A design method for rigid-flexible pile composite foundation

Abstract

The present invention discloses a rigid-flexible pile composite foundation design method, comprising the following steps: determining the constraints of the rigid-flexible pile composite foundation design method; calculating the vertical forces acting on the superstructure, rigid piles, flexible piles, and inter-pile soil through vertical static equilibrium; calculating the deformation of the rigid piles, flexible piles, and inter-pile soil based on the vertical force calculation results; calculating the composite foundation bearing capacity correction coefficient based on the deformation calculation results using deformation coordination conditions, and then calculating the composite foundation settlement, composite foundation bearing capacity f1, and minimum cushion thickness d. The present invention obtains an analytical solution for the correction coefficient of the bearing capacity characteristic value of the rigid piles, flexible piles, and inter-pile soil through vertical static equilibrium of the piles and pile-soil and pile-soil deformation coordination analysis, making the composite foundation bearing capacity calculation results closer to engineering practice and resolving the defects of existing standard calculation methods, which result in a large composite compression modulus and a small settlement calculation result.

Description

Technical Field

[0001] The present invention relates to the technical field of composite foundation treatment, and in particular to a design method for a rigid-flexible pile composite foundation. Technical Background

[0002] In recent years, rigid-flexible pile composite foundation treatment technology, consisting of long rigid piles (such as precast piles) and short flexible piles (such as cement-soil mixing piles), has been widely used. Longer rigid piles transfer superstructure loads to deeper soil layers, increasing the bearing capacity of the composite foundation while effectively reducing deformation. Shorter flexible piles can effectively improve the bearing capacity of shallow foundation soils and offer better economic benefits. Existing composite foundation specifications provide basic regulations for rigid-flexible pile composite foundation treatment technology in terms of design, construction, and quality inspection, greatly promoting its widespread adoption.

[0003] Since the rigid-flexible pile composite foundation is a new foundation treatment technology, the existing specifications have provided preliminary solutions to the two key issues of composite foundation bearing capacity and deformation calculation in this technology. For example, the bearing capacity calculation involves the degree to which the bearing capacity characteristic values ​​of the rigid piles, flexible piles and soil between the piles are exerted (bearing capacity correction coefficient). The specifications provide a range of values ​​for these correction coefficients, which requires engineering and technical personnel with rich geotechnical experience to determine them more accurately, which to some extent hinders the development and application of this technology.

[0004] Furthermore, deformation calculation for rigid-flexible pile composite foundations has not been well addressed. Currently, research using analytical methods for deformation calculation is rare, and numerical calculation methods are far from mature enough for widespread application. Engineers prefer standard methods based on the layered summation method. The presence of vertical reinforcements made of different materials (rigid and flexible piles) complicates deformation calculation. Research has shown that existing standards simplify the actual pile-soil stress ratio to the pile-soil modulus ratio or the ratio of the composite foundation bearing capacity to the natural foundation bearing capacity. The former, because the pile-soil stress ratio is smaller than the pile-soil modulus ratio, results in an overstated composite compression modulus and understated settlement calculations. The latter, because existing standards simply assume that the pile and soil bearing capacities are 100% utilized, when in reality, the actual utilization of the pile and soil bearing capacities is less than 100%, the actual pile-soil stress ratio should be the ratio of the actual stresses borne by the pile and soil. This standard approach also results in an overstated composite compression modulus and understated settlement calculations.

[0005] Furthermore, existing standards and methods for designing the stiffness and thickness of composite foundation cushions are relatively qualitative and empirical, often causing designers to overlook the formation conditions of composite foundations. Improper cushion thickness and stiffness design can result in rigid piles piercing the cushion and directly supporting the rigid foundation, leading to a separation between the rigid foundation and the natural ground. Since the natural ground no longer shares the load of the superstructure, the rigid piles, flexible piles, and inter-pile soil cannot form a composite foundation. In this case, using composite foundation calculation methods for design can result in a dangerous outcome. Therefore, the design of the cushion in composite foundations must be given due attention.

[0006] In summary, it is necessary to propose a new design method of rigid-flexible pile composite foundation to solve the above problems. Summary of the Invention

[0007] The present invention provides a design method for a rigid-flexible pile composite foundation to solve the problems in existing specifications that the bearing capacity of a rigid-flexible pile composite foundation is difficult to accurately determine, the composite compression modulus obtained by the settlement calculation method is too large, resulting in a small settlement calculation result, and the cushion layer design is based on experience.

[0008] The present invention discloses a method for designing a rigid-flexible pile composite foundation, comprising the following steps:

[0009] Determining the constraints of the rigid-flexible pile composite foundation design method;

[0010] Calculate the vertical forces on the superstructure, rigid piles, flexible piles and soil between piles through vertical static equilibrium;

[0011] Based on the vertical force calculation results, deformation calculation is performed on the rigid piles, the flexible piles and the soil between the piles;

[0012] According to the deformation calculation results, the deformation coordination condition is used to calculate the correction coefficient of the composite foundation bearing capacity;

[0013] Calculating the composite compression modulus of the composite foundation according to the calculation result of the composite foundation bearing capacity correction coefficient;

[0014] Calculating the composite foundation settlement according to the calculation result of the composite compression modulus of the composite foundation;

[0015] Calculate the composite foundation bearing capacity f1 according to the calculation result of the composite foundation bearing capacity correction coefficient;

[0016] According to the calculation result of the composite foundation bearing capacity correction coefficient, the minimum thickness d of the cushion layer is calculated.

