 represents the fifth threshold.

[0015] When Δ m <0 and Δ min ×Δ m When η > 0, take η min =η m η max Remain unchanged and return to step S7;

[0016] When Δ m >0 and Δ min ×Δ m When η < 0, take η max =η m η minRemain unchanged and return to step S7.

[0017] Furthermore, in step S2, the maximum value of the load distribution coefficient η max The initial value is 1, and the minimum load distribution factor η is... min The initial value is 0.

[0018] Further, step S4 includes:

[0019] S401, Configure the minimum axial tensile deformation s at the top of the first pile unit of the lower pile segment. min,pt1 and the maximum axial tensile deformation s at the pile top max,pt1 The initial values ​​of both;

[0020] S402, Average tensile deformation s of the first pile unit of the lower section pile e1 for:

[0021]

[0022] Among them, E p A represents the elastic modulus of the entire pile. p The cross-sectional area of ​​the entire pile body is represented by h; the length of the lower pile unit is h; the average axial tensile force V in the first pile unit of the lower pile body is h. pm1 =V pt1 ;

[0023] S403, Tensile deformation s at the middle position of the first pile unit of the lower pile segment. em1 for:

[0024] s em1 =s pt1 -0.5s e1

[0025] S404, s em1 Substituting into the pre-selected τ-s curve model, the average side friction τ1 of the pile body of the first pile unit of the lower pile segment is obtained;

[0026] S405. Calculate the sum of resistance T generated by the side friction of the first pile unit in the lower section of the pile. p1 :

[0027] T p1 =πdhτ1

[0028] Where d represents the pile diameter;

[0029] S406, Axial tensile force V at the end of the first pile unit of the lower section pile pb1 for:

[0030] V pb1 =V pt1 -T p1

[0031] S407, Correction value of average axial tensile force V for the first pile unit of the lower section pile mod,pm1 for:

[0032]

[0033] S408, Correction value for tensile deformation at the middle position of the first pile unit of the lower pile segment s mod,e1 for:

[0034]

[0035] S409. Determine whether the average tensile deformation of the lower pile unit converges. The determination process is as follows:

[0036] When |s e1 -s mod,e1 When |≤ε1, the convergence requirement is satisfied, let s mod,e1 =s e1 Then proceed to step S410; ε1 represents the first threshold;

[0037] When |s e1 -s mod,e1 When |>ε1, let s e1 =s mod,e1 Return to step S403;

[0038] S410. Calculate the deformation value s at the end of the first pile unit of the lower pile segment. pb1 :

[0039] s pb1 =s pt1 -s mod,e1

[0040] S411. According to the interface continuity condition, the relationship between the top of the (i+1)th pile element and the end of the i-th pile element is as follows:

[0041]

[0042] Among them, V pti and s pti V represents the axial tensile force and axial tensile deformation at the top section of the i-th pile element, respectively; pbi and s pbi These represent the axial tensile force and axial tensile deformation at the end section of the i-th pile unit, respectively.

[0043] Following the method in steps S402 to S410, the axial tensile force V at the end of each pile unit is calculated step by step in a top-down recursive process. pbi and the end axial tensile deformation value s pbi The condition for recursion interruption is spbi ≤ε2, where ε2 represents the second threshold;

[0044] S412. Calculate the total side friction resistance T of the lower section of the pile. pt :

[0045]

[0046] Where m is the number of unit segments at which the load transfer terminates, and m≤n;

[0047] S413. Based on steps S402 to S412, determine the minimum axial tensile deformation s at the top of the first pile unit of the lower pile segment. min,pt1 The total side friction resistance T of the lower section of the pile at that time min,pt ;

[0048] S414. Based on steps S402 to S413, determine the vertical deformation s at the pile top. pt1 =(s min,pt1 +s max,pt1 The total side friction resistance T of the lower pile segment at ) / 2 m,pt ;

[0049] S415, Uplift Load V pt1 The convergence criteria for load transfer in the lower pile segment during operation are as follows:

[0050] When |V pt1 -T m,pt | / V pt1 When the first set error value is met, the load transfer convergence condition of the lower pile segment is satisfied, and the upward pull-out load V pt1 The deformation value under the action is s pt1 ;

[0051] When (T) min,pt -V pt1 (T) m,pt -V pt1 When )≤0, let s max,pt1 =s pt1 s min,pt1 Remain unchanged and return to step S414;

[0052] When (T) min,pt -V pt1 (T) m,pt -V pt1 When ) > 0, let s min,pt1 =s pt1 s max,pt1 Remain unchanged and return to step S414.

[0053] Furthermore, in step S401, the minimum axial tensile deformation s at the top of the first pile unit of the lower pile segment is... min,pt1The initial value is 0, and the maximum axial tensile deformation s at the pile top is... max,pt1 The initial value is taken as the pile diameter d.

