Group pile foundation p-y curve correction method considering frozen soil foundation rigid shell effect

Abstract

The invention relates to a pile group foundation p-y curve correction method considering the frozen soil foundation rigid shell effect. The pile group foundation p-y curve correction method comprises the steps that a foundation is divided into an upper frozen layer and a lower unfrozen layer in the depth direction; based on the average ratio of the average soil resistance of the group piles of the unfrozen soil layer at the depth z of the frozen soil field to the average soil resistance of the group piles at the depth z under the natural unfrozen foundation condition in different horizontal displacement y states, the rigid shell effect influence coefficient is obtained; introducing into a natural unfrozen foundation pile group reference p-y curve model for correction, and constructing a corrected p-y curve model of an unfrozen layer in the frozen soil foundation; and in combination with a pile group p-y curve model in a frozen layer, a total pile group foundation p-y curve model is constructed and used for horizontal bearing analysis and design of the frozen soil foundation pile group foundation, so that the weakening rule of the development degree of the rigid shell effect on the horizontal bearing capacity of an unfrozen layer is quantitatively described, and the precision of horizontal bearing analysis of the pile group foundation is improved.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering and foundation engineering technology, specifically relating to a method for analyzing the horizontal bearing capacity of pile foundations, and more specifically, to a method for correcting the py curve of pile group foundations that is applicable to frozen soil foundations and considers the rigid shell effect. Background Technology

[0002] In high-altitude and permafrost regions, wind turbines, bridges, and high-rise buildings extensively utilize pile group foundations to bear wind loads, seismic forces, and horizontal environmental loads. Due to the influence of permafrost sites, the strength and stiffness of the foundation soil change significantly with temperature, resulting in marked differences in pile-soil interaction and the horizontal bearing capacity of pile group foundations compared to areas with normal temperatures. In engineering practice, the Py curve method recommended by API and other standards is typically used to analyze individual piles, and the pile group effect is considered through methods such as an overall reduction factor. This type of method has been widely applied under normal-temperature sandy and clay conditions.

[0003] In permafrost sites, the frozen soil layer above the surface forms a high-rigidity "rigid shell" due to ice cementation, which, together with the pile caps, bears most of the horizontal soil reaction force. The potential bearing capacity of the unfrozen soil layer below it is difficult to fully utilize, and its actual contribution to the total lateral soil resistance of the pile group is significantly lower than that in the naturally unfrozen state. Moreover, its contribution is lowest near the frozen-unfrozen interface and gradually recovers with depth. As the thickness of the frozen layer increases, the range and intensity of the "rigid shell's" inhibitory effect on the horizontal bearing capacity of the unfrozen soil layer both increase significantly.

[0004] Existing methods for correcting the Py curve of frozen soil pile foundations mostly reflect the effects of ice cementation and low temperature enhancement by increasing the ultimate soil resistance and initial foundation reaction modulus of the frozen layer, or by establishing temperature-related Py curves. These methods typically only adjust soil parameters within the frozen layer and lack a unified description of the inhibition law of the actual extent of the unfrozen soil below the frozen layer. They have not yet abstracted the spatial effect into a clear influence coefficient and embedded it into the Py curve framework, which easily leads to a systematic overestimation of the horizontal bearing capacity of pile foundations in frozen soil areas. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, the purpose of this invention is to introduce a depth-dependent factor in the horizontal bearing capacity analysis of pile foundations in frozen soil. and freezing thickness Variational rigid shell effect drag reduction coefficient A unified functional expression is proposed and embedded into the existing pile group py curve framework to correct the soil resistance of the unfrozen layer below the frozen layer, thereby quantitatively describing the weakening law of the rigid shell effect on the horizontal bearing capacity of the unfrozen layer and improving the accuracy of the horizontal bearing capacity analysis of pile group foundations.