[0017] Furthermore, the constraints of the rigid-flexible pile composite foundation design method include:

[0018] The composite foundation is a deep soft soil foundation, and the rigid piles and flexible piles are friction piles. The pile tip pressure is zero, and the pressure on the superstructure is entirely borne by the lateral friction resistance of the soil around the piles.

[0019] The length of the rigid pile is greater than that of the flexible pile, and the rigidity of the rigid pile is greater than that of the flexible pile;

[0020] The composite soil layer composed of rigid piles, flexible piles and soil between piles is the first reinforced area; the composite soil layer composed of rigid piles and soil between piles below the flexible pile ends is the second reinforced area; the natural soil layer below the rigid pile ends is the non-reinforced area.

[0021] Furthermore, the vertical static equilibrium calculation step includes:

[0022]

[0023] in: are the number of rigid piles and flexible piles respectively; Q s1 , F are the pressures shared by each rigid pile, each flexible pile, the soil between piles and the superstructure load (kN);

[0024] The pressure shared by each rigid pile, each flexible pile, and the soil between the piles is:

[0025]

[0026]

[0027]

[0028] n 11 =σ p11 / σ s1 =β1f p1 / β3f s1 (5)

[0029] n 21 =σ p21 / σ s1 =β2f p2 / β3f s1 (6)

[0030] in: are the soil stresses between piles at the top of the rigid pile, the top of the flexible pile, and the 1-1' interface (kPa); A s are the cross-sectional area of ​​each rigid pile, the cross-sectional area of ​​each flexible pile and the soil area between piles (m 2 ); β1, β2, and β3 are the correction coefficients of the characteristic values ​​of the bearing capacity of rigid piles, flexible piles, and soil between piles, respectively; fs1 are the characteristic values ​​of bearing capacity of rigid pile, flexible pile and soil between piles (kPa); n 11 、n 21 are the stress ratios of the rigid pile, flexible pile and soil between piles in the first reinforcement zone (kPa);

[0031] Substituting formulas (2) to (4) into formula (1), we have:

[0032]

[0033] Assuming the total area of ​​the composite foundation is A, we have:

[0034]

[0035] Among them: m1 and m2 are the area replacement rates of rigid piles and flexible piles respectively.

[0036] Furthermore, the deformation calculation includes deformation calculation of rigid piles and flexible piles:

[0037] The deformation of the rigid pile includes the penetration amount s of the pile into the cushion layer. p1 (mm) and its own compression s' p1 (mm) are:

[0038]

[0039]

[0040] The deformation of the flexible pile includes the penetration amount s of the pile into the cushion layer. p2 (mm) and its own compression s' p2 (mm) are:

[0041]

[0042]

[0043] Where: E d 、ν d are the deformation modulus and Poisson's ratio of the cushion layer respectively; r1 and r2 are the radius of the rigid pile and the flexible pile respectively (m); l1 and l2 are the thickness of the first reinforcement area and the second reinforcement area respectively (m); E p1 、E p2 are the compression modulus of the rigid pile and the flexible pile (MPa);

[0044] For the first and second reinforcement areas, the compression of the soil between piles s s1 、s s2 (mm) are:

[0045]

[0046]

[0047] Where: s1 , σ s2 , σ s3 are the soil stresses between piles at the interfaces 1-1', 2-2' and 3-3' (kPa); E s1 、E s2 are the compression modulus of the foundation soil in the first and second reinforcement zones (MPa); η1 and η2 are the soil stresses between piles at the interface 1-1' on the foundation surface, σ s1 Stress diffusion coefficient at the 2-2' and 3-3' interfaces.

[0048] Furthermore, the calculation formulas of η1 and η2 are:

[0049]

[0050]

[0051] Wherein: a and b are the lengths of the long side and short side of the composite foundation treatment range respectively (m), wherein A=ab, A is the total area of ​​the composite foundation; θ is the stress diffusion angle.

