A method for modifying p-y curve of pile group foundation considering rigid shell effect of frozen soil foundation

Abstract

This invention relates to a pile group foundation that takes into account the rigid crust effect of frozen soil foundation. p - y Curve correction methods include dividing the foundation along the depth direction into an upper frozen layer and a lower unfrozen layer; based on the depth of the frozen soil site. z Average soil resistance of pile groups in unfrozen soil layer and depth under natural unfrozen foundation conditions z The average soil resistance of the pile group at different horizontal displacements y The average ratio under the condition is used to obtain the influence coefficient of the rigid shell effect; and it is introduced into the benchmark of the pile group on the natural unfrozen foundation. p - y The curve model was corrected to construct the unfrozen layer in the permafrost foundation. p - y Curve model; combined with pile groups in the frozen layer p - y Curve model for constructing pile foundations p - y The overall curve model is used for the horizontal bearing capacity analysis and design of pile group foundations in frozen soil, 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.

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 objectives, this invention proposes a method for correcting the py curve of a pile group foundation considering the rigid crust effect of frozen soil foundations, comprising the following steps:

[0007] 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;

[0008] S2, based on the depth of the frozen soil site Average soil resistance of pile groups in unfrozen soil layer and depth under natural unfrozen foundation conditions The average soil resistance of the pile group at different horizontal displacements The average ratio under the condition is used to obtain the influence coefficient of the rigid shell effect. 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.

[0009] S3. Establishing a Py-curve model for pile groups in the frozen layer based on the frozen soil Py-curve model. ;

[0010] 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.

[0011] Preferably, in S1, based on years of on-site ground temperature monitoring and / or numerical analysis of heat conduction, a temperature field of the frozen soil site is established, and the distribution of soil temperature with depth under design conditions is obtained; the maximum depth where the temperature does not exceed 0℃ is taken as the freezing boundary, and the foundation is frozen along the depth... The direction is divided into frozen layers and unfrozen layer ,in, This refers to the pile length or calculated depth.

[0012] Preferably, the formula for calculating the rigid shell effect influence coefficient is as follows:

[0013] ;

[0014] in, For depth, For the depth of the frozen soil site Average soil resistance of pile groups in unfrozen soil layer Depth under natural unfrozen foundation conditions Average soil resistance of the pile group at the location.

[0015] Preferably, the depth of the frozen soil site is [details to be added]. Average soil resistance of pile groups in unfrozen soil layer and depth under natural unfrozen foundation conditions The distribution curve of the average soil resistance ratio of the pile group along the depth direction is used to obtain the influence coefficient of the rigid shell effect. With depth z and frozen thickness Based on the pattern, optimize the influence coefficient of the rigid shell effect. :

[0016] ;

[0017] in, This is the proportionality coefficient; Use the reference depth parameter; and satisfy the following conditions: , .

[0018] Preferably, the corrected py curve model for the unfrozen layer in the frozen soil foundation is as follows:

[0019] ;

[0020] in, This is a model of the reference py curve for pile groups under natural, unfrozen foundation conditions.

[0021] Preferably, the model of the pile group benchmark py curve under natural unfrozen foundation conditions is modified based on the pile group effect, including:

[0022] Establishing a single-pile Py curve based on a single-pile Py curve model ;

[0023] 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. :

[0024] .

[0025] Preferably, the rigid shell effect influence coefficient Satisfy: In It reaches its minimum value at a certain depth, and this value increases with depth. It increases monotonically until it approaches 1.0.

[0026] Preferably, in S4, the overall model of the pile group foundation py curve is:

[0027] .

[0028] The beneficial effects provided by the above technical solution are as follows:

[0029] First, this invention, for the first time, abstracts the physical mechanism of "the reduction in the horizontal bearing capacity of the underlying unfrozen soil layer due to the upper frozen rigid shell" in permafrost foundations into a rigid shell effect influence coefficient. And propose a unified function form. Theoretically, it strictly satisfies the laws of minimum at the interface, monotonically increasing with depth, and approaching 1.0 at depth. It can be directly 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.

[0030] Secondly, the correction method of this invention is compatible with any existing single-pile Py model and pile group correction method, requiring only the addition of a multiplication factor to the unfrozen layer of the frozen soil foundation. The rigid shell effect can be considered, which has good versatility and portability.

[0031] Third, this method can explicitly reflect the quantitative impact of the thickness and depth of freezing in frozen soil foundations on the extent to which the horizontal bearing capacity of the unfrozen layer is utilized, avoiding the systematic overestimation of the resistance of the unfrozen soil by traditional methods, and improving the reliability of the horizontal bearing capacity analysis and design of pile foundations in frozen soil areas.

[0032] Fourth, based on the three-dimensional solid finite element analysis verification of representative engineering examples, the modified py curve model of this invention shows good agreement with the pile top displacement and pile body bending moment obtained under various freezing thickness conditions, and the accuracy meets the requirements of engineering applications. Attached Figure Description

[0033] Figure 1 The flowchart shows the method for correcting the py curve of a pile group foundation considering the rigid shell effect of frozen soil foundation according to the present invention.