[0054] Further, step S5 includes:

[0055] S501, Configure the minimum axial compressive deformation s at the pile tip of the first pile unit of the upper pile section. min,u1 and the maximum value of axial compressive deformation at the pile end s max,u1 The initial values ​​of both;

[0056] S502, Average compressive deformation s of the first pile unit of the upper section pile c1 for:

[0057]

[0058] Among them, E p A represents the elastic modulus of the entire pile body. p The cross-sectional area of ​​the entire pile body is represented by l; the length of the upper pile unit is l; the average axial pressure V of the first pile unit of the upper pile body is l. a1 =V u1 ;

[0059] S503, the compressive deformation s at the middle position of the first pile unit of the upper pile segment. cm1 for:

[0060] s cm1 =s u1 -0.5s c1

[0061] S504, s cm1 Substituting into the pre-selected τ-s curve model, the average side friction τ′1 of the first pile unit of the upper pile is obtained;

[0062] S505. Calculate the sum of resistance T generated by the side friction of the first pile unit in the upper section of the pile. u1 :

[0063] T u1 =πdlτ′1

[0064] Where d represents the pile diameter;

[0065] S506, Axial pressure V at the top of the first pile unit of the upper section pile h1 for:

[0066] V h1 =V u1 -T u1

[0067] S507, Correction value of average axial pressure V for the first pile unit of the upper section pile mod,a1 for:

[0068]

[0069] S508, Correction value for compression deformation at the middle position of the first pile unit of the upper pile segment s mod,c1 for:

[0070]

[0071] S509. Determine whether the average compressive deformation of the upper pile unit has converged. The determination process is as follows:

[0072] When |s c1 -s mod,c1 When |≤ε3, the convergence requirement is satisfied, let s mod,c1 =s c1 Then proceed to step S510; ε3 represents the third threshold;

[0073] When |s c1 -s mod,c1 When |>ε3, let s c1 =s mod,c1 Return to step S503;

[0074] S510. Calculate the deformation value s at the top of the first pile unit of the upper pile segment. h1 :

[0075] s h1 =s u1 -s mod,c1

[0076] S511. According to the interface continuity condition, the relationship between the end of the (i+1)th pile unit and the top of the i-th pile unit is as follows:

[0077]

[0078] Among them, V ui and s ui V represents the axial pressure and axial compressive deformation at the end section of the i-th pile element, respectively; hi and s hi These represent the axial pressure and axial compressive deformation at the top section of the i-th pile element, respectively.

[0079] Following the method in steps S502 to S510, the axial pressure V at the end of each pile unit is calculated step by step in a bottom-up recursive process. ui and end axial compression deformation value s ui The condition for recursion interruption is s hi ≤ε4, where ε4 represents the fourth threshold;

[0080] S512. Calculate the total side friction resistance T of the upper section of the pile.ut :

[0081]

[0082] Where k is the number of unit segments at which the load transfer terminates, k≤n;

[0083] S513. Based on steps S502 to S512, determine the minimum axial compressive deformation s at the pile end of the first pile unit of the upper pile segment. min,u1 The total side friction resistance T of the upper section of the pile at that time min,ut ;

[0084] S514. Based on steps S502 to S513, determine the vertical deformation s at the pile end. u1 =(s min,u1 +s max,u1 The total side friction resistance T of the lower pile segment at ) / 2 m,ut ;

[0085] S515, Upper support load V u1 The convergence criteria for load transfer in the upper pile section during operation are as follows:

[0086] When |V u1 -T m,ut | / V u1 When the second set error value is met, the convergence condition of the upper pile load transfer is satisfied, and the upper support load V u1 The deformation value under the action is s u1 ;

[0087] When (T) min,ut -V u1 (T) m,ut -V u1 When )≤0, let s max,u1 =s u1 s min,u1 Remain unchanged and return to step S514;

[0088] When (T) min,ut -V u1 (T) m,ut -V u1 When ) > 0, let s min,u1 =s u1 s max,u1 Remain unchanged and return to step S514.

[0089] Furthermore, in step S501, the minimum axial compressive deformation s at the pile tip of the first pile unit of the upper pile segment is... min,u1 The initial value is 0, and the maximum axial compression deformation s at the pile end is... max,u1 The initial value is taken as the pile diameter d.

[0090] Furthermore, the τ-s curve model employs an arbitrary model that can characterize the shear behavior of the pile-soil interface.

[0091] Furthermore, the method for calculating the vertical bearing capacity of pile-anchor foundations considering the location of loading anchor points also includes:

[0092] S9, Continuously change the vertical load V AL Take values ​​and repeat steps S3 to S8 to obtain different vertical loads V. AL Corresponding η, V pt1 V u1 s pt1 s u1 .

[0093] Furthermore, the vertical load V AL By changing the vertical load F AL Adjust the angle θ between the anchor load and the horizontal plane.

[0094] Furthermore, the values ​​of each threshold can be flexibly adjusted in conjunction with the calculation objectives, engineering requirements, and calculation efficiency.

[0095] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0096] The study considered the distribution of the vertical component of the anchor load at the anchor point and the different stress states of the upper and lower pile segments. It can accurately reflect the changes in the axial force distribution, side friction, and bearing capacity of the pile body with the anchor point position and the anchor load angle. It also obtained the load distribution coefficients at the pile end of the upper pile segment and the pile top of the lower pile segment at the loading point interface when the total uplift load is applied. This is the first time that the complete relationship between the load distribution coefficient at the loading point and the total uplift load has been obtained.

[0097] This invention is applicable to the vertical bearing capacity analysis of pile-anchor foundations under complex working conditions such as different anchor point depths and oblique angles, and provides more comprehensive theoretical support for the design of pile-anchor foundations for floating platforms such as floating photovoltaic, floating wind power, and floating bridges. Attached Figure Description

[0098] Figure 1 This is a schematic flowchart of a method for calculating the vertical bearing capacity of a pile-anchor foundation considering the location of the loading anchor point, provided by an embodiment of the present invention.

[0099] Figure 2 This is a schematic diagram of the decomposition of the pull-out load of the pile-anchor foundation in an embodiment of the present invention;

[0100] Figure 3 This is a schematic diagram of the load transfer on the lower section of the pile in an embodiment of the present invention;

[0101] Figure 4 This is a schematic diagram of the load transfer on the upper section of the pile in an embodiment of the present invention;

[0102] Figure 5 This is a diagram showing the pull-out load and vertical deformation at a loading point depth of 0.2 times the pile length in an embodiment of the present invention.

