Jack-up platform pile-soil coupling analysis method and system
By acquiring structural and soil data of the self-elevating platform, a finite element model was constructed to determine the preload and pile depth. Combined with soil properties and stiffness constraint data, the problem of neglecting the pile-soil coupling effect in the self-elevating platform was solved, achieving a more accurate assessment of the foundation bearing capacity and improving safety.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANGHAI ZHENHUA HEAVY IND
- Filing Date
- 2026-05-11
- Publication Date
- 2026-07-31
AI Technical Summary
Existing designs for self-elevating platforms neglect the pile-soil coupling effect between the pile legs and the foundation soil, leading to safety accidents such as pile leg punctures. Furthermore, the mechanical modeling is not precise enough, making it impossible to accurately assess the foundation bearing capacity.
By acquiring structural data of the self-elevating platform and soil bearing capacity data, a finite element model is constructed to determine the preload and pile depth. Combining soil properties and stiffness constraint data, it is determined whether the soil at the pile depth meets the bearing requirements. Finite element analysis is then used to update and iteratively adjust the load.
It improves the accuracy and reliability of foundation bearing capacity assessment, avoids safety accidents such as pile leg puncture, and enhances the safety and precision of self-elevating platform operations.
Smart Images

Figure CN122154360B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of marine engineering technology, specifically to a pile-soil coupling analysis method and system for self-elevating platforms. Background Technology
[0002] Jack-up platforms are indispensable core equipment in the field of marine resource development, widely used in offshore oil and gas drilling, offshore wind power construction, and temporary offshore accommodation. However, current jack-up platform design often neglects the pile-soil coupling effect between the legs and the foundation soil. Specifically, when determining the design preload, only the vertical load applied to the pile shoe at the bottom of the legs is considered, without fully taking into account the bending moment and horizontal load between the legs / shoes and the foundation soil. This approximation leads to an overly optimistic assessment of the foundation's bearing capacity, easily resulting in safety accidents such as leg puncture during actual operations. Furthermore, the pile-soil coupling effect has a significant impact on load transfer between the pile shoe and the soil. Existing technologies, in mechanical modeling, simply use boundary conditions with simply supported pile shoe positions, which fails to accurately reflect the complex stress state during actual ship operations. This results in insufficient accuracy in the analysis of the jack-up platform's operational capabilities and cannot provide reliable support for risk warning under complex offshore conditions. Summary of the Invention
[0003] In view of this, the present invention provides a pile-soil coupling analysis method for self-elevating platform, which can accurately determine whether the soil at the pile insertion depth meets the bearing requirements.
[0004] To solve at least one of the above-mentioned technical problems, the present invention adopts the following technical solution:
[0005] The first aspect of this invention provides a pile-soil coupling analysis method for a self-elevating platform, comprising:
[0006] Obtain structural data of the self-elevating platform, as well as soil bearing capacity data;
[0007] The preload to be applied to the jack-up platform is determined based on structural data;
[0008] Based on the preload and soil bearing capacity data, the pile insertion depth of the self-elevating platform was determined;
[0009] Based on the soil properties, structural data, and pile depth at the pile insertion depth, the anisotropic stiffness constraint data and anisotropic basic bearing capacity data of the soil at the pile insertion depth on the pile leg are determined.
[0010] Based on the pile insertion depth and anisotropic stiffness constraint data, the anisotropic updated loads at the bottom of the pile legs of the self-elevating platform are determined.
[0011] Based on the basic bearing capacity data and updated loads in each direction, it is determined whether the soil at the pile depth meets the bearing requirements.
[0012] In one embodiment of the invention, determining the preload to be applied to the jack-up platform based on structural data includes:
[0013] Construct a finite element model based on structural data;
[0014] Based on the finite element model, the initial vertical load at the bottom of the pile legs of the self-elevating platform is determined;
[0015] Based on the initial vertical load, determine the preload to be applied to the jack-up platform.
[0016] Furthermore, when determining the anisotropic update load, the anisotropic update load at the bottom of the pile legs of the self-elevating platform is determined by using a finite element model based on the pile depth and anisotropic stiffness constraint data.
[0017] In one embodiment of the present invention, the structural data includes geometric parameters and material parameters. Based on the structural data, a finite element model is constructed, including:
[0018] A geometric model of the self-elevating platform is constructed based on geometric parameters;
[0019] Assign material parameters to the geometric model based on the material parameters;
[0020] The geometric model is discretized into finite element units, and the topological relationship between each finite element unit is established based on the spatial affiliation of the finite element units.
[0021] A finite element model is constructed based on finite element elements and topological relationships.
[0022] In one embodiment of the present invention, the initial vertical load at the bottom of the pile legs of the self-elevating platform is determined based on a finite element model, including:
[0023] Set the bottom constraint of the pile leg in the finite element model as a simply supported constraint that is in initial contact with the seabed surface;
[0024] The design load is applied to the finite element model, and a static analysis is performed based on the finite element model to determine the initial vertical load at the bottom of the pile leg.
[0025] In one embodiment of the present invention, the preload applied to the self-elevating platform is determined based on the initial vertical load using a preset preload coefficient.
[0026] The determination of the pile insertion depth for the self-elevating platform based on preload and soil bearing capacity data includes:
[0027] The soil bearing capacity curve as a function of depth is obtained based on soil bearing capacity data;
[0028] The preload and bearing capacity curves are matched to determine the pile insertion depth of the self-elevating platform.
[0029] In one embodiment of the present invention, based on the soil properties, structural data, and pile depth at the pile depth, the anisotropic stiffness constraint data and anisotropic basic bearing capacity data of the soil at the pile depth on the pile leg are determined, including:
[0030] Based on soil properties, determine the soil mechanical parameters at the pile insertion depth;
[0031] Based on soil mechanical parameters and structural data, the basic bearing capacity of the soil to the pile leg in all directions at the pile insertion depth was determined.
[0032] Based on soil mechanical parameters and pile insertion depth, the anisotropic stiffness constraint data of the soil on the pile leg at the pile insertion depth are determined.