[0006] To achieve the above object, the application provides a p-y curve correction method for group pile foundation considering the rigid shell effect of frozen soil foundation, which comprises the following steps: S1, establishing a temperature field of the frozen soil site and determining the frozen layer thickness based on the temperature field , the foundation is divided into an upper frozen layer and a lower unfrozen layer along the depth direction; S2, based on the frozen soil site depth , the average soil resistance of the group pile at the unfrozen layer is obtained , the average soil resistance of the group pile at the depth under the natural unfrozen foundation condition is obtained, and the average ratio of the two is obtained under different horizontal displacement states to obtain the rigid shell effect influence coefficient ; and the rigid shell effect influence coefficient is introduced into the natural unfrozen foundation group pile reference p-y curve model for correction to construct the corrected p-y curve model of the unfrozen layer in the frozen soil foundation; S3, based on the frozen soil p-y curve model, the group pile p-y curve model in the frozen layer is established ;

[0007] Preferably, in S1, based on the results of on-site multi-year ground temperature monitoring and / or heat conduction numerical analysis, the temperature field of the frozen soil site is established, and the distribution of the soil temperature with the depth under the design working condition is obtained; the maximum depth with the temperature not higher than 0℃ is taken as the frozen boundary, and the foundation is divided into the frozen layer and the unfrozen layer along the depth direction, wherein is the pile length or the calculation depth.

[0008] Preferably, the rigid shell effect influence coefficient calculation formula is: ; wherein is the depth, is the average soil resistance of the group pile at the unfrozen layer of the frozen soil site depth , and is the average soil resistance of the group pile at the depth under the natural unfrozen foundation condition.

[0009] Preferably, the average soil resistance ratio of the group pile at the unfrozen layer of the frozen soil site depth to the average soil resistance of the group pile at the depth under the natural unfrozen foundation condition is constructed along the depth direction to obtain the rigid shell effect influence coefficient with the depth z and the frozen thickness the rigid shell effect influence coefficient is optimized according to the law that the rigid shell effect influence coefficient is minimum at the interface and monotonically increases with the depth until approaching to 1.0 : ; wherein, is a proportional coefficient; is a reference depth parameter; and satisfies , .

[0010] Preferably, the unfrozen layer modified p-y curve model in the frozen soil foundation is: ; wherein, is a group pile reference p-y curve model under the natural unfrozen soil foundation condition.

[0011] Preferably, the group pile effect is used to modify the group pile reference p-y curve model under the natural unfrozen soil foundation condition, comprising: a single pile p-y curve is established based on the single pile p-y curve model ; a group pile reduction coefficient is introduced the single pile p-y curve is converted into a group pile p-y curve to obtain the modified group pile reference p-y curve model : .

[0012] Preferably, the rigid shell effect influence coefficient satisfies: the minimum value is obtained at the interface, and monotonically increases with the depth until approaching to 1.0.

[0013] Preferably, in S4, the group pile foundation p-y curve total model is: .

[0014] The beneficial effects provided in the above technical solutions are: First, the physical mechanism of "the degree of exertion reduction of the upper frozen rigid shell on the horizontal bearing capacity of the underlying unfrozen layer soil in the frozen soil foundation" is abstracted into a rigid shell effect influence coefficient for the first time, a unified function form is proposed, which strictly satisfies the laws of minimum at the interface, monotonically increasing with the depth, and approaching to 1.0 in the deep part in theory, can be directly embedded into the existing group pile p-y curve framework, and is used to modify the soil resistance of the unfrozen layer under the frozen layer, so as to quantitatively describe the weakening law of the rigid shell effect on the exertion degree of the horizontal bearing capacity of the unfrozen layer, and improve the accuracy of the horizontal bearing analysis of the group pile foundation.

[0015] ​Secondly, the correction method of the present application is compatible with any existing single pile p-y model and pile group correction method, only need to add a multiplier in the unfrozen layer of the frozen soil foundation That is, the rigid shell effect can be considered, and the method has good universality and portability.

[0016] Thirdly, the method can explicitly reflect the quantitative influence of the frozen thickness and depth in the frozen soil foundation on the degree of play of the horizontal bearing capacity of the unfrozen layer, avoid the systematic overestimation of the soil resistance of the unfrozen layer in the traditional method, and improve the reliability of the horizontal bearing analysis and design of the pile group foundation in the frozen soil area.

[0017] Fourthly, based on the three-dimensional solid finite element analysis verification of the representative engineering examples, the pile group top displacement and pile body bending moment obtained by the corrected p-y curve model of the present application under various frozen thickness conditions are in good agreement with the high-precision numerical results, and the precision meets the engineering application requirements. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 The flow chart of the p-y curve correction method of the pile group foundation considering the rigid shell effect of the frozen soil foundation of the present application; Figure 2 The foundation plane and foundation pile numbering diagram in the embodiment of the present application; Figure 3 The pile-soil finite element boundary selection and three-dimensional model diagram in the embodiment of the present application; Figure 4 The ground temperature data diagram during 2015-2019 in the embodiment of the present application; Figure 5 The diagram of the frozen depth of the soil body changing with time in the embodiment of the present application; Figure 6 The average p-y curve comparison diagram of the foundation pile at different depths of the natural soil pile group and the frozen soil pile group in the embodiment of the present application; Figure 7 The distribution curve diagram of the soil resistance ratio along the depth direction of the frozen soil working condition and the natural soil working condition under different frozen depths in the embodiment of the present application; Figure 8 The comparison diagram of the corrected p-y curve and the three-dimensional solid element numerical simulation horizontal displacement results under different frozen depths in the embodiment of the present application. DETAILED DESCRIPTION