[0103] Figure 6 This is a load distribution coefficient-pull-out load diagram at a loading point depth of 0.2 times the pile length in an embodiment of the present invention;

[0104] Figure 7 (a) is a diagram showing the axial load distribution of the pile body at 0.2 times the pile length with a load of 5000kN in an embodiment of the present invention. Figure 7 (b) is a distribution diagram of the side friction resistance around the pile when a load of 5000kN is applied at 0.2 times the pile length in an embodiment of the present invention. Detailed Implementation

[0105] The invention will now be further described with reference to the accompanying drawings.

[0106] like Figure 2 As shown, when the anchor load is applied at any point on the pile body other than the pile top and pile end, the vertical component of the anchor load acts on the pile body. For the pile section above the anchor point, it acts as an upward force, while for the pile section below the anchor point, it acts as an upward pull force. Under the upward force, the upper pile section experiences axial pressure. As the upward displacement increases, the negative skin friction gradually develops, and the axial force at the pile top decreases to zero. Under the upward pull force, the lower pile section experiences axial tension. Similarly, as the upward displacement increases, the negative skin friction gradually develops, and the axial force at the pile end decreases to zero.

[0107] The upper and lower pile segments satisfy the force equilibrium and displacement compatibility conditions at the anchor points. The differential governing equations for the pile body at this point are as follows:

[0108]

[0109] Where z is the pile depth, w(z) is the tensile deformation of the pile, and U p Let E be the circumference of the pile, τ(z) be the side friction at depth z of the pile, and E be the side friction at depth z of the pile. p Let A be the elastic modulus of the pile. p Let be the cross-sectional area of ​​the pile. Since linear shear action at the pile-anchor-soil interface is almost nonexistent in reality, plastic shear behavior is always present. Therefore, to obtain the solution for the pull-out bearing capacity of the pile-anchor foundation considering the influence of the anchor loading position, an iterative solution using the "bisection method" is employed.

[0110] This embodiment compares the calculation method with the standard method that does not consider the influence of various partial factors or safety factors. For ease of verification, the calculation formula of the "Code for Design of Building Pile Foundations" (JGJ94-2008) is used as the prototype, as follows:

[0111] Tuk =∑λ i q sik u i l i (2)

[0112] Among them, T uk λ represents the standard value of the ultimate vertical uplift bearing capacity of a single pile. i Let q be the pull-out coefficient of the i-th soil layer. sik Let u be the standard value of the ultimate lateral resistance of the i-th layer of soil along the pile. i Let l be the perimeter of the cross-section of the i-th soil pile. i Let be the length of the pile body corresponding to the i-th soil layer.

[0113] When the uplift load is located at a certain depth in the pile body, the upper pile is subjected to the upward force and the lower pile is subjected to the upward force, and the side friction of both piles is negative. For the lower pile subjected to the upward force, the reduction of the pile side friction can be directly referred to the pull-out coefficient λ in formula (2); however, for the upper pile subjected to the upward force, the pile side friction is essentially still negative, which is still different from the positive side friction given under the traditional compression pile state, and the influence of the reduction effect still needs to be considered. Because the state of the upper pile under the upward force is consistent with the stress state of the upper pile under the "self-balancing method", the pile side friction under the upward force can be reduced by referring to the conversion coefficient β in the "self-balancing method". Therefore, the ultimate tensile bearing capacity of the pile foundation is obtained by superimposing the side friction of each pile after considering the reduction. The theoretical calculation formula is as follows:

[0114] T uk =∑λ i q sik u i l i +∑β j q sjk u j l j (3)

[0115] Among them, T uk λ represents the standard value of the ultimate vertical uplift bearing capacity of the lower pile segment. i Let q be the pull-out coefficient of the i-th soil layer in the lower pile segment. sik u is the standard value of the ultimate lateral resistance of the i-th soil layer on the side of the lower pile segment. i Let l be the perimeter of the cross-section of the i-th layer of soil pile in the lower section. i β represents the length of the pile body corresponding to the i-th soil layer in the lower segment of the pile; j q is the reduction factor for the upward force of the j-th layer of soil in the upper section of the pile. sjk u is the standard value of the ultimate lateral resistance of the j-th soil layer on the side of the upper pile. j Let l be the perimeter of the cross-section of the j-th layer of soil pile in the upper section. jThis represents the length of the pile body corresponding to the j-th soil layer of the upper section of the pile.

[0116] This embodiment uses the parameters shown in Table 1 for calculation. The total pile length L = 25m, the pile diameter d = 2m, and the loading point depth is 5m (0.2L). The τ-s curve model uses a hyperbola model.

[0117]

[0118] Where τ is the side frictional resistance of the pile, s is the settlement of the pile, and τ u Let k be the ultimate frictional resistance, and k be the initial stiffness of the hyperbolic model. To avoid the initial stiffness k being too large, k is generally taken as 4τ. u / s u s u The ultimate displacement of the relative sliding displacement at the pile-soil interface is s. In this case, s is taken as... u =2mm for initial stiffness k calculation.

[0119] Table 1 Calculation parameters for layered soil

[0120]

[0121] like Figure 1 As shown in the figure, this embodiment of the invention provides a method for calculating the vertical bearing capacity of a pile-anchor foundation considering the location of the loading anchor point, including the following steps:

[0122] S1. Based on the anchor point location, the pile anchor is divided into upper pile segment and lower pile segment. The upper pile segment and lower pile segment are each divided into n pile units. The upper pile units are ordered from bottom to top as 1, 2, ..., n, and the lower pile units are ordered from top to bottom as 1, 2, ..., n.

