Pile wall composite anchorage foundation deformation analysis method and system

Abstract

This invention discloses a method and system for deformation analysis of pile-wall composite anchorage foundations, belonging to the technical field of bridge anchorage foundation deformation analysis. The method includes obtaining the geometric parameters, soil-rock layering parameters, and external load parameters of the pile-wall composite foundation; correcting the interface stiffness of the Winkel foundation model based on the mud cake reduction factor to generate corrected foundation parameters; setting the initial displacement vector of the foundation reference point; determining the contact state of the wall-soil interface based on the rigid body displacement mode and the assumption that the soil is not tensile; calculating the horizontal resistance, vertical frictional resistance, and corresponding resisting bending moment of the diaphragm wall end face and sidewalls by piecewise integration according to the contact state; establishing a system of overall equilibrium equations; and solving the actual displacement of the foundation reference point using a numerical method combining incremental loading and the Newton-Raphson iteration method, and outputting the result. This invention can solve the problems of low deformation prediction accuracy and dangerous results caused by neglecting the mud cake gradient weakening effect and the nonlinearity of the wall-soil contact in the prior art.

Description

Technical Field

[0001] This invention belongs to the field of deformation analysis technology for bridge anchorage foundations, and more specifically, relates to a method and system for deformation analysis of pile-wall composite anchorage foundations. Background Technology

[0002] In long-span bridge projects such as suspension bridges, strip-wall diaphragm wall composite foundations (or pile-wall composite anchorage foundations) are widely used due to their excellent load-bearing performance. This type of foundation typically consists of a reinforced concrete cap and multiple parallel diaphragm walls, which resist enormous vertical loads and horizontal cable forces by embedding themselves in deep soil and rock layers.

[0003] However, in actual construction, due to limitations in the trenching process for diaphragm walls, a weak, poorly permeable "mud cake" layer forms between the wall and the surrounding soil. Existing technologies typically have the following shortcomings when performing foundation deformation analysis: Ignoring the nonlinear weakening effect of mud cake: Traditional calculation methods often treat the wall-soil interface as an ideal rigid contact or directly use a fixed friction coefficient for reduction, failing to accurately simulate the gradient weakening effect of mud cake on the foundation resistance (including normal passive earth pressure and tangential friction), resulting in an underestimation of the calculated foundation displacement and potential safety hazards.

[0004] Simplified treatment of contact surface conditions: Under the action of inclined cable force and bending moment, the foundation will rotate, causing the contact state between the front and rear sides of the diaphragm wall and the soil to change (one side is squeezed, the other side is detached). Existing simplified models often assume that the soil around the wall always provides full resistance, which violates the basic mechanical principle that soil is "not tensile", making the calculation results too optimistic.

[0005] Lack of efficient solution algorithms: Analytical solutions are difficult to obtain for complex mechanical models involving clay reduction and nonlinear contact determination. Existing finite element software, while capable of simulation, is computationally expensive, hindering rapid iteration and parameter sensitivity analysis in the engineering design phase.

[0006] Therefore, there is an urgent need for a deformation analysis method for pile-wall composite anchor foundations that can comprehensively consider mud skin effect, wall-soil contact nonlinearity, and differential stiffness of multiple soil layers, so as to improve the accuracy and safety of anchor foundation design for long-span bridges. Summary of the Invention

[0007] To address the problems in existing technologies, such as neglecting the gradient weakening of the force transmission performance of the wall-soil interface due to the weak mud cake formed during trenching construction, and the overly risky prediction of foundation deformation due to simplified treatment of the wall-soil contact surface state, this invention provides a method and system for deformation analysis of pile-wall composite anchor foundations. First, the interface stiffness parameters in the Winkler foundation model are corrected based on the mud cake reduction factor to quantitatively simulate construction defects. Then, based on the rigid body displacement mode and the assumption of soil non-tensile strength, the wall-soil contact state (compression or separation) is dynamically identified by judging the horizontal displacement at each depth of the foundation, and the nonlinear resistance of the end face and sidewalls is calculated by piecewise integration. Finally, a system of overall equilibrium equations is established, and the actual displacement of the foundation is obtained by solving the equations using incremental loading and the Newton-Raphson iterative method. This invention significantly improves the accuracy and reliability of the deformation analysis results of pile-wall composite anchor foundations under large overturning moments by introducing the mud cake reduction factor and the contact separation judgment mechanism, providing a safer quantitative basis for engineering design.