[0019] In order to make the purpose and advantages of the present application more clear and explicit, the present application will be specifically described below in combination with the embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present application, and does not strictly limit the specific protection scope of the present application.

[0020] Embodiment: as Figure 1As shown, a p-y curve correction method for group pile foundation considering the rigid shell effect of frozen soil foundation includes the following steps: S1: Establish the temperature field of the frozen soil site, and determine the thickness of the frozen layer based on the temperature field , the foundation is divided into upper frozen layer and lower unfrozen layer along the depth direction; In this embodiment, the group pile foundation of an 18 MW lattice wind turbine in the typical frozen soil foundation of Naqu, Tibet is taken as the research object; in the foundation design scheme adopted, the pile cap is circular with a diameter of 10 m and a thickness of 3 m, and the pile foundation is arranged in three concentric circles: 8 piles are uniformly distributed along the circumference of the radius 4.2 m, 8 piles are uniformly distributed along the circumference of the radius 3.2 m, and 4 piles are uniformly distributed along the circumference of the radius 2.2 m; the foundation arrangement and pile position number are shown in Figure 2 , Figure 2 The left figure is a schematic diagram of the boundary of the finite element model, and the right figure is a three-dimensional finite element model of the pile-soil.

[0021] Based on ABAQUS, a group pile-frozen soil numerical model is established, as shown in Figure 3 , wherein the foundation pile is a concrete pipe pile with a diameter of 0.6 m and a length of 30 m, and an elastic constitutive model is used; the soil model has a diameter of 100 m and a thickness of 60 m, the side surface is horizontally displaced, the bottom surface is fixed, and the Mohr-Coulomb constitutive model is used; the heat transfer model uses C3DC8 unit, and the mechanical model uses C3D8R unit; the temperature distribution field of the soil is determined through heat conduction analysis; the temperature field result is imported into the mechanical model, and the frost heaving response of the soil is simulated based on the equivalent linear expansion coefficient, so as to determine the initial temperature stress field inside the soil; a reference point RP-1 is established on the top of the pile cap, and then the horizontal load is gradually applied to the top of each pile through RP-1.

[0022] The thermal expansion coefficient is used to simulate the freezing and thawing and expansion behavior of frozen soil, and the freezing temperature is set to 0 ℃; the temperature of a certain point in the unsteady heat conduction soil is ; Based on Fourier's law, the heat transfer equation considering the latent heat of phase change is: ; In the formula, is the soil density; is the ice density; is the volumetric heat capacity; is the thermal conductivity; L is the latent heat of phase change; θ is the volumetric water content; is the volumetric ice content. The thermal parameters of the soil are shown in Table 1.

[0023] Table 1 Thermal parameters of soil at different temperatures ​

[0024] The heat transfer model has a Dirichlet boundary at the bottom with a temperature of 4.5 ℃, and the left and right side boundaries are set as adiabatic boundaries; the initial temperature field of the entire model is 4.5 ℃. Surface temperature data from 2015 to 2019 (a total of 1825 days) were used as the temperature input, such as... Figure 4 As shown, the soil mechanical parameters are related to temperature; specific parameters are shown in Table 2.

[0025] Table 2 Soil mechanical parameters at different temperatures

[0026] The tangential mechanical behavior between the pile and the soil is calculated using the penalty contact method, and the calculation formula is as follows: ; In the formula: and These are the coefficient of friction and the angle of friction, respectively.

[0027] The normal behavior of the pile-soil interface exhibits hard contact, and its mechanical behavior is described by the following formula: ; in, and These represent the interfacial normal stress and the contact gap size, respectively.