[0123] like Figure 3 As shown, the total length of the lower pile embedded in the foundation soil is L. b If the pile is divided into n equal segments, then the length of each segment is h = L. b / n, the pile diameter is d. The axial tensile force and axial tensile deformation at the top section of the i-th pile element are denoted as V. pti and s pti The axial tensile force and axial tensile deformation at the end section of the i-th pile element are denoted as V. pbi and s pbi .

[0124] like Figure 4 As shown, let the total length of the upper pile embedded in the foundation soil be L. a If the pile is divided into n equal segments, then the length of each segment is l = L. a / n, the pile diameter is d. The axial pressure and axial compressive deformation at the end section of the i-th pile unit are denoted as V.ui and s ui The axial pressure and axial compressive deformation at the top section of the i-th pile element are denoted as V, respectively. hi and s hi .

[0125] S2, Configure vertical load V AL V AL =F AL sinθ, F AL The anchor load is represented by θ, which represents the angle between the anchor load and the horizontal plane; the maximum value of the load distribution coefficient η is specified. max and the minimum value of the load distribution factor η min The initial values ​​of both;

[0126] In this embodiment, the maximum load distribution coefficient η max The initial value is 1, meaning that the upper pile section has no load. As will be known later, Δ... max >0 is used to determine the range of reasonable η values ​​in S8, thereby re-evaluating η. max Assign values; minimum load distribution factor η min The initial value of Δ is 0, meaning that there is no load on the lower pile segment. As will be known later... min <0 is used to determine the range of reasonable η values ​​in S8, thereby re-evaluating η. min Perform the assignment.

[0127] S3, based on the vertical load V AL The load distribution coefficient η determines the vertical pull-out load V at the top of the first pile unit of the lower pile segment. pt1 Vertical upward load V at the pile tip of the first pile unit of the upper section pile u1 :

[0128]

[0129] S4. Solve for the uplift load V using the bisection method iteratively. pt1 The axial tensile deformation value s at the top of the first pile element of the lower pile segment that satisfies the load transfer convergence condition of the lower pile segment under the action. pt1 ;

[0130] Combination Figure 3 Step S4 includes:

[0131] S401, Configure the minimum axial tensile deformation s at the top of the first pile unit of the lower pile segment. min,pt1 and the maximum axial tensile deformation s at the pile top max,pt1 The initial values ​​of both; in this embodiment, the minimum axial tensile deformation s at the top of the first pile unit of the lower pile segment. min,pt1 The initial value is 0, and the maximum axial tensile deformation s at the pile top is... max,pt1The initial value is taken as the pile diameter d.

[0132] S402, Average tensile deformation s of the first pile unit of the lower section pile e1 for:

[0133]

[0134] Among them, E p A represents the elastic modulus of the entire pile. p The cross-sectional area of ​​the entire pile body is represented by h; the length of the lower pile unit is h; the average axial tensile force V in the first pile unit of the lower pile body is h. pm1 =V pt1 ;

[0135] S403, Tensile deformation s at the middle position of the first pile unit of the lower pile segment. em1 for:

[0136] s em1 =s pt1 -0.5s e1 (7)

[0137] S404, s em1 Substituting into the pre-selected τ-s curve model, the average side friction τ1 of the pile body of the first pile unit of the lower pile segment is obtained;

[0138] S405. Calculate the sum of resistance T generated by the side friction of the first pile unit in the lower section of the pile. p1 :

[0139] T p1 =πdhτ1 (8)

[0140] Where d represents the pile diameter;

[0141] S406, Axial tensile force V at the end of the first pile unit of the lower section pile pb1 for:

[0142] V pb1 =V pt1 -T p1 (9)

[0143] S407, Correction value of average axial tensile force V for the first pile unit of the lower section pile mod,pm1 for:

[0144]

[0145] S408, Correction value for tensile deformation at the middle position of the first pile unit of the lower pile segment s mod,e1 for:

[0146]

[0147] S409. Determine whether the average tensile deformation of the lower pile unit converges. The determination process is as follows:

[0148] When |s e1 -s mod,e1 When |≤ε1, the convergence requirement is satisfied, let s mod,e1 =s e1 Then proceed to step S410; ε1 represents the first threshold. The value of ε1 is flexibly adjusted based on the calculation objective, engineering requirements, and calculation efficiency. The thresholds mentioned later are also determined according to this principle. In this embodiment, ε1 = 1 × 10 -6 .

[0149] When |s e1 -s mod,e1 When |>ε1, the convergence requirement is not met, let s e1 =s mod,e1 Return to step S403;

[0150] S410. Calculate the deformation value s at the end of the first pile unit of the lower pile segment. pb1 :

[0151] s pb1 =s pt1 -s mod,e1 (12)

[0152] S411. According to the interface continuity condition, the relationship between the top of the (i+1)th pile element and the end of the i-th pile element is as follows:

[0153]

[0154] Following the method in steps S402 to S410, the axial tensile force V at the end of each pile unit is calculated step by step in a top-down recursive process. pbi and the end axial tensile deformation value s pbi The condition for recursion interruption is s pbi ≤ε2 (Second threshold ε2=1×10 -6 );

[0155] S412. Calculate the total side friction resistance T of the lower section of the pile. pt :

[0156]

[0157] Where m is the number of unit segments at which the load transfer terminates, and m≤n;

[0158] S413. Based on steps S402 to S412, determine the minimum axial tensile deformation s at the top of the first pile unit of the lower pile segment. min,pt1 The total side friction resistance T of the lower section of the pile at that time min,pt ;