[0033] In one embodiment of the present invention, based on the pile insertion depth and anisotropic stiffness constraint data, the anisotropic updated loads at the bottom of the pile legs of the self-elevating platform are determined by a finite element model, including:
[0034] Based on the anisotropic stiffness constraint data, the bottom of the pile leg of the finite element model is modeled as an elastic support, and the bottom of the pile leg of the finite element model is set as a spring constraint.
[0035] Based on the pile insertion depth, design loads are applied to the finite element model, and static analysis is performed based on the finite element model to determine the updated loads in all directions at the bottom of the pile leg.
[0036] In one embodiment of the present invention, determining whether the soil at the pile depth meets the bearing requirements based on basic bearing capacity data and updated loads in all directions includes:
[0037] Based on the basic bearing capacity data and updated loads in all directions, the judgment value used to characterize the pile-soil coupling state is determined by using the pre-acquired interaction yield surface function.
[0038] If the judgment value is less than the preset threshold, it is determined that the soil at the pile depth meets the bearing capacity requirements.
[0039] If the judgment value is greater than or equal to the preset threshold, it is determined that the soil at the pile depth does not meet the bearing requirements, and the update load or pile depth in each direction is iterated until the judgment value is less than the preset threshold.
[0040] In one embodiment of the present invention, the stiffness constraint data in each direction includes rotational stiffness. If the determination value is greater than or equal to a preset threshold, it is determined that the soil at the pile depth does not meet the bearing requirements, and the updated load or pile depth in each direction is iterated until the determination value is less than the preset threshold, including:
[0041] If the judgment value is greater than the preset threshold, the rotational stiffness is reduced based on the preset reduction rule, and the updated loads in each direction are re-determined based on the pile depth and the stiffness constraint data in each direction after the rotational stiffness is reduced.
[0042] If the judgment value is equal to the preset threshold, the preload is increased based on the preload increase / decrease rules, and the pile insertion depth of the self-elevating platform is re-determined based on the increased preload and soil bearing capacity data.
[0043] In one embodiment of the present invention, the pile-soil coupling analysis method for self-elevating platforms further includes:
[0044] Obtain the operating parameters of the self-elevating platform at the pile insertion depth;
[0045] Based on the pile insertion depth, structural data, and operational parameters, the strength and length of the pile leg structure of the self-elevating platform are checked to determine whether the pile leg structure meets the operational requirements.
[0046] Secondly, the present invention also provides a pile-soil coupling analysis system for a self-elevating platform, comprising:
[0047] The data acquisition module is used to acquire structural data of the self-elevating platform and soil carrying capacity data;
[0048] The preload determination module is used to determine the preload to be applied to the self-elevating platform based on structural data.
[0049] The pile driving depth determination module is used to determine the pile driving depth of the self-elevating platform based on preload and soil bearing capacity data.
[0050] The soil parameter determination module is used to determine the anisotropic stiffness constraint data and anisotropic basic bearing capacity data of the soil at the pile depth on the pile leg based on the soil properties, structural data and pile depth at the pile depth.
[0051] The updated load determination module is used to determine the updated loads in all directions at the bottom of the pile legs of the self-elevating platform based on the pile depth and all-directional stiffness constraint data.
[0052] The bearing capacity assessment module is used to determine whether the soil at the pile depth meets the bearing requirements based on the basic bearing capacity data and updated loads in each direction.
[0053] The above-described technical solution of the present invention has at least one of the following beneficial effects:
[0054] The pile-soil coupling analysis method for self-elevating platforms of the present invention acquires structural data and soil bearing capacity data of the self-elevating platform, determines the preload based on the structural data, and then accurately determines the pile insertion depth by combining the soil bearing capacity data. On this basis, according to the soil characteristics, structural data, and pile insertion depth at the pile insertion depth, the anisotropic stiffness constraint data and anisotropic basic bearing capacity data of the soil around the pile on the pile leg are simultaneously determined. Furthermore, based on the pile insertion depth and anisotropic stiffness constraint data, the anisotropic updated load at the bottom of the pile leg is solved, and the anisotropic basic bearing capacity data and anisotropic updated load are used to check the bearing capacity and determine whether the soil at the pile insertion depth meets the bearing requirements. This avoids safety accidents such as pile leg puncture caused by inaccurate assessment in the prior art, and effectively improves the accuracy and reliability of foundation bearing capacity assessment. Attached Figure Description
[0055] Figure 1 This is a schematic diagram illustrating the implementation environment of the pile-soil coupling analysis method for a self-elevating platform in one embodiment of the present invention;
[0056] Figure 2 This is a flowchart of a pile-soil coupling analysis method for a self-elevating platform according to one embodiment of the present invention;
[0057] Figure 3 This is a flowchart illustrating the determination of preload in one embodiment of the present invention;
[0058] Figure 4 This is a flowchart of constructing a finite element model in one embodiment of the present invention;
[0059] Figure 5 This is a flowchart illustrating the determination of the initial vertical load in one embodiment of the present invention;
[0060] Figure 6 This is a flowchart illustrating the determination of stake insertion depth in one embodiment of the present invention;
[0061] Figure 7 This is a flowchart illustrating the determination of anisotropic stiffness constraint data in one embodiment of the present invention;
[0062] Figure 8 This is a flowchart of determining the anisotropic update load in one embodiment of the present invention;
[0063] Figure 9 This is a flowchart illustrating the process of determining whether the soil at the pile insertion depth meets the bearing capacity requirements in one embodiment of the present invention.
[0064] Figure 10 This is a flowchart illustrating the iterative process of updating loads or stake depths in all directions, as described in one embodiment of the present invention.
[0065] Figure 11This is a schematic diagram of the structure of a self-elevating platform pile-soil coupling analysis system in one embodiment of the present invention. Detailed Implementation
[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.
[0067] The following section describes, with reference to the accompanying drawings, a pile-soil coupling analysis method for a self-elevating platform according to an embodiment of the present invention.
[0068] Reference manual attached Figure 1 , Figure 1 A schematic diagram illustrating the implementation environment of the self-elevating platform pile-soil coupling analysis method of the present invention is shown. For example... Figure 1 As shown, the implementation environment may include a jack-up platform 1001 and a computing device 1010 electrically connected to the jack-up platform 1001 via wired / wireless means. The jack-up platform includes a platform body 1002, legs 1003 disposed within the platform body 1002 for contact with the seabed foundation, and a lifting device 1004 for controlling the raising and lowering of the legs 1003. The computing device 1010 may be, but is not limited to, various servers, personal computers, laptops, smartphones, tablets, and portable wearable devices. The server may be a standalone server, a server cluster composed of multiple servers, or a distributed computing device 1010. It may also be an edge server or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks (CDNs), and big data and artificial intelligence platforms.