[0028] refer to Figure 5 As shown, the maximum freezing depth during the entire simulation process was approximately 1.42m, occurring in March of each year. The duration of soil freezing was 150-170 days per year. In this embodiment, the soil temperatures on January 1st (freezing depth 0.8m), March 5th (freezing depth 1.4m), April 6th (freezing depth 1.1m), and November 18th (freezing depth 0.5m) of the fifth year were used as frozen soil conditions, and the soil temperature on July 1st of the fifth year was used as thawing soil conditions for subsequent pile-soil interaction analysis.

[0029] refer to Figure 6As shown, the soil resistance of the unfrozen soil layer (yellow shaded area) in the frozen soil foundation is lower than that of the foundation in the non-frozen soil area at the same depth; and at the same depth, the soil resistance in the unfrozen soil layer of the frozen soil foundation decreases with the increase of the freezing thickness. The main reason for the decrease in soil resistance of the pile foundation group in the unfrozen soil layer of the frozen soil foundation is that after the upper soil is cooled and frozen, the frozen soil has extremely high strength and stiffness due to the cementing effect of ice. The surface of the frozen soil foundation forms a very stiff "rigid shell", which becomes the main load-bearing body of the pile foundation. This causes the load to concentrate in the "rigid shell" area and cannot be effectively transferred to the lower pile body. As a result, the pile-unfrozen soil interface cannot generate sufficient relative displacement to fully stimulate its side friction resistance. The bearing potential of the lower soil is thus left idle. Therefore, the "rigid shell" effect causes the soil resistance around the pile in this area to be significantly lower than that of the original natural soil.

[0030] S2. Based on the ratio of the average soil resistance of the pile group at depth z in the unfrozen soil layer of the frozen soil site to the average soil resistance of the pile group at depth z under different horizontal displacement y states under natural unfrozen foundation conditions, obtain the rigid shell effect influence coefficient. The formula for calculating the influence coefficient of the rigid shell effect is: ; Where z is the depth, Let z be the average soil resistance of the pile group at depth z in the unfrozen soil layer of the frozen soil site. Average soil resistance of pile group at depth z under natural unfrozen foundation conditions.

[0031] refer to Figure 7 As shown, the ratio of the average soil resistance of a pile group foundation in unfrozen soil layer in frozen soil foundation to the average soil resistance of a pile group foundation at the same depth in natural soil is given, which is also the rigid shell effect influence coefficient. The relationship between soil resistance and depth was investigated. It was found that when a frozen soil layer exists above the foundation, the soil resistance around the piles in the lower unfrozen soil layer is significantly lower than that of a natural foundation. The closer to the frozen soil layer, the more significant the soil resistance reduction effect. As the depth increases further, the soil resistance gradually approaches the level of a natural foundation. On the other hand, the thickness of the frozen soil layer has a significant impact on the soil resistance reduction effect; the thicker the frozen soil layer, the deeper the area affected by the reduction in soil resistance in the unfrozen soil layer, and the greater the reduction ratio. Further analysis is needed. Figure 7 It can be seen that the rigid shell effect influence coefficient In unfrozen soil layers, its value gradually increases with depth to 1.0; the rigid shell effect influence coefficient is optimized. : ; Where A is the proportionality coefficient; Use the reference depth parameter; and satisfy the following conditions: , .

[0032] The corrected Py curve model for the unfrozen layer in a frozen soil foundation is as follows: ; in, Model of pile group reference py curve under natural unfrozen foundation conditions S3. Establish a py curve model for pile groups in the frozen layer based on the frozen soil py curve model; The model of the pile group benchmark py curve under natural unfrozen foundation conditions is modified based on the pile group effect, including: Establishing a single-pile Py curve based on a single-pile Py curve model ; Introducing the reduction factor for pile groups The single-pile Py curve is converted into a group-pile Py curve to obtain the corrected group-pile benchmark Py curve model. : .

[0033] S4. Integrate the corrected py curve model of the unfrozen layer in the frozen soil foundation and the py curve of the pile group in the frozen layer to construct a general py curve model for the pile group foundation, which is used for the horizontal bearing analysis and design of the pile group foundation in frozen soil foundation: The general py curve model of the pile group foundation is as follows: .

[0034] Validation of the modified Py curve model: First, the modified Py curve calculation model established in this embodiment is used in finite element software to represent the soil as a horizontal nonlinear spring. A horizontal static load is applied 3 m above the mud surface. In the simplified model, the pile foundation uses beam elements B31, and the pile cap uses shell elements S4R for simulation. The loading method is the same as described in Section 1.1. (Reference) Figure 8 As shown, the freezing depths under horizontal static loads are given as follows: and The results of the horizontal displacement simulation of the pile group foundation using three-dimensional solid element finite element simulation and the simulation results of the simplified model of the modified py curve of the pile group foundation in the frozen soil region proposed in this paper show that the horizontal displacement results of the two are close, which verifies the applicability of the modified py curve model proposed in this embodiment to the pile group foundation in the frozen soil region.