[0008] To achieve the above objectives, one aspect of the present invention provides a deformation analysis method for a pile-wall composite anchor foundation, comprising the following steps: S1: Obtain the geometric parameters, soil and rock layering parameters, and external load parameters of the pile-wall composite foundation; S2: Based on the geometric parameters and soil-rock layering parameters, a Winkel foundation model is established, and the normal subgrade coefficient and tangential shear stiffness coefficient of the wall-soil interface in the Winkel foundation model are reduced according to the preset mud cake reduction coefficient to generate the corrected foundation parameters. S3: Set the initial displacement vector of the basic reference point, calculate the horizontal displacement distribution of the diaphragm wall in the depth direction based on the initial displacement vector and the corrected foundation parameters, and determine the contact state of the wall-soil contact surface based on the assumption that the soil is not tensile. S4: Based on the contact state determination result, the horizontal resistance, vertical frictional resistance and the resisting bending moment of the diaphragm wall end face, side wall and bottom are calculated by segmenting and integrating the reaction force micro-elements of the diaphragm wall end face, side wall and bottom of the wall. S5: Establish a set of overall equilibrium equations that include horizontal force balance, vertical force balance and moment balance, and use a numerical algorithm that combines incremental loading and Newton-Raphson iteration method to solve for displacement increment by constructing Jacobian matrix until residual convergence, and obtain the actual displacement of the foundation reference point. S6: The actual displacement and corresponding deformation analysis results obtained from the solution are formatted and output, and the resistance sharing ratio provided by each soil layer to the foundation is further calculated. Based on the resistance sharing ratio, the stability of the pile-wall composite anchor foundation under different load conditions is evaluated.

[0009] Furthermore, the geometric parameters in step S1 include the pile cap parameters, diaphragm wall parameters, and soil layer thickness; Foundation parameters: including foundation length ,width ,high Diaphragm wall parameters: including diaphragm wall length ,width Soil layer thickness: Cohesive soil layer thickness Thickness of strongly weathered rock layers Thickness of moderately weathered rock layers ; The layered parameters of the soil and rock mass include the subgrade coefficient and the wall base stiffness; the subgrade coefficient includes the passive subgrade coefficient of each soil layer. Horizontal shear stiffness of sidewalls Vertical shear stiffness of sidewalls The wall base stiffness includes the horizontal stiffness of the bottom surface of the moderately weathered rock layer. and vertical stiffness ; External load parameters include top cable force Angle between the cable tension and the horizontal plane Structural self-weight Initial bending moment .

[0010] Furthermore, in step S2, the Winkler foundation model expression is: in, For the foundation reaction force; The subgrade coefficient is further subdivided according to the direction of force: [The rest of the text is incomplete and requires further context.] normal subgrade coefficient at the end face of the soil layer , No. Horizontal shear stiffness of the sidewalls of the soil layer , No. Vertical shear stiffness of the sidewalls of the soil layer ; The relative displacement at that point is based on the body displacement assumption; under the assumption of rigid body displacement, the horizontal displacement... and vertical displacement This is the displacement that triggers the foundation reaction force.

[0011] Furthermore, the corrected first step in step S2 normal subgrade coefficient at the end face of the soil layer Horizontal shear stiffness of sidewalls Vertical shear stiffness of sidewalls The expressions are as follows: , in, This is the mud skin reduction factor.

[0012] Furthermore, the initial displacement vector mentioned in step S3 includes the horizontal displacement, vertical settlement, and foundation rotation of the reference point; Horizontal displacement of diaphragm wall in the depth direction The calculation formula is: in, Stiffness-weighted reference depth; For reference depth Horizontal displacement at the location; The depth of the current calculation point; Based on the corner.

[0013] Furthermore, in step S3, the state of the wall-soil contact surface is determined by the horizontal displacement of the diaphragm wall in the depth direction. Decision; the judgment rule is: when At that time, it is determined that the front wall end face of the diaphragm wall at that depth is under compression with the soil, activating the horizontal passive thrust and vertical frictional resistance in that area; when At that depth, it is determined that the end face of the diaphragm wall at that depth is under compression with the soil, thus activating the normal passive earth pressure and vertical frictional resistance in that area. when When the wall moves away from the soil at that depth, the soil is separated, and the normal resistance and vertical frictional resistance fail simultaneously.