[0052] Furthermore, the composite foundation bearing capacity correction coefficient step includes:

[0053] For the first reinforcement zone, the deformation of the flexible pile is equal to the compression of the soil between the piles in the first reinforcement zone:

[0054] s p2 +s′ p2 =s s1 (17)

[0055] According to the formulas (11) to (13), we have:

[0056]

[0057] The stress ratio n between the flexible pile and the soil between the piles in the first reinforcement zone can be obtained from formula (18): 21 The value of

[0058] For the first and second reinforcement zones, the deformation of the rigid pile is equal to the sum of the compression of the soil between the piles in the first and second reinforcement zones:

[0059] s p1 +s′ p1 =s s1 +s s2 (19)

[0060] According to formulas (9) to (10) and (13) to (14), we have:

[0061]

[0062] The stress ratio n between the rigid pile and the soil between the piles in the first reinforcement zone can be obtained from formula (20): 11 ;

[0063] Using the obtained n 21 and n 11 Substituting into the formula (8) we can obtain the correction coefficient β3 of the characteristic value of soil bearing capacity between piles;

[0064] By substituting the obtained characteristic value correction coefficient β3 of the bearing capacity of soil between piles into the above formulas (5) and (6), the characteristic value correction coefficient β1 of the bearing capacity of rigid piles and the characteristic value correction coefficient β2 of the bearing capacity of flexible piles can be obtained respectively.

[0065] Furthermore, the step of calculating the composite compression modulus of the composite foundation includes:

[0066] The composite compression modulus of the composite foundation includes the composite compression modulus of the composite foundation in the first reinforcement area ξ1E s1 and composite compression modulus ξ2E of composite foundation in the second reinforcement area s2 , where ξ1 represents the increase multiple of the composite compression modulus of the composite foundation in the first reinforcement area, and ξ2 represents the increase multiple of the composite compression modulus of the composite foundation in the second reinforcement area;

[0067] Calculate the pile-soil stress ratio in the second reinforcement zone using the following expression:

[0068] n 12 =σ p12 / σ s2 =β1f p1 / β3f s2 (twenty one)

[0069] σ p11 =σ p12 (twenty two)

[0070] in: is the stress of the rigid pile in the second reinforcement zone (kPa);

[0071] Substituting the obtained correction coefficient β3 of the bearing capacity characteristic value of soil between piles and the correction coefficient β1 of the bearing capacity characteristic value of rigid piles into formula (21), we can obtain n 12 ;

[0072] Calculate the composite compression modulus of the composite foundation separately, including the composite compression modulus of the composite foundation in the first reinforcement area ξ1E s1 and composite compression modulus ξ2E of composite foundation in the second reinforcement areas2 ;

[0073] Where ξ1=1+m1(n 11 -1)+m2(n 21 -1)(23)

[0074] ξ2=1+m1(n 12 -1) (24).

[0075] Furthermore, the composite foundation settlement includes the settlement of the reinforced area and the settlement of the non-reinforced area:

[0076] For the settlement of the reinforced area, the conventional layered summation method is used to calculate the settlement of the first reinforced area and the second reinforced area. The calculation formula is:

[0077]

[0078] Where: ψ s is the empirical coefficient for settlement calculation; n is the number of soil layers divided within the depth range of foundation deformation calculation; p0 is the additional pressure at the bottom of the foundation corresponding to the quasi-permanent combination (kPa); z i 、z i-1 are the distances from the bottom of the foundation to the bottom of the i-th soil layer and the i-1-th soil layer (m); are the average additional stress coefficients from the calculation point of the foundation bottom to the bottom of the i-th soil layer and the i-1-th soil layer respectively;

[0079] The settlement of the non-reinforced area can be calculated as follows:

[0080]

[0081] Where: ψ s is the empirical coefficient for settlement calculation; n is the number of soil layers divided within the depth range of foundation deformation calculation; p0 is the additional pressure at the bottom of the foundation corresponding to the quasi-permanent combination (kPa); E si The compression modulus (MPa) of the i-th layer of soil below the foundation bottom surface should be calculated from the pressure section from the soil's own weight pressure to the sum of the soil's own weight pressure and the additional pressure; i 、z i-1 are the distances from the bottom of the foundation to the bottom of the i-th soil layer and the i-1-th soil layer (m); are the average additional stress coefficients from the calculation point of the foundation bottom to the bottom of the i-th soil layer and the i-1-th soil layer, respectively.

[0082] Furthermore, the composite foundation bearing capacity f1 is obtained based on the obtained correction coefficient β1 of the rigid pile bearing capacity characteristic value, the correction coefficient β2 of the flexible pile bearing capacity characteristic value, and the correction coefficient β3 of the bearing capacity characteristic value of the soil between piles. The calculation formula is:

[0083] f1=m1β1f p1 +m2β2f p2 +(1-m1-m2)β3f s1 (27).

[0084] Furthermore, the steps for calculating the minimum thickness d of the cushion layer are as follows:

[0085] According to the obtained correction coefficient β3 of the soil bearing capacity characteristic value between piles, the depth s of the rigid pile penetrating the cushion layer is calculated according to the formula (9): p1 ;

[0086] The minimum thickness d of the cushion layer is greater than the depth s of the rigid pile penetrating upward into the cushion layer. p1 The value of .

[0087] Compared with the prior art, the present invention has the following beneficial effects:

[0088] 1. The present invention obtains analytical solutions to the correction coefficients of the bearing capacity characteristic values ​​of rigid piles, flexible piles, and inter-pile soil through the vertical static equilibrium of piles and the coordinated analysis of pile-soil deformation, making the calculation results of the composite foundation bearing capacity closer to engineering practice.