[0069] The pile-soil coupling analysis method for a self-elevating platform may include the following steps: The computing device 1010 first acquires the structural data of the self-elevating platform 1001 and the soil bearing capacity data; then, based on the structural data, it determines the preload applied to the self-elevating platform 1001 by the lifting device 1004. Based on this, the pile insertion depth of the self-elevating platform 1001 is accurately determined using the preload and soil bearing capacity data. Furthermore, the computing device 1010 can determine the all-directional stiffness constraint data and all-directional basic bearing capacity data of the soil at the pile depth for the pile leg 1003 based on the soil characteristics, structural data, and pile depth. Then, based on the pile depth and all-directional stiffness constraint data, it determines the all-directional updated load at the bottom of the pile leg 1003 of the self-elevating platform 1001, and uses the all-directional basic bearing capacity data and the all-directional updated load to check the bearing capacity and determine whether the soil at the pile depth meets the bearing requirements. This avoids safety accidents such as pile leg 1003 puncture caused by inaccurate assessment in the prior art, and effectively improves the accuracy and reliability of the foundation bearing capacity assessment.
[0070] Below, please refer to the attached instruction manual. Figure 2 This illustrates a pile-soil coupling analysis method for a self-elevating platform provided by an embodiment of the present invention, which can be applied to... Figure 1 In the computing device 1010. Specifically, the method may include the following steps:
[0071] S100: Obtain structural data of the self-elevating platform and soil bearing capacity data.
[0072] In this embodiment, the computing device first acquires structural data of the jack-up platform, such as the length and segmentation of the pile legs, the outline shape and size of the pile shoes, and the overall dimensions of the platform. This provides data input for subsequent finite element analysis. Furthermore, the computing device can simultaneously acquire soil bearing capacity data, which can be used to characterize the ultimate load that the seabed foundation soil can withstand at different depths. This provides data input for subsequently determining the pile insertion depth.
[0073] S200, Determine the preload to be applied to the self-elevating platform based on structural data.
[0074] In this embodiment, the computing device can analyze the load distribution of the jack-up platform based on structural data, thereby determining the preload to be applied to the platform. Thus, by determining the preload, the effect of the jack-up platform on the seabed foundation can be reflected, providing a basis for subsequent analysis based on soil bearing capacity data.
[0075] S300. Based on preload and soil bearing capacity data, determine the pile insertion depth of the self-elevating platform.
[0076] In this embodiment, the computing device can compare the soil bearing capacity at different depths of the seabed foundation based on the matching relationship between the preload and soil bearing capacity data, thereby determining the depth position corresponding to the bearing capacity that matches the preload, and using this depth position as the pile insertion depth of the self-elevating platform, thus realizing the determination of the pile insertion depth.
[0077] S400. Based on the soil properties, structural data, and pile depth at the pile depth, determine the anisotropic stiffness constraint data and anisotropic basic bearing capacity data of the soil at the pile depth on the pile leg.
[0078] In this embodiment, the computing device can analyze the stress characteristics of the soil at the pile depth based on the soil properties obtained in advance, combined with structural data and pile depth, and then determine the constraint effect of the soil on the pile leg in each direction and the corresponding bearing capacity, thereby obtaining the stiffness constraint data and basic bearing capacity data of the soil on the pile leg at the pile depth.
[0079] S500, based on the pile insertion depth and anisotropic stiffness constraint data, determines the anisotropic updated load at the bottom of the pile legs of the self-elevating platform.
[0080] In this embodiment, the computing device can update the stress state of the self-elevating platform based on the pile insertion depth and anisotropic stiffness constraint data, and correct the constraint conditions at the bottom of the pile legs, thereby determining the updated anisotropic loads at the bottom of the self-elevating platform's pile legs. This avoids safety accidents such as pile leg punctures caused by inaccurate assessments in existing technologies, effectively improving the accuracy and reliability of foundation bearing capacity assessment.
[0081] S600. Based on the basic bearing capacity data and updated loads in each direction, determine whether the soil at the pile depth meets the bearing requirements.
[0082] In this embodiment, the computing device can comprehensively evaluate the bearing capacity of the soil at the pile depth under the combined action of multiple loads based on the relationship between the basic bearing capacity data in each direction and the updated load in each direction. Then, it can determine whether the soil at that depth can meet the bearing requirements of the self-elevating platform. If the bearing requirements are not met, the relevant parameters can be adjusted and verified to achieve an accurate determination of the soil bearing capacity.
[0083] Below, each step will be explained in detail.
[0084] (a) Obtaining structural data and soil bearing capacity data.
[0085] Next, the steps for acquiring structural data and soil bearing capacity data (i.e., step S100) are described. In one embodiment of the present invention, in step S100, the computing device can first acquire the structural data of the self-elevating platform. The structural data may include the overall length, segmentation form, and cross-sectional dimension parameters of the pile legs, the geometric contour, diameter, and contact area of the pile shoes, as well as the external dimensions, mass distribution, and arrangement of key structural components of the platform body, thereby providing basic data for subsequent finite element analysis that reflects the overall stress characteristics of the platform. Simultaneously, the computing device also acquires soil bearing capacity data. This soil bearing capacity data can be used to characterize the changes in the bearing capacity of the seabed foundation soil under different depth conditions, reflecting the seabed foundation soil's ability to withstand external loads within the corresponding depth range, thus providing data support for subsequently determining the pile insertion depth that matches the preload.
[0086] (ii) Determine the preload applied to the self-elevating platform.
[0087] The following describes the determination of the preload to be applied to the self-elevating platform based on structural data (i.e., step S200). Figure 3 As shown, in one embodiment of the present invention, step S200 may include the following steps S210-S230:
[0088] S210. Construct a finite element model based on structural data.