[0014] Further, step S4 includes: For the front wall, when At that time, calculate its horizontal passive thrust. and vertical frictional resistance Horizontal passive thrust The expression is: ; By horizontal passive thrust The generated resisting bending moment The expression is: ; Vertical frictional resistance The expression is: ; Vertical frictional resistance The generated resisting bending moment The expression is: ; For the back wall, when At that time, calculate its horizontal passive thrust. and vertical frictional resistance ; Horizontal passive thrust The expression is: ; By horizontal passive thrust The generated resisting bending moment The expression is: ; Vertical frictional resistance The expression is: ; Vertical frictional resistance The generated resisting bending moment The expression is: ; Calculate the lateral horizontal frictional resistance of the two side walls of the diaphragm wall. and lateral and vertical frictional resistance Lateral horizontal frictional resistance The expression is: ; Lateral horizontal friction The generated resisting bending moment The expression is: ; Lateral and vertical frictional resistance The expression is: ; Lateral and vertical frictional resistance The expression for the resisting overturning moment is: .

[0015] Furthermore, the equilibrium equations in step S5 include the horizontal force equilibrium equations: , The horizontal passive thrust at the front wall end face; The horizontal passive thrust at the rear wall end face; The horizontal frictional resistance of the two side walls; This refers to the horizontal friction force at the bottom of the wall. For the top cable force Horizontal component of force; Vertical force equilibrium equations: , The vertical frictional resistance of the front wall end face; The vertical frictional resistance of the rear wall end face; The vertical frictional resistance of the two side walls; This is the vertical reaction force at the base of the wall; For the top cable force The vertical component of the force; For structural transverse load; Moment equilibrium equation: These are the torques generated by the horizontal force; These are the torques generated by the vertical force; These are the torques generated by the horizontal frictional force and the vertical reaction force at the bottom of the wall, respectively. This is the external equivalent bending moment.

[0016] Further, step S5 includes: Based on the resistances and moments calculated in step S4, a three-dimensional residual equation is constructed that includes horizontal force balance, vertical force balance, and moment balance. ; External load The loading process is divided into several smaller loading steps, gradually increasing from 0 to the target load; each step uses the converged solution of the previous step as the initial value. Within each loading step, based on the current displacement vector Calculate the three residuals of the equilibrium equation. ; This is an unbalanced force in the horizontal direction; This is an unbalanced force in the vertical direction; To circumvent the reference point Unbalanced overturning moment force; The partial derivatives of the residuals with respect to displacement are calculated using the central difference method, forming the Jacobian matrix. ; Solving the linear equations using the Gauss-Jordan elimination method To obtain the displacement increment ; ,in, The displacement increment of the base reference point in the horizontal direction; This represents the vertical displacement increment of the base reference point; This represents the increment of the base's rotation angle about an axis perpendicular to the ground. For the residual vector, ; Displacement increment Adding it to the old displacement vector yields a new displacement vector that more closely approximates the true equilibrium state. The expression is: ; Check the norm of the residual vector Is it less than the preset convergence threshold? If it is, then the current loading step is considered converged; otherwise, use a new displacement vector. Recalculate the residuals And continue iterating; Once all loading steps are complete and the residuals converge, the final displacement vector is output. This refers to the actual displacement of the pile-wall composite anchor foundation.