[0089] 2. Based on the analytical solution of the correction coefficient, the present invention can obtain an accurate pile-soil stress ratio or the ratio of the actual composite foundation bearing capacity to the natural foundation bearing capacity. Compared with the existing standard method, by calculating the corresponding bearing capacity characteristic value correction coefficients β1, β2 and β3, the final composite compression modulus obtained is more accurate, and the settlement calculation result is more consistent with the actual project, which solves the defects of the existing standard calculation method that the composite compression modulus obtained is too large and the settlement calculation result is too small;

[0090] 3. Compared with the existing standard methods, the present invention takes into account the important position of the cushion layer in the formation conditions of the composite foundation. The cushion layer thickness and stiffness design method proposed on this basis can ensure that the rigid piles, flexible piles and soil between the piles form a composite foundation, and avoid the rigid piles piercing the cushion layer and directly supporting the rigid foundation, which will cause the rigid foundation to be separated from the natural ground. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 This is a cross-sectional view of the rigid-flexible pile composite foundation of the present invention;

[0092] Figure 2 This is the soil stress analysis diagram between piles of the present invention;

[0093] Figure 3 This is a force analysis diagram of the flexible pile of the present invention;

[0094] Figure 4 This is the force analysis diagram of the rigid pile of the present invention. DETAILED DESCRIPTION

[0095] The following is combined with Figures 1 to 4 The present invention is further described in detail with reference to specific embodiments.

[0096] The present invention discloses a method for designing a rigid-flexible pile composite foundation, comprising the following steps:

[0097] Determining the constraints of the rigid-flexible pile composite foundation design method;

[0098] Calculate the vertical forces on the superstructure, rigid piles, flexible piles and soil between piles through vertical static equilibrium;

[0099] Based on the vertical force calculation results, deformation calculation is performed on the rigid piles, the flexible piles and the soil between the piles;

[0100] According to the deformation calculation results, the deformation coordination condition is used to calculate the correction coefficient of the composite foundation bearing capacity;

[0101] Calculating the composite compression modulus of the composite foundation according to the calculation result of the composite foundation bearing capacity correction coefficient;

[0102] Calculating the composite foundation settlement according to the calculation result of the composite compression modulus of the composite foundation;

[0103] Calculate the composite foundation bearing capacity f1 according to the calculation result of the composite foundation bearing capacity correction coefficient;

[0104] According to the calculation result of the composite foundation bearing capacity correction coefficient, the minimum thickness d of the cushion layer is calculated.

[0105] The present invention obtains analytical solutions to the correction coefficients of the bearing capacity characteristic values ​​of rigid piles, flexible piles, and inter-pile soil through the vertical static equilibrium of piles and the coordinated analysis of pile-soil deformation, making the calculation results of the composite foundation bearing capacity closer to engineering practice.

[0106] In this embodiment, the constraints of the rigid-flexible pile composite foundation design method include:

[0107] The composite foundation is a deep soft soil foundation, and the rigid piles and flexible piles are friction piles. The pile tip pressure is zero, and the pressure on the superstructure is entirely borne by the lateral friction resistance of the soil around the piles.

[0108] The length of the rigid pile is greater than that of the flexible pile, and the rigidity of the rigid pile is greater than that of the flexible pile;

[0109] The composite soil layer composed of rigid piles, flexible piles and soil between piles is the first reinforced area; the composite soil layer composed of rigid piles and soil between piles below the flexible pile ends is the second reinforced area; the natural soil layer below the rigid pile ends is the non-reinforced area.

[0110] In this embodiment, the vertical static equilibrium calculation step includes:

[0111]

[0112] in: are the number of rigid piles and flexible piles respectively; Q p1 、 F is the pressure shared by each rigid pile, each flexible pile, the soil between piles and the superstructure load (kN);

[0113] The pressure shared by each rigid pile, each flexible pile, and the soil between the piles is:

[0114]

[0115]

[0116]

[0117] n 11 =σ p11 / σ s1 =β1f p1 / β3f s1 (5)

[0118] n 21 =σ p21 / σ s1 =β2f p2 / β3f s1 (6)

[0119] in: are the soil stresses at the top of the rigid pile, the top of the flexible pile, and the 1-1' interface (kPa); A p1 、A p2 、A s are the cross-sectional area of ​​each rigid pile, the cross-sectional area of ​​each flexible pile and the soil area between piles (m 2 ); β1, β2, and β3 are the correction coefficients of the characteristic values ​​of the bearing capacity of rigid piles, flexible piles, and soil between piles, respectively; f s1 are the characteristic values ​​of bearing capacity of rigid pile, flexible pile and soil between piles (kPa); n 11 、n 21 are the stress ratios of the rigid pile, flexible pile and soil between piles in the first reinforcement zone (kPa);

[0120] Substituting formulas (2) to (4) into formula (1), we have:

[0121]

[0122] Assuming the total area of ​​the composite foundation is A, we have:

[0123]

[0124] Among them: m1 and m2 are the area replacement rates of rigid piles and flexible piles respectively.