[0159] S414. Based on steps S402 to S413, determine the vertical deformation s at the pile top. pt1 =(s min,pt1 +s max,pt1 The total side friction resistance T of the lower pile segment at ) / 2 m,pt ;

[0160] S415, Uplift Load V pt1 The convergence criteria for load transfer in the lower pile segment during operation are as follows:

[0161] When |V pt1 -T m,pt | / V pt1 When the load transfer convergence condition of the lower pile segment is met (taken as 0.001, i.e., 0.1% error), the upward pull-out load V is increased. pt1 The deformation value under the action is s pt1 ;

[0162] When (T) min,pt -V pt1 (T) m,pt -V pt1 When )≤0, the convergence condition for load transfer of the lower pile segment is not met. Let s max,pt1 =s pt1 s min,pt1 Remain unchanged and return to step S414;

[0163] When (T) min,pt -V pt1 (T) m,pt -V pt1 When ) > 0, the convergence condition for load transfer of the lower pile segment is not met. Let s min,pt1 =s pt1 s max,pt1 Remain unchanged and return to step S414.

[0164] S5. Solve the upper load V using the bisection method iteratively. u1 The axial compression deformation value s at the pile tip of the first pile element of the upper pile segment that satisfies the convergence condition of load transfer in the upper pile segment under the action. u1 ;

[0165] Combination Figure 4 Step S5 includes:

[0166] S501, Configure the minimum axial compressive deformation s at the pile tip of the first pile unit of the upper pile section. min,u1 and the maximum value of axial compressive deformation at the pile end s max,u1 The initial values ​​of both; in this embodiment, the minimum axial compressive deformation s at the pile tip of the first pile unit of the upper pile segment. min,u1 The initial value is 0, and the maximum axial compression deformation s at the pile end is...max,u1 The initial value is taken as the pile diameter d.

[0167] S502, Average compressive deformation s of the first pile unit of the upper section pile c1 for:

[0168]

[0169] Among them, E p A represents the elastic modulus of the entire pile. p The cross-sectional area of ​​the entire pile body is represented by l; l is the length of the upper pile unit; V is the average axial pressure of the first pile unit of the upper pile body. a1 =V u1 ;

[0170] S503, the compressive deformation s at the middle position of the first pile unit of the upper pile segment. cm1 for:

[0171] s cm1 =s u1 -0.5s c1 (16)

[0172] S504, s cm1 Substituting into the pre-selected τ-s curve model, the average side friction τ′1 of the first pile unit of the upper pile is obtained;

[0173] S505. Calculate the sum of resistance T generated by the side friction of the first pile unit in the upper section of the pile. u1 :

[0174] T u1 =πdlτ′1 (17)

[0175] Where d represents the pile diameter;

[0176] S506, Axial pressure V at the top of the first pile unit of the upper section pile h1 for:

[0177] V h1 =V u1 -T u1 (18)

[0178] S507, Correction value of average axial pressure V for the first pile unit of the upper section pile mod,a1 for:

[0179]

[0180] S508, Correction value for compression deformation at the middle position of the first pile unit of the upper pile segment s mod,c1 for:

[0181]

[0182] S509. Determine whether the average compressive deformation of the upper pile unit has converged. The determination process is as follows:

[0183] When |s c1 -s mod,c1 When |≤ε3, the convergence requirement is satisfied, let s mod,c1 =s c1 Then proceed to step S510; the third threshold ε3 = 1 × 10 -6 .

[0184] When |s c1 -s mod,c1 When |>ε3, the convergence requirement is not met, let s c1 =s mod,c1 Return to step S503;

[0185] S510. Calculate the deformation value s at the top of the first pile unit of the upper pile segment. h1 :

[0186] s h1 =s u1 -s mod,c1 (twenty one)

[0187] S511. According to the interface continuity condition, the relationship between the end of the (i+1)th pile unit and the top of the i-th pile unit is as follows:

[0188]

[0189] Following the method in steps S502 to S510, the axial pressure V at the end of each pile unit is calculated step by step in a bottom-up recursive process. ui and end axial compression deformation value s ui The condition for recursion interruption is s hi ≤ε4 (fourth threshold ε4=1×10 -6 );

[0190] S512. Calculate the total side friction resistance T of the upper section of the pile. ut :

[0191]

[0192] Where k is the number of unit segments at which the load transfer terminates, k≤n;

[0193] S513. Based on steps S502 to S512, determine the minimum axial compressive deformation s at the pile end of the first pile unit of the upper pile segment. min,u1 The total side friction resistance T of the upper section of the pile at that time min,ut ;

[0194] S514. Based on steps S502 to S513, determine the vertical deformation s at the pile end. u1 =(s min,u1 +s max,u1 The total side friction resistance T of the lower pile segment at ) / 2 m,ut ;

[0195] S515, Upper support load V u1 The convergence criteria for load transfer in the upper pile section during operation are as follows:

[0196] When |V u1 -T m,ut | / V u1 When the second set error value (taken as 0.001, 0.1% error) is less than the condition for convergence of the load transfer of the upper pile section, the upper support load V is satisfied. u1 The deformation value under the action is s u1 ;

[0197] When (T) min,ut -V u1 (T) m,ut -V u1 When )≤0, the convergence condition for load transfer of the upper pile segment is not satisfied. Let s max,u1 =s u1 s min,u1 Remain unchanged and return to step S514;

[0198] When (T) min,ut -V u1 (T) m,ut -V u1 When ) > 0, the convergence condition for load transfer of the upper pile segment is not met. Let s min,u1 =s u1 s max,u1 Remain unchanged and return to step S514.