[0017] A second aspect of the present invention provides a deformation analysis system for a pile-wall composite anchor foundation, used to implement the aforementioned deformation analysis method for a pile-wall composite anchor foundation, comprising: The parameter acquisition module is used to acquire the geometric parameters, soil and rock layering parameters, and external load parameters of the pile-wall composite foundation. The model construction and correction module is used to build a Winkel foundation model based on the geometric parameters and soil-rock layering parameters, and to reduce the normal subgrade coefficient and tangential shear stiffness coefficient of the wall-soil interface in the Winkel foundation model according to the preset mud cake reduction coefficient, so as to generate the corrected foundation parameters. The contact state determination module is used to set the initial displacement vector of the foundation reference point, calculate the horizontal displacement distribution of the diaphragm wall in the depth direction based on the initial displacement vector and the corrected foundation parameters, and determine the contact state of the wall-soil contact surface based on the assumption that the soil is not tensile. The resistance calculation module is used to calculate the horizontal resistance, vertical frictional resistance and resisting bending moment of the diaphragm wall end face and side wall based on the contact state determination result by performing piecewise integration on the reaction force micro-elements of the diaphragm wall end face, side wall and bottom wall. The equilibrium equation construction and iterative solution module is used to establish a set of overall equilibrium equations that include horizontal force equilibrium, vertical force equilibrium, and moment equilibrium. It adopts a numerical algorithm that combines incremental loading and the Newton-Raphson iterative method to solve for the displacement increment by constructing the Jacobian matrix until the residual converges, and obtains the actual displacement of the foundation reference point. The resistance inversion and safety assessment module is used to output the actual displacement and corresponding deformation analysis results obtained from the solution in a formatted manner, and further calculate the resistance sharing ratio provided by each soil layer to the foundation. Based on the resistance sharing ratio, the stability of the pile-wall composite anchor foundation under different load conditions is evaluated.

[0018] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: (1) This invention corrects the normal subgrade coefficient and tangential shear stiffness of the wall-soil interface by introducing a mud cake reduction factor, and quantitatively simulates the gradient weakening effect of the weak mud cake generated during trenching construction on the interface force transmission performance. Compared with the simplified treatment of treating the wall-soil interface as an ideal rigid contact or using a fixed friction coefficient reduction method in traditional methods, this invention can more realistically reflect the mechanical behavior of the pile-wall composite anchor foundation under actual construction conditions, thereby effectively avoiding the problem of dangerous calculation results caused by overestimating the foundation resistance, and providing more accurate data support for engineering design.

[0019] (2) Based on the fundamental mechanical assumption that "soil is not tensile," this invention dynamically identifies the state (compression or separation) of the wall-soil contact surface by determining the horizontal displacement at any depth of the foundation. This method overcomes the shortcomings of existing simplified models that often assume the surrounding soil always provides full resistance. Especially under large overturning moments, it can accurately simulate the nonlinear characteristics of the wall separating from the soil at the rear and being compressed at the front, preventing safety hazards caused by incorrectly calculating the virtual resistance in the separation zone and ensuring the accuracy of the stability assessment results of the foundation under complex load conditions.

[0020] (3) This invention employs a numerical solution strategy combining incremental loading and the Newton-Raphson iterative method, efficiently solving the nonlinear equilibrium equations by constructing the Jacobian matrix and using Gaussian elimination. This method, while ensuring computational accuracy, avoids relying on expensive and time-consuming commercial finite element software for large-scale mesh generation and computation, enabling rapid parameter sensitivity analysis and iterative optimization during the design phase. Simultaneously, by setting a stiffness-weighted reference depth, the automatic adjustment of the force balance mechanism is ensured, enhancing the stability and robustness of the algorithm under different reference frame selections. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating a method for analyzing the deformation of a pile-wall composite anchor foundation according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the Newton-Raphson iteration process in a deformation analysis method for a pile-wall composite anchor foundation according to an embodiment of the present invention. Figure 3 This is a structural schematic diagram of a pile-wall composite anchor foundation deformation analysis system according to an embodiment of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0023] like Figure 1 As shown, one aspect of the present invention provides a method for deformation analysis of a pile-wall composite anchor foundation, comprising the following steps: S1: Obtain the geometric parameters, soil and rock layering parameters, and external load parameters of the pile-wall composite foundation; S2: Based on the geometric parameters and soil-rock layering parameters, a Winkel foundation model is established, and the normal subgrade coefficient and tangential shear stiffness coefficient of the wall-soil interface in the Winkel foundation model are reduced according to the preset mud cake reduction coefficient to generate the corrected foundation parameters, thereby quantifying the weakening effect of mud cake effect on the interface force transmission performance during construction. S3: Set the initial displacement vector of the foundation reference point, which includes the horizontal displacement, vertical settlement and foundation rotation of the reference point; calculate the horizontal displacement distribution of the diaphragm wall in the depth direction based on the initial displacement vector and the corrected foundation parameters, and determine the contact state of the wall-soil interface based on the assumption that the soil is not tensile, so as to accurately remove the soil area that fails due to tension when calculating the resistance. S4: Based on the contact state determination result, the horizontal resistance, vertical frictional resistance and the resisting bending moment of the diaphragm wall end face, side wall and bottom are calculated by segmenting and integrating the reaction force micro-elements of the diaphragm wall end face, side wall and bottom of the wall. S5: Establish a set of overall equilibrium equations that include horizontal force balance, vertical force balance and moment balance, and use a numerical algorithm that combines incremental loading and Newton-Raphson iteration method to solve for displacement increment by constructing Jacobian matrix until residual convergence, and obtain the actual displacement of the foundation reference point. S6: The actual displacement and corresponding deformation analysis results obtained from the solution are formatted and output, and the resistance sharing ratio provided by each soil layer to the foundation is further calculated. Based on the resistance sharing ratio, the stability of the pile-wall composite anchor foundation under different load conditions is evaluated.