[0089] In this embodiment, the computing device can simplify and model the main structure, leg structure, and pile shoes of the self-elevating platform based on the acquired structural data. The main platform is modeled as a structural unit reflecting the overall stress characteristics, and the leg structure is modeled as load-bearing and force-transmitting components. The connection between the leg structure and the main platform is established in the model, thereby constructing a finite element model that reflects the overall stress behavior of the self-elevating platform, providing a foundation for subsequent load calculations. Specifically, the structural data may include geometric parameters and material parameters, such as... Figure 4 As shown, step S210 may further include steps S211-S214:
[0090] S211. Construct a geometric model of the self-elevating platform based on geometric parameters.
[0091] In this embodiment, the computing device can perform geometric modeling processing on the self-elevating platform based on the acquired geometric parameters. The geometric parameters may include the external dimensions of the platform body, the length and segmentation information of the pile legs, the cross-sectional dimensions of the pile legs, and the outline shape and dimensions of the pile shoes, etc. By uniformly modeling the above geometric information, a geometric model that can reflect the overall spatial layout and structural composition relationship of the self-elevating platform is formed, thereby providing a basic geometric expression for subsequent finite element analysis.
[0092] S212. Assign material parameters to the geometric model based on the material parameters.
[0093] In this embodiment, the computing device can assign corresponding material properties to each component in the geometric model based on the acquired material parameters. The material parameters may include elastic modulus, Poisson's ratio, and density, so that different structural components can reflect their respective mechanical response characteristics in the subsequent analysis process, thereby ensuring that the finite element model can truly reflect the stiffness and mass distribution of the structure when performing stress calculations.
[0094] S213. The geometric model is discretized into finite element units, and the topological relationship between each finite element unit is established based on the spatial affiliation of the finite element units.
[0095] In this embodiment, the computing device can discretize the geometric model, divide the continuous structure into multiple finite element units, and establish the topological relationship between them according to the connection relationship between each finite element unit in space, so as to clarify the connection method and force transmission path between each unit, thereby forming a discretized structural model that can be used for numerical calculation, providing a computational basis for subsequent stress analysis.
[0096] S214. Construct a finite element model based on finite element elements and topological relationships.
[0097] In this embodiment, the computing device can assemble each finite element unit into a unified finite element model after completing the finite element unit division and topological relationship establishment. This allows each structural part to participate in the stress analysis according to the predetermined connection relationship during the calculation process, thereby constructing a finite element model that can reflect the overall mechanical behavior of the self-elevating platform for subsequent load calculation and analysis.
[0098] S220. Based on the finite element model, determine the initial vertical load at the bottom of the pile legs of the self-elevating platform.
[0099] In this embodiment, the computing device can calculate the transmission of the overall load of the platform to the bottom of the pile legs based on the constructed finite element model, thereby obtaining the initial vertical load at the bottom of the pile legs to reflect the level of the platform's action on the foundation under initial working conditions. Specifically, as shown... Figure 5 As shown, step S220 may further include steps S221-S222:
[0100] S221. Set the bottom constraint of the pile leg in the finite element model to a simply supported constraint that is in initial contact with the seabed surface.
[0101] In this embodiment, the computing device can set the boundary conditions at the bottom of the pile leg based on the constructed finite element model, so that it is in the initial contact state with the seabed surface, that is, the state when the pile leg insertion depth is zero, and simplify this contact state into a simply supported constraint form. Thus, the bottom of the pile leg only bears the reaction force transmitted from the structure during the calculation process without providing additional constraint effects. This establishes an idealized connection relationship between the pile leg and the foundation under the initial working condition, providing a unified boundary condition for subsequent load transfer analysis.
[0102] S222. Apply the design load to the finite element model and perform static analysis based on the finite element model to determine the initial vertical load at the bottom of the pile leg.
[0103] In this embodiment, after the computing device completes the constraint setting at the bottom of the pile legs, it can apply the design load to the finite element model to characterize the platform's operating state, and perform static analysis based on the finite element model to calculate the transmission path and distribution of the overall load of the platform in the structure, thereby obtaining the vertical load borne by the bottom of each pile leg, which serves as the basis for subsequently determining the preload and pile insertion depth.
[0104] S230. Based on the initial vertical load, determine the preload to be applied to the self-elevating platform.
[0105] In this embodiment, the computing device can determine the preload applied to the self-elevating platform based on the initial vertical load at the bottom of the pile legs calculated in step S222, using a preset preload coefficient. Specifically, the preload coefficient can be preset according to the self-elevating platform operation specifications and safety design requirements, for example, a value of 1.2 to 1.5, or selected according to the provisions in relevant design specifications. This ensures that the determined preload can cover or exceed the maximum vertical load effect transmitted to the bottom of the pile legs under the actual working conditions of the platform. The preload can be used as an external load applied to the platform during the subsequent pile driving stage to simulate the compaction effect of the self-elevating platform on the foundation.
[0106] (iii) Determine the pile insertion depth of the self-elevating platform.
[0107] The following describes how to determine the pile insertion depth of a self-elevating platform based on preload and soil bearing capacity data (i.e., step S300). Figure 6 As shown, in one embodiment of the present invention, step S300 may include the following steps S310-S320:
[0108] S310. Obtain the soil bearing capacity curve as a function of depth based on soil bearing capacity data.
[0109] In this embodiment, the computing device can construct a bearing capacity curve of soil bearing capacity as a function of depth based on the soil bearing capacity data obtained in step S100, which is used to reflect the bearing capacity level of the soil at different depths, thereby providing a basis for determining the subsequent pile insertion depth.
[0110] S320. Match the preload with the bearing capacity curve to determine the pile insertion depth of the self-elevating platform.
[0111] In this embodiment, the computing device can search and compare the soil bearing capacity curve based on the preload to determine the location where the soil bearing capacity first reaches or exceeds the preload along the depth direction, and extract the depth corresponding to that location, using this depth as the pile insertion depth of the jack-up platform. In other embodiments of the invention, when there is no discrete point in the bearing capacity curve that perfectly corresponds to the preload, interpolation calculations can be performed using the bearing capacity variation relationship between adjacent depth points to obtain an accurate depth value matching the preload, thereby improving the accuracy of pile insertion depth determination.
[0112] (iv) Determine the stiffness constraint data and the basic bearing capacity data in each direction.