[0199] S6. Based on steps S3 to S5 and Δ = (s pt1 -s u1 )| η Obtain the maximum value η of the load distribution coefficient respectively. max The pile anchor deformation value Δ max and the minimum value of the load distribution factor η min The pile anchor deformation value Δ min (Δ max It is not used in subsequent convergence judgments. Its function is to provide an initial upper limit deformation benchmark to support the reasonable construction and adjustment of the load distribution coefficient iteration interval (it needs to be retained);

[0200] S7, Load distribution factor η is taken as η m =(η min +η max) / 2, based on steps S3 to S5 and Δ=(s pt1 -s u1 )| η Obtain the corresponding pile-anchor deformation value Δ m ;

[0201] S8. Determine whether the load distribution coefficient η converges. The determination process is as follows:

[0202] When Δ m ≤ε5 (Fifth threshold ε5=1×10 -6 When the convergence requirement is met, outputs η and V. pt1 V u1 s pt1 s u1 ;

[0203] When Δ m <0 and Δ min ×Δ m A value greater than 0 indicates that the assumed load distribution factor η is too small, and also suggests that a reasonable value for η falls within the range of η. m ~η max Between; at this time, take η min =η m η max Remain unchanged and return to step S7;

[0204] When Δ m >0 and Δ min ×Δ m When η < 0, it means that the assumed load distribution factor η is too large, and it also indicates that a reasonable value of η falls within the range of η. min ~η m Between; at this time, take η max =η m η min Remain unchanged and return to step S7.

[0205] S9, Continuously change the vertical load V AL Take values ​​and repeat steps S3 to S8 to obtain different vertical loads V. AL Corresponding η, V pt1 V u1 s pt1 s u1 Vertical load V AL By changing the vertical load F AL Adjust the angle θ between the anchor load and the horizontal plane.

[0206] In situations where the axial bearing stiffness of the upper and lower anchor piles is unknown and the specific load distribution value cannot be directly determined, this invention proposes a "bisection method" to iteratively solve the distribution coefficient to obtain the specific uplift force and uplift force, and to solve the overall bearing performance of the pile and anchor under the total vertical load.

[0207] like Figure 5 The figure shows the pull-out bearing capacity versus pull-out displacement curve when the pull-out loading point is located at a pile depth of 5m. From the figure, it can be seen that the pull-out ultimate bearing capacity calculated according to formula (3) is 1.07 × 10⁻⁶. 4 kN is the limit value of the pull-out bearing capacity curve obtained by the multiple "bisection method" iterative solution of the present invention, which proves the correctness of the numerical iterative solution method proposed in the present invention.

[0208] like Figure 6 The figure shows the load distribution coefficients at the top of the upper pile segment and the top of the lower pile segment at the interface of the loading point under total uplift load. This is one of the main innovations of this invention, obtaining for the first time the complete relationship between the load distribution coefficients at the loading point and the total uplift load. From Figure 6 As can be seen from the data, as the total uplift load increases, the uplift load distribution coefficient at the top of the upper pile gradually increases, which means that the uplift force also gradually increases. Meanwhile, the uplift load distribution coefficient at the top of the lower pile gradually decreases, which means that the uplift force also gradually decreases.

[0209] exist Figure 6 Based on this, when the total uplift load is selected as 5000kN, the load distribution factor for the upper pile section is 0.346, and the received uplift load is 1729.5kN; the load distribution factor for the lower pile section is 0.654, and the received uplift load is 3270.5kN. Therefore, the distribution of axial force and side friction of the pile body under a total uplift load of 5000kN is as follows: Figure 7 As shown.

[0210] from Figure 7 It is clearly visible that because the loading point is approximately 5m deep, which is 0.2 times the pile length, the axial stiffness of the upper pile is relatively weak, resulting in a lower load distribution. Simultaneously, the upper pile's bearing capacity is realized more quickly. In contrast, the lower pile still has considerable room to reach its full potential, indicating an asynchronous development of the bearing capacity of the upper and lower piles. The upper pile bears axial pressure under the upward force, therefore... Figure 7 (a) shows a negative value, while the lower section of the pile is under the action of the upward pull force and is in the state of axial tension of the pile body, so the axial force is represented by a positive value; Figure 7 (b) The negative skin friction values ​​are because the skin friction around the entire tension pile is in a negative state. It should be clarified that after the upper section of the pile enters the ultimate limit state, it does not cease to function, but continues to work in synergy with the lower section of the pile in the ultimate bearing state, continuously improving the overall tension resistance of the complete tension pile.

[0211] In summary, this invention divides the pile anchor into upper and lower sections according to the anchor point location. The upper section is subjected to upward force (axial pressure), while the lower section is subjected to upward force (axial tension). By assuming vertical load and load distribution coefficient, and combining the τ-s curve model to calculate the pile side friction, the "bisection method" is used to iteratively solve the load distribution coefficient to satisfy the force balance and displacement coordination conditions. Finally, the load distribution coefficient, the bearing capacity and deformation values ​​of the upper and lower pile sections are obtained. This invention can accurately reflect the changes in pile axial force distribution, side friction, and bearing capacity with anchor point location and load angle. For the first time, the relationship between the load distribution coefficient at the loading point and the total upward load is established. It is applicable to complex working conditions such as different anchor point depths and inclination angles, and provides more comprehensive theoretical support for the design of pile anchor foundations for deep-sea floating platforms.