[0024] The steps of the method of the present invention will be described in detail below.

[0025] (1) Obtain the geometric parameters, soil and rock layering parameters, and external load parameters of the pile-wall composite foundation. The pile-wall composite anchor foundation described in step S1 includes a pile cap and multiple parallel underground continuous walls; The geometric parameters include the pile cap parameters, diaphragm wall parameters, and soil layer thickness; Foundation parameters: including foundation length ,width ,high Diaphragm wall parameters: including diaphragm wall length (Up the bridge direction), width (Transverse direction); Soil layer thickness: Cohesive soil layer thickness Thickness of strongly weathered rock layers Thickness of moderately weathered rock layers ; This allows us to determine the depth of the wall base. ; The layered parameters of the soil and rock mass include the subgrade coefficient and the wall base stiffness; the subgrade coefficient includes the stiffness of each soil layer ( The passive bed coefficient (End face normal stiffness), side wall horizontal shear stiffness Vertical shear stiffness of sidewalls The wall base stiffness includes the horizontal stiffness of the bottom surface of the moderately weathered rock layer. and vertical stiffness (kN / m) 3 ); Support stiffness of the bottom surface of moderately weathered rock layer (without reduction); External load parameters include top cable force (Initial total tension acting on the center of the top surface of the pier, unit: kN), Angle between cable force and the horizontal plane (Unit: °) , Structural self-weight (Total weight of foundation and vertical load above, in kN) Initial bending moment (Initial concentrated bending moment acting on the top surface of the foundation, in kN·m); (2) Establish the Winkler foundation model and perform mud cake reduction Step S2 specifically includes: Obtain the original passive subgrade coefficient, original horizontal shear stiffness of the sidewall, and original vertical shear stiffness of the sidewall for each soil and rock layer; Multiply the original passive subgrade coefficient, the original horizontal shear stiffness of the sidewall, and the original vertical shear stiffness of the sidewall by the mud cake reduction factor to obtain the corrected passive subgrade coefficient, the corrected horizontal shear stiffness of the sidewall, and the corrected vertical shear stiffness of the sidewall. The mud cake reduction factor ranges from 0.6 to 0.9. In step S2, it is assumed that the foundation is a series of independent springs (Winkler model), and the foundation reaction force is proportional to the relative displacement at that point; The Winkler foundation model expression is: in, Ground reaction force (or spring force) represents the resistance provided by the foundation per unit area (the unit is usually 1000 liters). ); The subgrade stiffness coefficient (or foundation stiffness coefficient) is a parameter reflecting the softness or hardness of the foundation soil (the unit is usually 1000 ppm). Based on the different directions of the force, it is further subdivided into: the first normal subgrade coefficient at the end face of the soil layer (Resisting wall-end compression); the first Horizontal shear stiffness of the sidewalls of the soil layer (Resisting lateral slippage); the first Vertical shear stiffness of the sidewalls of the soil layer (Resisting vertical settlement); The relative displacement at that point (unit: Under the assumption of rigid body displacement, horizontal displacement and vertical displacement This is the displacement that triggers the foundation reaction force; Since the weak "mud cake" formed during trenching construction weakens the force transmission performance of the wall-soil interface, a mud cake reduction factor needs to be introduced. The interface stiffness is reduced to obtain the corrected first... normal subgrade coefficient at the end face of the soil layer Horizontal shear stiffness of sidewalls Vertical shear stiffness of sidewalls (Unit: kN / m3); the expressions are as follows: , (3) Set the displacement vector and calculate the horizontal displacement distribution to determine the contact state. Step S3, based on the rigid body assumption, defines the deformation mode of the foundation and determines the wall-soil contact state according to the principle that "soil is not tensile". The basic assumptions include: Rigid body assumption: The foundation and the diaphragm wall have extremely high rigidity and do not undergo bending deformation; Winkler foundation model: The foundation reaction force is proportional to the relative displacement at that point, and different soil layers are assigned different subgrade coefficients; Assumption that soil has no tensile strength: Normal and vertical resistance are generated only when the end face compresses the soil; the resistance is recorded as 0 when detached. The contribution of the soil at the bottom and around the foundation to the resistance of the foundation