[0113] The following describes how, based on soil properties, structural data, and pile depth at the pile insertion depth, the anisotropic stiffness constraint data and anisotropic basic bearing capacity data of the soil at the pile insertion depth on the pile leg are determined (i.e., step S400). Figure 7 As shown, in one embodiment of the present invention, step S400 may include the following steps S410-S430:
[0114] S410. Based on soil characteristics, determine the soil mechanical parameters at the pile insertion depth.
[0115] In this embodiment, the computing device can analyze the physical and mechanical properties of the foundation soil at the pile depth based on the soil characteristics corresponding to the pile depth, and determine the soil mechanical parameters used to describe the soil stress behavior, such as soil shear modulus, Poisson's ratio, etc., which may include parameters reflecting the soil shear strength characteristics and soil deformation characteristics, thereby providing basic input for subsequent calculation of anisotropic bearing capacity and stiffness constraints.
[0116] S420. Based on soil mechanical parameters and structural data, determine the basic bearing capacity data of the soil on the pile leg at the pile insertion depth in all directions.
[0117] In this embodiment, the basic bearing capacity data in each direction includes the basic bearing capacity of the soil at the pile depth relative to the pile leg in the vertical direction, the basic bearing capacity of the soil relative to the pile leg in the horizontal direction, and the basic bearing capacity of the soil relative to the pile leg in the bending moment direction. The computing device can combine the soil mechanical parameters and structural data to calculate the bearing capacity of the foundation soil at the pile depth under multi-directional stress conditions, determining the basic bearing capacity of the soil in the horizontal, vertical, and bending moment directions respectively. Specifically, taking clay as an example, the formula for calculating the basic bearing capacity of the soil at the pile depth relative to the pile leg in the vertical direction is:
[0118]
[0119] The formula for calculating the basic horizontal bearing capacity of the soil at the pile insertion depth on the pile leg is as follows:
[0120]
[0121] The formula for calculating the basic bearing capacity of the soil at the pile depth to the pile leg in the bending moment direction is:
[0122]
[0123]
[0124] Taking sandy soil as an example, the formula for calculating the basic vertical bearing capacity of the soil at the pile insertion depth on the pile leg is as follows:
[0125]
[0126] The formula for calculating the basic horizontal bearing capacity of the soil at the pile insertion depth on the pile leg is as follows:
[0127]
[0128] The formula for calculating the basic bearing capacity of the soil at the pile depth to the pile leg in the bending moment direction is:
[0129]
[0130] in, This is the bearing capacity depth correction factor. This is the clay cohesion bearing capacity coefficient. For undrained clay shear strength, This is the shape correction factor for load-bearing capacity. The effective overburden pressure at the maximum burial depth corresponding to the maximum bearing area. Let be the equivalent diameter of the pile shoe. This is the correction factor for the horizontal bearing capacity. For depth interpolation parameters, Here, D is a dimensionless parameter, and D is the pile insertion depth. The overload depth coefficient under consolidated drainage conditions. The depth coefficient based on self-weight under consolidated drainage conditions. The effective buoyant weight of the soil, , This is the bearing capacity coefficient of the circular foundation. From this, the basic bearing capacity of the soil at the pile depth on the pile leg in the horizontal, vertical, and bending moment directions can be obtained.
[0131] S430. Based on soil mechanical parameters and pile insertion depth, determine the anisotropic stiffness constraint data of the soil on the pile leg at the pile insertion depth.
[0132] In this embodiment, the stiffness constraint data includes the horizontal stiffness, vertical stiffness, and rotational stiffness of the soil at the pile insertion depth. Specifically, the computing device can further determine the stiffness constraints of the soil at the pile insertion depth in the horizontal, vertical, and rotational directions based on soil mechanical parameters and the influence of pile insertion depth on the soil stress state. Specifically, the horizontal stiffness of the soil at the pile insertion depth is:
[0133]
[0134] The vertical stiffness of the soil at the pile insertion depth is:
[0135]
[0136] The rotational stiffness of the soil at the pile insertion depth is:
[0137]
[0138] in, Let be the equivalent diameter of the pile shoe. The shear modulus of the soil. Poisson's ratio of the soil , , These are the soil stiffness coefficients, which are related to the pile insertion depth and can be obtained through prototype tests, table lookups, etc. Therefore, the anisotropic stiffness constraint data of the soil on the pile leg at the pile insertion depth can be determined.
[0139] (v) Determine the regeneration loads in each direction at the bottom of the pile legs of the self-elevating platform.
[0140] The following describes how to determine the anisotropic updating loads at the bottom of the pile legs of a jack-up platform using a finite element model based on pile depth and anisotropic stiffness constraint data. In this embodiment, the computing device can determine the anisotropic updating loads at the bottom of the pile legs of the jack-up platform using a finite element model based on pile depth and anisotropic stiffness constraint data. Specifically, as... Figure 8As shown, step S500 may include the following steps S510-S520:
[0141] S510. Based on the anisotropic stiffness constraint data, the bottom of the pile leg of the finite element model is modeled as an elastic support, and the bottom of the pile leg of the finite element model is set as a spring constraint.
[0142] In this embodiment, the computing device can import the anisotropic stiffness constraint data obtained in step S400 into the finite element model, and construct the corresponding soil spring stiffness matrix for the degrees of freedom of the bottom nodes of the pile leg. Spring stiffness matrix It can be used to describe the constraint effect of soil on the displacement and rotation of pile legs in various directions; spring stiffness matrix. The calculation formula is:
[0143]
[0144] The soil spring stiffness matrix describes the constraint effect of the soil on the displacement and rotation of the pile legs in the horizontal, vertical, and rotational directions. Further, the computing device can utilize the discretized structural model obtained in step S213 to map the local stiffness of each finite element based on a Boolean mapping matrix, obtaining the structural stiffness matrix of the self-elevating platform. Then, the computing device can assemble the soil spring stiffness matrix into the structural stiffness matrix according to the degree of freedom correspondence of the pile leg bottom nodes, thereby forming a global stiffness matrix K superimposed with the soil spring stiffness. The global stiffness matrix K is composed of the structural stiffness matrix of the self-elevating platform structure itself and the soil spring stiffness matrix, reflecting the overall stiffness characteristics under pile-soil coupling. Thus, the original simply supported constraints at the bottom of the pile legs are replaced with spring constraints with elastic properties, transforming the force response at the bottom of the pile legs in each direction from rigid constraints to displacement-related elastic reaction responses.