Claims

1. A method for calculating the vertical bearing capacity of a pile-anchor foundation considering the position of a loaded anchor point, characterized in that, Comprise: S1, according to the anchor position is divided into upper section pile and lower section pile, respectively, the upper section pile and lower section pile is divided into n section pile unit, upper section pile unit from bottom to top order is 1, 2,..., n, lower section pile unit from top to bottom order is 1, 2,..., n; S2, configure vertical load V AL , V AL = F AL sin θ, F AL represents the anchoring load, θ represents the angle between the anchoring load and the horizontal plane; configure the initial values of the maximum load distribution coefficient η max and the minimum load distribution coefficient η min two S3、According to the vertical load V AL and the load distribution coefficient η to determine the pile top vertical uplift load V of the lower section pile first pile unit pt1 , the pile end vertical uplift load V of the upper section pile first pile unit u1 : S4, solving the uplift load V by dichotomy iteration pt1 s, the axial tensile deformation value of the pile top of the first pile unit of the lower section pile satisfying the lower section pile load transfer convergence condition under the action of the lower section pile pt1 ; S5, solving the uplift load V by dichotomy iteration u1 s, the axial compression deformation value of the pile end of the first pile unit of the upper section pile under the action of the upper section pile load transfer convergence condition of the upper section pile u1 ; S6、According to steps S3 to S5 and Δ = (s pt1 -s u1 | η , respectively, the maximum load distribution coefficient η max The pile anchor deformation value Δ max and the minimum load distribution coefficient η min The pile anchor deformation value Δ min ; S7, the load distribution coefficient η is taken as η m = (η min + η max ) / 2, according to steps S3 to S5 and Δ = (s pt1 -s u1 )| η The corresponding pile anchor deformation value Δ m is obtained; S8, judge load distribution coefficient η whether convergence, the judgment process is as follows: When Δ m ≤ ε5, the convergence requirement is satisfied, and η, V pt1 , V u1 , s pt1 , s u1 are output; ε5 represents a fifth threshold value; When Δ m < 0 and Δ min > 0, take η m = η min = η m , η max remains unchanged, return to step S7; When Δ m >0 and Δ min ×Δ m When < 0, take η max =η m η min Remain unchanged and return to step S7.

2. The method for calculating the vertical bearing capacity of a pile anchor foundation considering the loading anchor position according to claim 1, characterized in that, In step S2, the maximum load distribution coefficient η max is initialized to 1, and the minimum load distribution coefficient η min is initialized to 0.

3. The method of calculating the vertical bearing capacity of a pile anchor foundation considering the loading anchor position according to claim 1, characterized in that, Step S4 includes: S401、configure the minimum axial tensile deformation of the pile top of the first pile unit of the lower section pile min,pt1 and the maximum axial tensile deformation of the pile top max,pt1 of the two initial values; S402, average tensile deformation amount s of the lower pile first pile unit e1 is: wherein E p represents the elastic modulus of the entire pile body, A p represents the cross-sectional area of the entire pile body; h is the length of the pile unit of the lower section pile; the average axial tension V pm1 of the pile unit of the first section of the lower section pile pt1 ; S403, the tensile deformation amount s at the middle position of the first section of the lower section pile unit em1 is: s em1 = s pt1 -0.5s e1 S404, s em1 Substituting into the pre-selected τ-s curve model, the average side friction τ1 of the first pile unit of the lower pile segment is obtained; S405, calculate the sum T of the resistance generated by the side friction of the first section of the lower section pile unit pile p1 : T p1 = πdht1 Wherein, d indicates the diameter of the pile; S406, axial tension V of the end of the first pile unit of the lower pile pb1 is: V pb1 = V pt1 - T p1 S407, the average axial tension correction value V of the lower pile and the first segment pile unit mod,pm1 is: S408, the tensile deformation amount correction value s at the middle position of the first section of the lower section pile unit mod,e1 is: S409, judge whether the average tensile deformation of the lower section pile unit is convergent, the judgment process is as follows: When |s e1 -s mod,e1 |≤ε1, the convergence requirement is met, and s mod,e1 = s e1 and enters step S410; ε1 represents a first threshold value. When |s e1 -s mod,e1 | > ε1, let s e1 = s mod,e1 , return to step S403; S410, calculate the deformation value s of the end of the first pile unit of the lower pile pb1 : s pb1 = s pt1 - s mod,e1 S411, according to the interface continuity condition, the relationship between the top of the i+1 section pile unit and the end of the i section pile unit is as follows: where V pti and s pti are the axial tensile force and axial tensile deformation at the top section of the i-th segment of pile element, respectively; V pbi and s pbi are the axial tensile force and axial tensile deformation at the end section of the i-th segment of pile element, respectively; According to the method of steps S402 to S410, the end axial tension V of each pile unit is calculated step by step in a "top-down" recursive process pbi and the end axial tensile deformation value s pbi The condition for interrupting the recursion is s pbi ≤ ε2, ε2 representing a second threshold value; S412, calculate the total side friction T of the lower section pile pt : Wherein, m is the unit section number of load transfer termination, m≤n; S413、According to steps S402-S412, the minimum axial tensile deformation value s of the pile top of the first pile unit of the lower section pile is determined min,pt1 The total side friction T of the lower section pile at the time min,pt ; S414、According to steps S402-S413, the vertical deformation amount s of the pile top is determined pt1 = (s min,pt1 + s max,pt1 ) / 2, the total side friction T of the lower section pile is determined m,pt ; S415, the pullout load V pt1 The judgment condition of the load transfer and convergence of the lower section pile when in action is as follows: When |V pt1 -T m,pt | / V pt1 When the first set error value, meet the following paragraph pile load transfer convergence conditions, the uplift load V pt1 The deformation value under the action is s pt1 ; When (T) min,pt -V pt1 (T) m,pt -V pt1 When )≤0, let s max,pt1 =s pt1 s min,pt1 Remain unchanged and return to step S414; When (T min,pt -V pt1 )(T m,pt -V pt1 )>0, let s min,pt1 =s pt1 , s max,pt1 remains unchanged, return to step S414.