[0034] Figure 2 This is a schematic diagram of the foundation plan and pile numbering in an embodiment of the present invention;

[0035] Figure 3 This is a schematic diagram of the selection of the pile-soil finite element boundary and the three-dimensional model in an embodiment of the present invention;

[0036] Figure 4 This is a schematic diagram of surface temperature data from 2015 to 2019 in an embodiment of the present invention;

[0037] Figure 5 This is a graph showing the change in soil freezing depth over time in an embodiment of the present invention;

[0038] Figure 6 This is a comparison diagram of the average py curves of the piles at different depths in natural soil pile groups and frozen soil pile groups in an embodiment of the present invention.

[0039] Figure 7 This is a graph showing the distribution of soil resistance ratios along the depth direction between frozen soil conditions and natural soil conditions at different freezing depths in embodiments of the present invention.

[0040] Figure 8 This is a comparison chart of the corrected py curve and the horizontal displacement results of the three-dimensional solid element numerical simulation at different freezing depths in this embodiment of the invention. Detailed Implementation

[0041] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0042] Example: Figure 1 As shown, a method for correcting the py curve of a pile group foundation considering the rigid shell effect of frozen soil foundation includes the following steps:

[0043] 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;

[0044] In this embodiment, the pile foundation of an 18 MW lattice-type wind turbine on a typical permafrost foundation in Nagqu, 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. The piles are arranged in three concentric circles: 8 piles are evenly distributed along a circumference of 4.2 m, 8 piles are evenly distributed along a circumference of 3.2 m, and 4 piles are evenly distributed along a circumference of 2.2 m. The foundation layout and pile numbering are shown in the figure. Figure 2 , Figure 2 The left image shows a schematic diagram of the boundary of the finite element model, and the right image shows a three-dimensional finite element model of the pile-soil system.

[0045] A numerical model of pile group-frozen soil was established based on ABAQUS, such as Figure 3 As shown, the foundation piles are concrete pipe piles with a diameter of 0.6 m and a length of 30 m, using an elastic constitutive model; the soil model has a diameter of 100 m and a thickness of 60 m, with horizontal displacement constraints on the sides and fixed constraints on the bottom, using a Mohr-Coulomb constitutive model; the heat transfer model uses C3DC8 elements, and the mechanical model uses C3D8R elements; the soil temperature distribution field is determined through heat conduction analysis; the temperature field results are imported into the mechanical model, and the frost heave response of the soil is simulated based on the equivalent linear expansion coefficient, thereby determining the initial temperature stress field inside the soil; a reference point RP-1 is established at the top of the pile cap, and then horizontal loads are gradually applied to RP-1 and transferred to the top of each pile.

[0046] The coefficient of thermal expansion is used to simulate the freeze-thaw and expansion behavior of frozen soil, with the freezing temperature set to 0 ℃; the temperature at a certain point in the unsteady heat conduction soil is also considered. for:

[0047] ;

[0048] Based on Fourier's law, the heat transfer equation considering the latent heat of phase change is:

[0049] ;

[0050] In the formula: Soil density; The density of ice; It is the volumetric heat capacity; θ is the thermal conductivity; L is the latent heat of phase change; θ is the volumetric water content; The volumetric ice content is given. The thermal parameters of the soil are shown in Table 1.

[0051] Table 1. Thermal parameters of soil at different temperatures

[0052]

[0053] 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.

[0054] Table 2 Soil mechanical parameters at different temperatures

[0055]

[0056] The tangential mechanical behavior between the pile and the soil is calculated using the penalty contact method, and the calculation formula is as follows:

[0057] ;

[0058] In the formula: and These are the coefficient of friction and the angle of friction, respectively.

[0059] The normal behavior of the pile-soil interface exhibits hard contact, and its mechanical behavior is described by the following formula:

[0060] ;

[0061] in, and These represent the interfacial normal stress and the contact gap size, respectively.

[0062] 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.

[0063] refer to Figure 6 As 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.

[0064] 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:

[0065] ;

[0066] 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.

[0067] 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. :

[0068] ;

[0069] Where A is the proportionality coefficient; Use the reference depth parameter; and satisfy the following conditions: , .

[0070] The corrected Py curve model for the unfrozen layer in a frozen soil foundation is as follows:

[0071] ;

[0072] in, A model of the reference py curve of pile groups under natural unfrozen foundation conditions.

[0073] S3. Establish a py curve model for pile groups in the frozen layer based on the frozen soil py curve model;

[0074] The model of the pile group benchmark py curve under natural unfrozen foundation conditions is modified based on the pile group effect, including:

[0075] Establishing a single-pile Py curve based on a single-pile Py curve model ;

[0076] 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. :

[0077] .

[0078] 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:

[0079] .

[0080] Validation of the modified Py curve model:

[0081] 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.

[0082] 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. 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; 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: , ; The corrected Py curve model for the unfrozen layer in the frozen soil foundation is as follows: ； in, A model of the reference py curve for pile groups 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; 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 according to claim 1, 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. : 。 4. 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 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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