[0145] S520. Based on the pile insertion depth, the design load is applied to the finite element model, and static analysis is performed based on the finite element model to determine the updated loads in all directions at the bottom of the pile leg.
[0146] In this embodiment, the updated loads in all directions include the updated loads at the bottom of the pile legs in the horizontal, vertical, and bending moment directions. Specifically, after completing the modeling of the elastic support at the bottom of the pile legs and obtaining the global stiffness matrix K, the computing device can update the finite element model based on the pile insertion depth determined in step S300, and apply the design load P, which characterizes the operating state of the self-elevating platform, to the model. By performing static solutions on the finite element model, the displacement of the overall platform structure under elastic support conditions is obtained, and the calculation process satisfies the structural static equilibrium equations: .
[0147] Where u is the nodal displacement vector. The displacement components of the bottom nodes of the pile leg are determined based on the static equilibrium equations. , and corners Subsequently, the computing device further calculates the soil reaction force at the bottom of the pile leg based on the spring stiffness matrix established in step S510, thereby obtaining the updated loads at the bottom of the pile leg in the horizontal, vertical, and bending moment directions. The relationship can be expressed as follows:
[0148]
[0149] Therefore, the updated load in the horizontal direction at the bottom of the pile leg can be obtained separately. Vertical update load and the updated load in the bending moment direction .
[0150] (vi) Determine whether the soil at the pile depth meets the bearing requirements.
[0151] The following section describes how to determine whether the soil at the pile depth meets the bearing capacity requirements based on basic bearing capacity data and updated loads in all directions. Specifically, as follows... Figure 9 As shown, in one embodiment of the present invention, step S600 may include the following steps S610-S630:
[0152] S610. Based on the basic bearing capacity data and updated loads in all directions, the judgment value used to characterize the pile-soil coupling state is determined using the pre-acquired interaction yield surface function.
[0153] In this embodiment, the computing device can determine a judgment value characterizing the pile-soil coupling state based on the basic bearing capacity data in all directions obtained in step S400 and the updated loads in all directions at the bottom of the pile leg obtained in step S500, using a pre-acquired interaction yield surface function. The interaction yield surface function can be used to characterize the overall bearing capacity of the soil at the pile depth under the combined action of multiple loads. The calculation formula for the interaction yield surface function is:
[0154]
[0155] in, The insertion depth factor is related to the pile insertion depth and soil properties. The calculation device substitutes the anisotropic updated loads and the anisotropic basic bearing capacities into the above-mentioned interactive yield surface function to obtain the corresponding function values as the judgment values.
[0156] S620. If the judgment value is less than the preset threshold, it is determined that the soil at the pile depth meets the bearing requirements.
[0157] In this embodiment, the preset threshold is 0. When the calculated judgment value is less than the preset threshold 0, it indicates that the combination of loads in all directions borne by the bottom of the current pile leg is within the interactive yield surface. That is, the foundation soil still has sufficient bearing margin under the combined action of horizontal, vertical and bending moments and has not reached its ultimate bearing state. Therefore, it can be judged that the soil at the pile insertion depth meets the bearing requirements.
[0158] S630. If the judgment value is greater than or equal to the preset threshold, it is determined that the soil at the pile depth does not meet the bearing requirements, and the update load or pile depth in each direction is iterated until the judgment value is less than the preset threshold.
[0159] In this embodiment, when the judgment value is greater than or equal to the preset threshold 0, it indicates that the current load combination has reached or exceeded the ultimate bearing capacity of the foundation, and the soil bearing capacity is insufficient. At this time, the calculation device can adjust the updated loads or pile depths in each direction and recalculate the judgment value until the judgment value is less than the preset threshold, thereby meeting the bearing requirements. Specifically, as shown in the example... Figure 10 As shown, in one embodiment of the present invention, step S630 may include the following steps S631-S632:
[0160] S631. If the judgment value is greater than the preset threshold, the rotational stiffness is reduced based on the preset reduction rule, and the updated loads in each direction are re-determined based on the pile depth and the stiffness constraint data in each direction after the rotational stiffness is reduced.
[0161] In this embodiment, when the judgment value is greater than the preset threshold 0, it indicates that the current load combination at the bottom of the pile leg has exceeded the ultimate bearing capacity of the foundation soil under multi-directional stress conditions. At this time, the foundation soil's constraint capacity on the pile leg is insufficient. The computing device can adjust the stiffness constraint data of the soil in the rotation direction according to the preset reduction rule. A reduction is performed to decrease the constraint strength at the bottom of the pile leg in the bending moment direction, thereby reflecting the actual mechanical properties of the soil after plastic development. For example, the rotational stiffness can be reduced according to a preset proportional coefficient, so that the rotational stiffness satisfies the following in each iteration:
[0162]
[0163] Where β is a reduction factor less than 1. After reducing the rotational stiffness, the calculation equipment, while keeping the pile depth constant, calculates the stiffness constraint data of the soil in the rotational direction after reduction. Following the above procedure, the elastic support conditions at the bottom of the pile leg are reconstructed, and a static analysis is performed again using a finite element model. The updated loads at the bottom of the pile leg in the horizontal, vertical, and bending moment directions are then substituted into the interaction yield surface function for judgment. If the judgment value is less than a preset threshold, the soil at the pile depth is deemed to meet the bearing requirements. If the judgment value is still greater than the preset threshold, the rotational stiffness is further adjusted according to the reduction rule, and the above process is repeated until the judgment value is less than the preset threshold.
[0164] S632. If the judgment value is equal to the preset threshold, increase the preload based on the preload increase / decrease rules, and redetermine the pile insertion depth of the self-elevating platform based on the increased preload and soil bearing capacity data.