[0125] In this embodiment, the deformation calculation includes deformation calculation of rigid piles and flexible piles:

[0126] The deformation of the rigid pile includes the penetration amount s of the pile into the cushion layer. p1 (mm) and its own compression s' p1 (mm) are:

[0127]

[0128]

[0129] The deformation of the flexible pile includes the penetration amount s of the pile into the cushion layer. p2 (mm) and its own compression s' p2 (mm) are:

[0130]

[0131]

[0132] Where: E d 、ν d are the deformation modulus and Poisson's ratio of the cushion layer respectively; r1 and r2 are the radius of the rigid pile and the flexible pile respectively (m); l1 and l2 are the thickness of the first reinforcement area and the second reinforcement area respectively (m); E p1 、E p2 are the compression modulus of the rigid pile and the flexible pile (MPa);

[0133] For the first and second reinforcement areas, the compression of the soil between piles s s1 、s s2 (mm) are:

[0134]

[0135]

[0136] Where: s1 , σ s2 , σ s3 are the soil stresses between piles at the interfaces 1-1', 2-2' and 3-3' (kPa); E s1 、E s2are the compression modulus of the foundation soil in the first and second reinforcement zones (MPa); η1 and η2 are the soil stresses between piles at the interface 1-1' on the foundation surface, σ s1 Stress diffusion coefficient at the 2-2' and 3-3' interfaces.

[0137] Furthermore, the calculation formulas of η1 and η2 are:

[0138]

[0139]

[0140] Where: a and b are the lengths of the long and short sides of the composite foundation treatment range (m), A = ab, A is the total area of ​​the composite foundation; θ is the stress diffusion angle. For a flexible cushion layer under a rigid base plate, such as gravel, when the foundation soil is relatively weak (undrained shear strength c u ≤20kPa), θ=25°.

[0141] Furthermore, the composite foundation bearing capacity correction coefficient step includes:

[0142] For the first reinforcement zone, the deformation of the flexible pile is equal to the compression of the soil between the piles in the first reinforcement zone:

[0143] s p2 +s′ p2 =s s1 (17)

[0144] According to the formulas (11) to (13), we have:

[0145]

[0146] The stress ratio n between the flexible pile and the soil between the piles in the first reinforcement zone can be obtained from formula (18): 21 The value of

[0147] For the first and second reinforcement zones, the deformation of the rigid pile is equal to the sum of the compression of the soil between the piles in the first and second reinforcement zones:

[0148] s p1 +s′ p1 =s s1 +s s2 (19)

[0149] According to formulas (9) to (10) and (13) to (14), we have:

[0150]

[0151] The stress ratio n between the rigid pile and the soil between the piles in the first reinforcement zone can be obtained from formula (20): 11 ;

[0152] Using the obtained n 21 and n 11 Substituting into the formula (8) we can obtain the correction coefficient β3 of the characteristic value of soil bearing capacity between piles;

[0153] By substituting the obtained inter-pile soil bearing capacity characteristic value correction coefficient β3 into the above formulas (5) and (6), the rigid pile bearing capacity characteristic value correction coefficient β1 and the flexible pile bearing capacity characteristic value correction coefficient β2 can be obtained respectively. The present invention can obtain an accurate pile-soil stress ratio or the ratio of the actual composite foundation bearing capacity to the natural foundation bearing capacity. Compared with the existing standard method, by calculating the corresponding bearing capacity characteristic value correction coefficients β1, β2 and β3, the final composite compression modulus obtained is more accurate, and the settlement calculation result is more consistent with the actual project, thus solving the defects of the existing standard calculation method that the composite compression modulus obtained is too large and the settlement calculation result is too small.

[0154] In this embodiment, the steps of calculating the composite compression modulus of the composite foundation include:

[0155] The composite compression modulus of the composite foundation includes the composite compression modulus of the composite foundation in the first reinforcement area ξ1E s1 and composite compression modulus ξ2E of composite foundation in the second reinforcement area s2 , where ξ1 represents the increase multiple of the composite compression modulus of the composite foundation in the first reinforcement area, and ξ2 represents the increase multiple of the composite compression modulus of the composite foundation in the second reinforcement area;

[0156] Calculate the pile-soil stress ratio in the second reinforcement zone using the following expression:

[0157] n 12 =σ p12 / σ s2 =β1f p1 / β3f s2 (twenty one)

[0158] σ p11 =σ p12 (twenty two)

[0159] in: is the stress of the rigid pile in the second reinforcement zone (kPa);

[0160] Substituting the obtained correction coefficient β3 of the bearing capacity characteristic value of soil between piles and the correction coefficient β1 of the bearing capacity characteristic value of rigid piles into formula (21), we can obtain n 12 ;

[0161] Calculate the composite compression modulus of the composite foundation separately, including the composite compression modulus of the composite foundation in the first reinforcement area ξ1E s1 and composite compression modulus ξ2E of composite foundation in the second reinforcement area s2 ;

[0162] Where ξ1=1+m1(n 11 -1)+m2(n 21 -1)(23)

[0163] ξ2=1+m1(n 12 -1) (24).