is ignored; Establish coordinate system and displacement mode: Coordinate system: The origin is the center of the top surface of the foundation ( ); The axis runs along the bridge direction (rightward is positive); The axis is along the depth direction (downward is positive); Displacement mode: The foundation is treated as a rigid body, and its deformation in the plane is determined by three independent variables: For the structure at the reference depth Horizontal displacement at the location (positive to the right, unit: m); Vertical settlement at the central axis of the structure (downward is positive, unit: m); For the structure around The rotation angle of the axis (clockwise is positive, unit: rad); To accurately calculate the overturning moment, the stiffness-weighted depth of the foundation's horizontal resistance is defined. As a reference point (center of curvature) for calculating the rotation angle: in, Stiffness-weighted reference depth (unit: ), that is, the depth of the center of rotation; For the first Soil layer thickness (unit: ); For the first Geometric center depth of soil layer (unit: ); This represents the total depth of the wall base. (unit: ); The formula for horizontal displacement distribution in the depth direction is based on rigid body kinematics, for any depth of the foundation. Horizontal displacement at the location Determined by the displacement vector: in, For reference depth Horizontal displacement at the location; The depth of the current calculation point (unit: ); Basic corner; Stress and mud skin effect analysis: When the foundation cap bears an external load, the foundation deforms within the soil. The mechanism by which it resists the external load is as follows: End face compression and friction: When the wall moves towards the soil (compression zone), the soil provides normal passive earth pressure and vertical friction; when the wall moves away from the soil (tension zone), due to soil separation, the normal resistance and vertical friction fail simultaneously. Sidewall shear: The two sidewalls of the diaphragm wall slip relative to each other in the rock and soil mass, generating horizontal and vertical frictional resistance to resist the translation and overturning of the foundation; Mud cake effect: The mud cake generated during trenching construction reduces the force transmission performance of the wall-soil interface, which is reflected in the calculation as a proportional reduction of the interface stiffness parameter. The state of the wall-soil contact surface is determined by horizontal displacement. Decision; the judgment rule is: Pressure zone (contact): When At that time, it is determined that the front wall end face of the diaphragm wall at that depth is under compression with the soil, activating the horizontal passive thrust (normal passive earth pressure) and vertical frictional resistance in that area; when At that depth, it is determined that the end face of the diaphragm wall at that depth is under compression with the soil, thus activating the normal passive earth pressure and vertical frictional resistance in that area. Pull zone (detachment): when When the wall moves away from the soil at that depth, the soil detaches, and the normal resistance and vertical frictional resistance fail simultaneously (i.e., the resistance is 0). This decision rule directly determines the valid range of the integration domain in the subsequent step S4: only within >0 (front wall) or Integral calculations are performed within the interval of (the back wall); Step S2 corrects the stiffness parameters of the foundation model by introducing a mud cake reduction factor and calculates the reference point depth for moment balance. Step S3 calculates the horizontal displacement at any depth based on the corrected parameters and rigid body displacement mode, and dynamically determines the wall-soil contact state (compression or separation) according to the principle that "soil is not tensile", providing boundary conditions for subsequent resistance integration. (4) Calculate resistance and bending moment by piecewise integration Along the wall height from to Perform integration; based on the horizontal displacement at that depth Determine the contact status; if the contact is broken, the area is not included in the integration calculation. For the front wall, when At that time, calculate its horizontal passive thrust. and vertical frictional resistance ; Horizontal passive thrust on micro-element segment The expression is: ; This is the corrected normal subgrade coefficient for the wall-soil interface; For depth coordinates; The width of the diaphragm wall; Integral resultant force: By horizontal passive thrust The generated resisting bending moment The expression is: ; The stiffness-weighted depth of the basic horizontal resistance (i.e., the reference point / momentum depth when calculating the overturning moment). Total vertical frictional resistance of the front end face of the diaphragm wall The expression is: The expression for the vertical frictional resistance on the