4. The method for calculating the vertical bearing capacity of a pile anchor foundation considering the loading anchor position according to claim 3, characterized in that, In step S401, the minimum value s of the axial tensile deformation of the pile top of the first pile unit of the lower section pile is set to 0 min,pt1 The initial value of the maximum value s of the axial tensile deformation of the pile top is set to the pile diameter d. max,pt1 The initial value of the maximum value s of the axial tensile deformation of the pile top is set to the pile diameter d.

5. The method of calculating the vertical bearing capacity of a pile anchor foundation considering the loading anchor position according to claim 1, characterized in that, Step S5 includes: S501, the minimum value s of the axial compression deformation of the pile end of the upper section pile first section pile unit is configured min,u1 and the maximum value s of the axial compression deformation of the pile end max,u1 of the two initial values; S502, average compression deformation amount s of the upper pile and the first pile unit c1 is: wherein E p represents the entire pile elastic modulus, A p represents the entire pile cross-sectional area; l is the length of the upper section pile unit; the average axial pressure of the first section pile unit of the upper section pile V a1 = V u1 ; S503, the compression deformation amount s at the middle position of the first pile unit of the upper pile cm1 is: s cm1 = s u1 -0.5s c1 S504, s cm1 Substituting into the pre-selected τ-s curve model, the average side friction τ'1 of the first pile unit of the upper pile is obtained; S505, calculate the sum T of the resistance generated by the side friction of the upper segment, the first segment, the first unit pile u1 : T u1 = πdIT'1 Wherein, d indicates the diameter of the pile; S506, axial pressure V on the top of the first pile unit h1 is: V h1 = V u1 - T u1 S507, the average axial pressure correction value V of the first pile unit of the upper pile mod,a1 is: S508, the correction value s of the compression deformation amount at the middle position of the upper pile and the first pile unit mod,c1 is: S509, judge whether the average compressive deformation of the upper section pile unit is convergent, the judgment process is as follows: When |s c1 -s mod,c1 |≤ε3, the convergence requirement is satisfied, and s mod,c1 = s c1 and enters step S510; ε3 represents a third threshold value. When |s c1 -s mod,c1 | > ε3, let s c1 = s mod,c1 , return to step S503; S510, calculate the deformation value s of the top of the first pile unit of the upper pile h1 : s h1 = s u1 - s mod,c1 S511, according to the interface continuity condition, the relationship between the end of the i+1 section pile unit and the top of the i section pile unit is as follows: where V ui and s ui are the axial compressive force and axial compressive deformation at the end section of the i-th pile segment, respectively; V hi and s hi are the axial compressive force and axial compressive deformation at the top section of the i-th pile segment, respectively. According to the method of steps S502 to S510, the end axial pressure V of each pile unit is calculated step by step in a "bottom-up" recursive process ui and the end axial compression deformation value s ui The condition for interrupting the recursion is s hi ≤ ε4, ε4 representing a fourth threshold value; S512, calculate the total side friction T of the upper section pile ut : Wherein, k is the unit section number of load transfer termination, k≤n; S513、According to steps S502-S512, the minimum axial compression deformation s of the pile end of the first pile unit of the upper pile is determined min,u1 The total side friction T of the upper pile at the time min,ut ; S514、According to steps S502-S513, the vertical deformation amount s of the pile tip is determined u1 = (s min,u1 + s max,u1 ) / 2, the total side friction T of the lower section pile is determined m,ut ; S515, the upper support load V u1 The judgment condition of the load transfer and convergence of the upper section pile during the action is as follows: When |V u1 -T m,ut | / V u1 When the second set error value, meet the pile load transfer convergence conditions, the upper load V u1 deformation value is s u1 ; When (T) min,ut -V u1 (T) m,ut -V u1 When )≤0, let s max,u1 =s u1 s min,u1 Remain unchanged and return to step S514; When (T) min,ut -V u1 (T) m,ut -V u1 When ) > 0, let s min,u1 =s u1 s max,u1 Remain unchanged and return to step S514.

6. The method for calculating the vertical bearing capacity of a pile anchor foundation considering the loading anchor position according to claim 5, characterized in that, In step S501, the minimum value s of the axial compression deformation of the pile tip of the first pile unit of the upper section pile min,u1 The initial value is 0, and the maximum value s of the axial compression deformation of the pile tip max,u1 The initial value is the pile diameter d.

7. The method for calculating the vertical bearing capacity of a pile anchor foundation considering the loading anchor position according to claim 4 or 6, characterized in that, The τ-s curve model adopts an arbitrary model that can represent the shearing behavior of the pile-soil interface.

8. The method of calculating the vertical bearing capacity of a pile anchor foundation considering the loaded anchor position according to any one of claims 1 to 6, characterized in that, Also include: S9, constantly changing vertical load V AL Take values and repeat S3 to S8, get different vertical load V AL Corresponding η, V pt1 , V u1 , s pt1 , s u1 .

9. The method for calculating the vertical bearing capacity of a pile anchor foundation considering the loading anchor position according to claim 8, characterized in that, Vertical load V AL By changing the vertical load F AL And the angle θ between the anchoring load and the horizontal plane is adjusted.

10. The method of calculating the vertical bearing capacity of a pile anchor foundation considering the loaded anchor position according to any one of claims 1 to 6, characterized in that, The value of each threshold is combined with the calculation target, engineering requirement and calculation efficiency to adjust flexibly.

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