[0164] In this embodiment, the composite foundation settlement includes the settlement of the reinforced area and the settlement of the non-reinforced area:

[0165] For the settlement of the reinforced area, the conventional layered summation method is used to calculate the settlement of the first and second reinforced areas. According to the Code for Design of Building Foundations (GB50007-2011), when calculating the deformation of the reinforced area foundation, the stress distribution within the foundation can be calculated using the isotropic homogeneous linear deformable body theory. The final deformation S (mm) can be calculated as follows:

[0166]

[0167] In the above equation, the left side represents the settlement of the first reinforcement area, and the right side represents the settlement of the second reinforcement area; s is the empirical coefficient for settlement calculation; n is the number of soil layers divided within the depth range of foundation deformation calculation; p0 is the additional pressure at the bottom surface of the foundation corresponding to the quasi-permanent combination (kPa); z i 、z i-1 are the distances from the bottom of the foundation to the bottom of the i-th soil layer and the i-1-th soil layer (m); are the average additional stress coefficients from the calculation point of the foundation bottom to the bottom of the i-th soil layer and the i-1-th soil layer respectively;

[0168] For the settlement of the non-reinforced area, according to the Code for Design of Building Foundations (GB50007-2011), when calculating the deformation of the natural foundation, the stress distribution within the foundation can be calculated using the isotropic homogeneous linear deformable body theory. The final deformation S (mm) can be calculated as follows:

[0169]

[0170] Where: ψ s is the empirical coefficient for settlement calculation; n is the number of soil layers divided within the depth range of foundation deformation calculation; p0 is the additional pressure at the bottom of the foundation corresponding to the quasi-permanent combination (kPa); E siThe compression modulus (MPa) of the i-th layer of soil below the foundation bottom surface should be calculated from the pressure section from the soil's own weight pressure to the sum of the soil's own weight pressure and the additional pressure; i 、z i-1 are the distances from the bottom of the foundation to the bottom of the i-th soil layer and the i-1-th soil layer (m); are the average additional stress coefficients from the calculation point of the foundation bottom to the bottom of the i-th soil layer and the i-1-th soil layer, respectively.

[0171] In this embodiment, the composite foundation bearing capacity f1 is obtained based on the obtained characteristic value correction coefficient β1 of the rigid pile bearing capacity, the characteristic value correction coefficient β2 of the flexible pile bearing capacity, and the characteristic value correction coefficient β3 of the soil bearing capacity between piles. The calculation formula is:

[0172] f1=m1β1f p1 +m2β2f p2 +(1-m1-m2)β3f s1 (27).

[0173] In this embodiment, the steps for calculating the minimum thickness d of the cushion layer are as follows:

[0174] According to the obtained correction coefficient β3 of the soil bearing capacity characteristic value between piles, the depth s of the rigid pile penetrating the cushion layer is calculated according to the formula (9): p1 ;

[0175] The minimum thickness d of the cushion layer is greater than the depth s of the rigid pile penetrating upward into the cushion layer. p1 The value of .

[0176] Compared with the existing standard methods, the present invention takes into account the important position of the cushion layer in the conditions for forming a composite foundation. The cushion layer thickness and stiffness design method proposed on this basis can ensure that the rigid piles, flexible piles and soil between the piles form a composite foundation, and avoid the consequence that the rigid piles pierce the cushion layer and directly support the rigid foundation, causing the rigid foundation to be separated from the natural ground.

[0177] The invention described above merely represents the implementation of the embodiments of the present invention and should not be construed as limiting the scope of the invention, nor does it impose any formal limitations on the structure of the embodiments of the present invention. It should be noted that a person of ordinary skill in the art may make a number of changes and improvements without departing from the concept of the embodiments of the present invention, and these shall fall within the scope of protection of the embodiments of the present invention.