[0165] In this embodiment, if the judgment value is equal to a preset threshold, it indicates the stiffness constraint data of the soil at the pile depth in the rotational direction. If the load-bearing capacity requirement cannot be met even after reduction, it is necessary to further enhance the bearing capacity by increasing the pile driving depth. In this case, the calculation equipment can increase the preload applied to the self-elevating platform according to the preload increase / decrease rules to increase the depth of the pile legs penetrating the soil. For example, the preload can be gradually increased according to a preset increment based on the current preload, ensuring that the preload after each adjustment meets the following requirements:
[0166]
[0167] in, For preload, The preload increment is set. Subsequently, based on the increased preload and the acquired soil bearing capacity data, the pile insertion depth is redetermined, allowing the pile legs to penetrate deeper soil layers with higher bearing capacity. The subsequent steps are repeated based on the new insertion depth to reassess the pile-soil coupling state until the bearing requirements are met.
[0168] In one embodiment of the present invention, the pile-soil coupling analysis method for self-elevating platforms further includes S700-S800:
[0169] S700: Obtain the operating parameters of the self-elevating platform at the pile insertion depth.
[0170] In this embodiment, after determining the pile insertion depth and completing the pile-soil coupling analysis, the computing device further obtains the operating condition parameters of the jack-up platform at the corresponding pile insertion depth. Specifically, the operating condition parameters may include water depth parameters, environmental load parameters, and platform operating load parameters. The water depth parameters are used to characterize the working height range of the pile legs above the seabed, the environmental load parameters are used to characterize the influence of external forces such as wind load, wave load, and current load on the platform structure, and the platform operating load parameters are used to characterize the loads generated during equipment operation and work. This comprehensively reflects the actual stress environment of the jack-up platform under the current pile insertion depth conditions, providing complete input conditions for subsequent pile leg structure verification.
[0171] S800, based on the pile insertion depth, structural data and working condition parameters, performs strength and length checks on the pile leg structure of the self-elevating platform to determine whether the pile leg structure meets the operational requirements.
[0172] In this embodiment, the computing device further performs a comprehensive analysis of the stress state of the pile leg structure under the current operating conditions based on the pile insertion depth and structural data, combined with the operating condition parameters. Specifically, during the strength verification process, the computing device evaluates the stress level of the key sections of the pile leg based on the axial force, bending moment, and their combined effects generated by the pile leg under the operating condition parameters, and compares it with the allowable bearing capacity of the structure to determine whether the pile leg structure meets the strength requirements. During the length verification process, the computing device determines the actual working length of the pile leg under the current operating conditions by combining the pile insertion depth, water depth parameters, and pile leg structural dimensions, and evaluates whether this length can meet the height range and structural stability requirements required for platform operation, thereby determining whether the pile leg has insufficient length or redundancy issues. Through a comprehensive analysis of the strength verification results and the length verification results, it is finally determined whether the pile leg structure meets the operating requirements of the self-elevating platform under the current pile insertion depth and operating conditions. It should be noted that the specific calculation methods and judgment rules for the above strength verification and length verification are all prior art in this field, and will not be elaborated here.
[0173] In summary, the pile-soil coupling analysis method for self-elevating platforms of the present invention acquires structural data and soil bearing capacity data of the self-elevating platform, determines the preload based on the structural data, and then accurately determines the pile insertion depth by combining the soil bearing capacity data. Based on this, according to the soil characteristics, structural data, and pile insertion depth at the pile insertion depth, the anisotropic stiffness constraint data and anisotropic basic bearing capacity data of the soil around the pile on the pile leg are simultaneously determined. Furthermore, based on the pile insertion depth and anisotropic stiffness constraint data, the anisotropic updated load at the bottom of the pile leg is solved, and the anisotropic basic bearing capacity data and anisotropic updated load are used to verify the bearing capacity, determining whether the soil at the pile insertion depth meets the bearing requirements. This avoids safety accidents such as pile leg puncture caused by inaccurate assessments in existing technologies, effectively improving the accuracy and reliability of foundation bearing capacity assessment.
[0174] Secondly, the present invention also provides a pile-soil coupling analysis system for a self-elevating platform, such as... Figure 11 As shown, the pile-soil coupling analysis system 1000 may include:
[0175] The data acquisition module 1100 is used to acquire structural data of the self-elevating platform and soil bearing capacity data;
[0176] The preload determination module 1200 is used to determine the preload to be applied to the self-elevating platform based on structural data.
[0177] The pile driving depth determination module 1300 is used to determine the pile driving depth of the self-elevating platform based on preload and soil bearing capacity data.
[0178] The soil parameter determination module 1400 is used to determine the all-directional stiffness constraint data and all-directional basic bearing capacity data of the soil at the pile depth to the pile leg based on the soil properties, structural data and pile depth at the pile depth.
[0179] The updated load determination module 1500 is used to determine the updated loads in all directions at the bottom of the pile legs of the self-elevating platform based on the pile depth and all-directional stiffness constraint data.
[0180] The bearing capacity judgment module 1600 is used to determine whether the soil at the pile depth meets the bearing requirements based on the basic bearing capacity data and updated loads in each direction.
[0181] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms "an" or "a" and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms "connected" or "linked" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up," "down," "left," "right," etc., are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship also changes accordingly.
[0182] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for pile-soil coupling analysis of a jack-up platform, characterized in that, include: Obtain structural data of the self-elevating platform, as well as soil bearing capacity data; The preload to be applied to the self-elevating platform is determined based on the structural data. Based on the preload and soil bearing capacity data, the pile insertion depth of the self-elevating platform is determined; Based on the soil properties at the pile insertion depth, the soil mechanical parameters at the pile insertion depth are determined. Based on the soil mechanical parameters and the structural data, the basic bearing capacity data of the soil at the pile insertion depth on the pile leg in all directions are determined. Based on the soil mechanical parameters and the pile insertion depth, the stiffness constraint data of the soil at the pile insertion depth on the pile leg in all directions are determined. Based on the pile insertion depth and the anisotropic stiffness constraint data, the anisotropic updated loads at the bottom of the pile legs of the self-elevating platform are determined; Based on the basic bearing capacity data and the updated load in each direction, it is determined whether the soil at the pile depth meets the bearing requirements. The basic bearing capacity data in each direction includes the basic bearing capacity of the soil at the pile insertion depth for the pile leg in the vertical direction, the basic bearing capacity of the soil for the pile leg in the horizontal direction, and the basic bearing capacity of the soil for the pile leg in the bending moment direction. The basic stiffness constraint data in each direction includes the horizontal stiffness, vertical stiffness, and rotational stiffness of the soil at the pile insertion depth. The updated load in each direction includes the updated load at the bottom of the pile leg in the horizontal, vertical, and bending moment directions.