[0035] The embodiments of the present invention have been described in detail above with reference to the examples. However, the present invention is not limited to the above embodiments. For those skilled in the art, after learning the contents described in the present invention, several equivalent changes and substitutions can be made without departing from the principle of the present invention. These equivalent changes and substitutions should also be considered to fall within the protection scope of the present invention.

Claims

1. A method for correcting the py curve of a pile group foundation considering the rigid crust effect of frozen soil foundation, characterized in that: Includes the following steps: S1. Establish the temperature field of the frozen soil site and determine the thickness of the frozen layer based on the temperature field. The foundation is divided into an upper frozen layer and a lower unfrozen layer along the depth direction; S2. Based on the ratio of the average soil resistance of the pile group at depth z in the unfrozen soil layer of the frozen soil site to the average soil resistance of the pile group at depth z under different horizontal displacement y states under natural unfrozen foundation conditions, obtain the rigid shell effect influence coefficient. Furthermore, the rigid shell effect influence coefficient is introduced into the benchmark py curve model of the pile group in natural unfrozen foundation for correction, and a corrected py curve model of the unfrozen layer in frozen soil foundation is constructed. S3. Establish a py curve model for pile groups in the frozen layer based on the frozen soil py curve model; S4. Integrate the corrected py curve model of the unfrozen layer in the frozen soil foundation and the py curve model of the pile group in the frozen layer to construct a general py curve model of the pile group foundation, which is used for the horizontal bearing analysis and design of the pile group foundation in the frozen soil foundation.

2. The method for correcting the py curve of a pile group foundation considering the rigid crust effect of frozen soil foundation according to claim 1, characterized in that: In S1, based on years of on-site ground temperature monitoring and / or numerical analysis of heat conduction, the temperature field of the frozen soil site is established, and the distribution of soil temperature with depth under the design conditions is obtained. The thickness of the frozen layer is determined by using the maximum depth at which the temperature does not exceed 0°C as the freezing boundary. .

3. The method for correcting the py curve of a pile group foundation considering the rigid crust effect of frozen soil foundation as described in claim 1, characterized in that: The formula for calculating the influence coefficient of the rigid shell effect is as follows: ； Where z is the depth, Let z be the average soil resistance of the pile group at depth z in the unfrozen soil layer of the frozen soil site. Average soil resistance of pile group at depth z under natural unfrozen foundation conditions.

4. The method for correcting the py curve of a pile group foundation considering the rigid crust effect of frozen soil foundation according to claim 3, characterized in that: A depth-direction distribution curve is constructed to show the ratio of the average soil resistance of pile groups at depth z in the unfrozen soil layer of a frozen soil site to the average soil resistance of pile groups at depth z under natural unfrozen foundation conditions, and the influence coefficient of the rigid shell effect is obtained. With depth z and frozen thickness Based on the pattern, optimize the influence coefficient of the rigid shell effect. : ； Where A is the proportionality coefficient; Use the reference depth parameter; and satisfy the following conditions: , .

5. A method for correcting the py curve of a pile group foundation considering the rigid crust effect of frozen soil foundation according to any one of claims 1-4, characterized in that: The corrected Py curve model for the unfrozen layer in the frozen soil foundation is as follows: ； in, This is a reference py curve model for pile groups under natural, unfrozen foundation conditions.

6. The method for correcting the py curve of a pile group foundation considering the rigid crust effect of frozen soil foundation according to claim 5, characterized in that: The model of the pile group benchmark py curve under natural unfrozen foundation conditions is modified based on the pile group effect, including: Establishing a single-pile Py curve based on a single-pile Py curve model ; Introducing the reduction factor for pile groups The single-pile Py curve is converted into a group-pile Py curve to obtain the corrected group-pile benchmark Py curve model. : 。 7. The method for correcting the py curve of a pile group foundation considering the rigid crust effect of frozen soil foundation according to claim 1, characterized in that: The rigid shell effect influence coefficient Satisfy: In It reaches its minimum value at z, and increases monotonically with depth z until it approaches 1.0.

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