Claims

1. A method for designing a rigid-flexible pile composite foundation, characterized in that: The following steps are involved: Determining the constraints of the rigid-flexible pile composite foundation design method; Calculate the vertical forces on the superstructure, rigid piles, flexible piles and soil between piles through vertical static equilibrium; Based on the vertical force calculation results, deformation calculation is performed on the rigid piles, the flexible piles and the soil between the piles; According to the deformation calculation results, the deformation coordination condition is used to calculate the correction coefficient of the composite foundation bearing capacity; Calculating the composite compression modulus of the composite foundation according to the calculation result of the composite foundation bearing capacity correction coefficient; Calculating the composite foundation settlement according to the calculation result of the composite compression modulus of the composite foundation; Calculate the composite foundation bearing capacity f1 according to the calculation result of the composite foundation bearing capacity correction coefficient; Calculate the minimum thickness d of the cushion layer according to the calculation result of the composite foundation bearing capacity correction coefficient; The composite foundation bearing capacity correction factor includes: For the first reinforcement zone, the deformation of the flexible pile is equal to the compression of the soil between the piles in the first reinforcement zone s. s1 : s p2 +s' p2 =s s1 (1) where s p2 is the penetration of the flexible pile into the cushion, s' p2 is the compression of the flexible pile itself; According to the penetration amount s of the flexible pile into the cushion layer p2 ,mm, the compression of the flexible pile itself s' p2 , mm, compression of soil between piles in the first reinforcement zone s s1 , mm, compression of soil between piles in the second reinforcement zone s s2 , mm, we have: where n 21 is the stress ratio between the flexible pile and the soil between piles in the first reinforcement zone, β3 is the correction coefficient of the characteristic value of the soil bearing capacity between piles, and f s1 is the characteristic value of soil bearing capacity between piles, r2 is the radius of flexible pile body, m; E d 、ν d are the deformation modulus and Poisson's ratio of the cushion layer, l1 represents the thickness of the first reinforcement zone, m, E p2 is the compression modulus of the flexible pile, MPa, η1 is the soil stress between piles at the 1-1' interface on the foundation surface, σ s1 Stress diffusion coefficient at the 2-2' interface, E s1 Compression modulus of foundation soil in the first reinforcement area, MPa; The stress ratio n between the flexible pile and the soil between the piles in the first reinforcement zone can be obtained from formula (2): 21 The value of For the first and second reinforcement zones, the deformation of the rigid pile is equal to the sum of the compression of the soil between the piles in the first and second reinforcement zones: s p1 +s' p1 =s s1 +s s2 (3) According to the penetration amount s of the rigid pile into the cushion layer p1 ,mm, rigid pile's own compression s' p1 , the compression of the soil between piles in the first reinforcement area s s1 The compression of the soil between piles in the second reinforcement area s s2 ,have: where n 11 is the stress ratio between the rigid pile and the soil between the piles in the first reinforcement zone, r1 is the radius of the rigid pile, m; η2 is the stress of the soil between the piles at the 1-1' interface on the foundation surface, σ s1 Stress diffusion coefficient at the 3-3' interface, l2 represents the thickness of the second reinforcement zone, m, E p1 is the compression modulus of the rigid pile, MPa, E s2 is the compression modulus of the foundation soil in the second reinforcement area, MPa; The stress ratio n between the rigid pile and the soil between the piles in the first reinforcement zone can be obtained from the formula (4): 11 ; Using the obtained n 21 and n 11 and the upper structure load F, the characteristic value correction coefficient β3 of the soil bearing capacity between piles can be obtained; The obtained inter-pile soil bearing capacity characteristic value correction coefficient β3 and the rigid piles in the first reinforcement area can be used to obtain the rigid pile bearing capacity characteristic value correction coefficient β1, and the obtained inter-pile soil bearing capacity characteristic value correction coefficient β3 and the stress ratio between the flexible pile and the soil between the piles can be used to obtain the flexible pile bearing capacity characteristic value correction coefficient β2.

2. A rigid-flexible pile composite foundation design method according to claim 1, characterized in that: The constraints of the rigid-flexible pile composite foundation design method include: The composite foundation is a deep soft soil foundation, and the rigid piles and flexible piles are friction piles. The pile tip pressure is zero, and the pressure on the superstructure is entirely borne by the lateral friction resistance of the soil around the piles. The length of the rigid pile is greater than that of the flexible pile, and the rigidity of the rigid pile is greater than that of the flexible pile; The composite soil layer composed of rigid piles, flexible piles and soil between piles is the first reinforced area; the composite soil layer composed of rigid piles and soil between piles below the flexible pile ends is the second reinforced area; the natural soil layer below the rigid pile ends is the non-reinforced area.

3. A rigid-flexible pile composite foundation design method according to claim 2, characterized in that: The calculation steps of the vertical static equilibrium include: in: are the number of rigid piles and flexible piles respectively; Q s1 and F are the pressures shared by each rigid pile, each flexible pile, the soil between piles and the superstructure load in kN respectively; The pressure shared by each rigid pile, each flexible pile, and the soil between the piles is: n 11 =s p11 / s s1 =β1f p1 / β3f s1 (9) n 21 =s p21 / s s1 =β2f p2 / β3f s1 (10) in: are the soil stresses at the top of the rigid pile, the top of the flexible pile and the 1-1' interface between piles, kPa; A s are the cross-sectional area of ​​each rigid pile, the cross-sectional area of ​​each flexible pile and the soil area between piles, m 2 β1 and β2 are the correction coefficients of the characteristic value of the bearing capacity of rigid piles and flexible piles respectively; are the characteristic values ​​of bearing capacity of rigid pile and flexible pile, kPa respectively; Substituting formulas (6) to (8) into formula (5), we have: Assuming the total area of ​​the composite foundation is A, we have: Among them: m1 and m2 are the area replacement rates of rigid piles and flexible piles respectively.