2. The jack-up platform soil coupling analysis method of claim 1, wherein, Based on the structural data, the preload to be applied to the self-elevating platform includes: Based on the structural data, a finite element model is constructed; Based on the finite element model, the initial vertical load at the bottom of the pile legs of the self-elevating platform is determined; Based on the initial vertical load, determine the preload to be applied to the jack-up platform. Furthermore, when determining the anisotropic update load, the anisotropic update load at the bottom of the pile legs of the self-elevating platform is determined by the finite element model based on the pile insertion depth and the anisotropic stiffness constraint data.
3. The jack-up platform soil coupling analysis method of claim 2, wherein, The structural data includes geometric parameters and material parameters. The construction of a finite element model based on the structural data includes: The geometric model of the self-elevating platform is constructed based on the aforementioned geometric parameters; Assign material parameters to the geometric model based on the material parameters; The geometric model is discretized using finite element method to form finite element elements, and the topological relationship between each finite element element is established based on the spatial affiliation of the finite element elements. The finite element model is constructed based on the finite element elements and the topological relationships.
4. The jack-up platform soil coupling analysis method of claim 2, wherein, Based on the finite element model, the initial vertical load at the bottom of the pile legs of the self-elevating platform is determined, including: The bottom constraint of the pile leg in the finite element model is set as a simply supported constraint that is in initial contact with the seabed surface; The design load is applied to the finite element model, and a static analysis is performed based on the finite element model to determine the initial vertical load at the bottom of the pile leg.
5. The pile-soil coupling analysis method for self-elevating platform according to claim 2, characterized in that, Based on the initial vertical load, the preload applied to the self-elevating platform is determined using a preset preload coefficient. The determination of the pile insertion depth of the self-elevating platform based on the preload and soil bearing capacity data includes: Based on the soil carrying capacity data, obtain the soil carrying capacity curve as a function of depth; The preload is matched with the bearing capacity curve to determine the pile insertion depth of the self-elevating platform.
6. The pile-soil coupling analysis method for self-elevating platforms according to claim 2, characterized in that, Based on the pile insertion depth and the anisotropic stiffness constraint data, the updated anisotropic loads at the bottom of the pile legs of the self-elevating platform are determined using the finite element model, including: Based on the anisotropic stiffness constraint data, elastic support modeling is performed on the bottom of the pile leg of the finite element model, and the bottom of the pile leg of the finite element model is set as a spring constraint. Based on the pile insertion depth, design loads are applied to the finite element model, and static analysis is performed based on the finite element model to determine the anisotropic updated loads at the bottom of the pile leg.
7. The pile-soil coupling analysis method for self-elevating platform according to claim 1, characterized in that, Based on the aforementioned basic bearing capacity data and the aforementioned updated loads in each direction, determining whether the soil at the pile depth meets the bearing requirements includes: Based on the basic bearing capacity data and the updated load in each direction, the judgment value used to characterize the pile-soil coupling state is determined using the pre-acquired interaction yield surface function. If the determination value is less than the preset threshold, it is determined that the soil at the pile depth meets the bearing capacity requirements. If the determination value is greater than or equal to a preset threshold, it is determined that the soil at the pile depth does not meet the bearing requirements, and the anisotropic update load or the pile depth is iterated until the determination value is less than the preset threshold.
8. The pile-soil coupling analysis method for self-elevating platform according to claim 7, characterized in that, The anisotropic stiffness constraint data includes rotational stiffness. The step of determining that the soil at the pile depth does not meet the bearing capacity requirements if the determination value is greater than or equal to a preset threshold, and iterating the anisotropic update load or the pile depth until the determination value is less than the preset threshold, includes: If the determination value is greater than the preset threshold, the rotational stiffness is reduced based on the preset reduction rule, and the updated load in each direction is re-determined based on the pile depth and the stiffness constraint data in each direction after reducing the rotational stiffness. If the determination value is equal to the preset threshold, the preload is increased based on the preload increase / decrease rules, and the pile insertion depth of the self-elevating platform is re-determined based on the increased preload and the soil bearing capacity data.
9. The pile-soil coupling analysis method for self-elevating platform according to claim 8, characterized in that, Also includes: Obtain the operating parameters of the self-elevating platform at the pile insertion depth; Based on the pile insertion depth, the structural data, and the operating condition parameters, the strength and length of the pile leg structure of the self-elevating platform are checked to determine whether the pile leg structure meets the operating requirements.
10. A pile-soil coupling analysis system for a self-elevating platform, characterized in that, include: The data acquisition module is used to acquire structural data of the self-elevating platform and soil carrying capacity data; A preload determination module is used to determine the preload to be applied to the self-elevating platform based on the structural data. The pile driving depth determination module is used to determine the pile driving depth of the self-elevating platform based on the preload and the soil bearing capacity data. The soil parameter determination module is used to determine the soil mechanical parameters of the soil at the pile depth based on the soil properties of the soil at the pile depth, determine the basic bearing capacity data of the soil at the pile depth to the pile leg based on the soil mechanical parameters and the structural data, and determine the stiffness constraint data of the soil at the pile depth to the pile leg based on the soil mechanical parameters and the pile depth. The update load determination module is used to determine the updated loads in all directions at the bottom of the pile legs of the self-elevating platform based on the pile insertion depth and the all-directional stiffness constraint data. The bearing capacity judgment module is used to determine whether the soil at the pile depth meets the bearing requirements based on the basic bearing capacity data in each direction and the updated load in each direction. The basic bearing capacity data in each direction includes the basic bearing capacity of the soil at the pile insertion depth for the pile leg in the vertical direction, the basic bearing capacity of the soil for the pile leg in the horizontal direction, and the basic bearing capacity of the soil for the pile leg in the bending moment direction. The basic stiffness constraint data in each direction includes the horizontal stiffness, vertical stiffness, and rotational stiffness of the soil at the pile insertion depth. The updated load in each direction includes the updated load at the bottom of the pile leg in the horizontal, vertical, and bending moment directions.