4. A rigid-flexible pile composite foundation design method according to claim 3, characterized in that: The deformation calculation includes the deformation calculation of rigid piles and flexible piles: The deformation of the rigid pile includes the penetration amount s of the pile into the cushion layer. p1 ,mm and its own compression s' p1 ,mm are: The deformation of the flexible pile includes the penetration amount s of the pile into the cushion layer. p2 ,mm and its own compression s' p2 ,mm are: For the first and second reinforcement areas, the compression of the soil between piles s s1 、s s2 ,mm, are respectively: Where: s1 , σ s2 , σ s3 are the soil stresses between piles at the 1-1', 2-2' and 3-3' interfaces in kPa.

5. A rigid-flexible pile composite foundation design method according to claim 4, characterized in that: The calculation formulas of η1 and η2 are respectively: Where: a and b are the lengths of the long and short sides of the composite foundation treatment range, respectively, in m; A=ab, A is the total area of ​​the composite foundation; θ is the stress diffusion angle.

6. A rigid-flexible pile composite foundation design method according to claim 5, characterized in that: The calculation steps of the composite compression modulus of the composite foundation include: The composite compression modulus of the composite foundation includes the composite compression modulus of the composite foundation in the first reinforcement area ξ1E s1 and composite compression modulus ξ2E of composite foundation in the second reinforcement area s2 , where ξ1 represents the increase multiple of the composite compression modulus of the composite foundation in the first reinforcement area, and ξ2 represents the increase multiple of the composite compression modulus of the composite foundation in the second reinforcement area; Calculate the pile-soil stress ratio n in the second reinforcement zone 12 , which is expressed as follows: n 12 =s p12 / s s2 =β1f p1 / β3f s2 (21) s p11 =s p12 (22) in: is the stress of the rigid pile in the second reinforcement area, kPa; Substituting the obtained correction coefficient β3 of the bearing capacity characteristic value of soil between piles and the correction coefficient β1 of the bearing capacity characteristic value of rigid piles into formula (21), we can obtain n 12 ; Calculate the composite compression modulus of the composite foundation separately, including the composite compression modulus of the composite foundation in the first reinforcement area ξ1E s1 and composite compression modulus ξ2E of composite foundation in the second reinforcement area s2 ; Where ξ1=1+m1(n 11 -1)+m2(n 21 -1) (23) ξ2=1+m1(n 12 -1) (24)。 7. A rigid-flexible pile composite foundation design method according to claim 6, characterized in that: The composite foundation settlement includes the settlement of the reinforced area and the settlement of the non-reinforced area: For the settlement of the reinforced area, the conventional layered summation method is used to calculate the settlement of the first reinforced area and the second reinforced area. The calculation formula is: Where: ψ s is the empirical coefficient for settlement calculation; n is the number of soil layers divided within the depth range of foundation deformation calculation; p0 is the additional pressure at the bottom surface of the foundation corresponding to the quasi-permanent combination of action, kPa; z i 、z i-1 are the distances from the bottom of the foundation to the bottom of the i-th soil layer and the i-1-th soil layer, respectively, in m; are the average additional stress coefficients from the calculation point of the foundation bottom to the bottom of the i-th soil layer and the i-1-th soil layer respectively; The settlement of the non-reinforced area can be calculated as follows: Where: ψ s is the empirical coefficient for settlement calculation; n is the number of soil layers divided within the depth range of foundation deformation calculation; p0 is the additional pressure at the bottom surface of the foundation corresponding to the quasi-permanent combination, kPa; E si The compression modulus of the i-th layer of soil below the foundation bottom surface, MPa, should be calculated from the pressure section from the soil's own weight pressure to the sum of the soil's own weight pressure and the additional pressure; i 、z i-1 are the distances from the bottom of the foundation to the bottom of the i-th soil layer and the i-1-th soil layer, respectively, in m; are the average additional stress coefficients from the calculation point of the foundation bottom to the bottom of the i-th soil layer and the i-1-th soil layer, respectively.

8. A rigid-flexible pile composite foundation design method according to claim 6, characterized in that: The composite foundation bearing capacity f1 is obtained based on the obtained correction coefficient β1 of the rigid pile bearing capacity characteristic value, the correction coefficient β2 of the flexible pile bearing capacity characteristic value, and the correction coefficient β3 of the bearing capacity characteristic value of the soil between piles. The calculation formula is: <h2 style=";text-align:left;direction:ltr">f1 = m1β1f<h2 style=";text-align:left;direction:ltr"> p1 <h2 style=";text-align:left;direction:ltr"> +m2β2f<h2 style=";text-align:left;direction:ltr"> p2 <h2 style=";text-align:left;direction:ltr"> +(1-m1-m2)β3f<h2 style=";text-align:left;direction:ltr"> s1 <h2 style=";text-align:left;direction:ltr"> (27) 9. A rigid-flexible pile composite foundation design method according to claim 6, characterized in that: The calculation steps for the minimum thickness d of the cushion layer are as follows: According to the obtained correction coefficient β3 of the soil bearing capacity characteristic value between piles, the depth s of the rigid pile penetrating the cushion layer is calculated according to the formula (13): p1 ; The minimum thickness d of the cushion layer is greater than the depth s of the rigid pile penetrating upward into the cushion layer. p1 value.

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