infinitesimal segment is: ; The corrected vertical shear stiffness of the wall-soil interface; Integral resultant force: ; The length of the diaphragm wall; For lever arm; Vertical frictional resistance The generated resisting bending moment The expression is: ; Under compression, the front side of the diaphragm wall provides not only horizontal thrust but also vertical frictional force. The magnitude of the vertical frictional force depends on the relative displacement caused by both vertical settlement and foundation rotation. By integrating along the wall height, the distributed force is transformed into a resultant force and a resultant moment. For the back wall, when At that time, calculate its horizontal passive thrust. and vertical frictional resistance ; The expression for the horizontal passive thrust on the infinitesimal segment is: Integral resultant force: By horizontal passive thrust The generated resisting bending moment The expression is: Vertical frictional resistance of the rear wall end face of the diaphragm wall The expression is: The expression for the vertical frictional resistance on the infinitesimal segment is: ; Integral resultant force: Vertical frictional resistance The expression for the resisting bending moment is: The lever arm is ; The two side walls of the diaphragm wall remain in contact with the foundation soil at all times, exerting resistance across the entire cross section, with no reduction due to separation; calculate the lateral horizontal skin friction of the two side walls of the diaphragm wall. and lateral and vertical frictional resistance ; The expression for the horizontal frictional resistance on the infinitesimal segment is: ; The corrected horizontal shear stiffness of the wall-soil interface; Integral resultant force: Lateral horizontal friction The generated resisting bending moment The expression is: ; Lateral vertical frictional resistance of the two side walls of the diaphragm wall The expression is: Lateral and vertical frictional resistance The expression for the resisting overturning moment is: The displacement at the base of the diaphragm wall induces elastic support resistance in the weathered rock layer of the foundation, which is the reaction force of the foundation at the base of the wall. This reaction force is directly expressed as a resultant force and moment without depth integration. The horizontal skin friction at the base of the diaphragm wall is then calculated. and vertical reaction force ; The expression for the horizontal frictional resistance generated at the bottom (foundation) of the diaphragm wall is: ; The horizontal subgrade coefficient (horizontal stiffness of moderately weathered rock strata) is given at the base of the wall, in kN / m. 3 ; Additional horizontal bending moment generated by horizontal friction at the bottom of the diaphragm wall The expression is: ; Vertical reaction force generated at the base of the wall (foundation) The expression is: ; This is the vertical subgrade coefficient of the foundation at the base of the wall (vertical stiffness of moderately weathered rock strata). The overturning moment generated by the vertical reaction force at the bottom of the diaphragm wall The expression is: ; When the foundation rotates At that time, the vertical reaction force at the bottom is unevenly distributed, thus generating a bending moment that resists rotation inside the foundation; The horizontal reaction force of the base is related to the horizontal displacement and rotation angle, generating horizontal friction and additional bending moment; The vertical reaction force of the foundation is related to the vertical settlement, and at the same time, it generates a bending moment to resist overturning through the elastic deformation (moment of inertia) of the foundation. The wall base stiffness is not reduced by mud skin because the mud skin effect only exists at the wall-soil interface, while the wall base is in direct contact with the rock strata.

[0026] (5) Establish a system of equilibrium equations and solve iteratively. Based on the resistances and moments calculated in step S4, a three-dimensional residual equation is constructed that includes horizontal force balance, vertical force balance, and moment balance. This system of equations describes the static equilibrium relationship between external loads and foundation resistance, where the residual vector... Includes unbalanced forces in the horizontal direction Vertical unbalanced force and the unbalanced overturning moment about the reference point ; External load directed to the reference point After equivalent translation, the external horizontal force is: External vertical force: External equivalent bending moment: ; The foundation of the diaphragm wall must satisfy static equilibrium in three directions: horizontal, vertical and angular. We transform these three equilibrium equations into residual functions, and the solution process is the process of making the residuals approach zero. Horizontal force equilibrium equations ( The expression is: The sum of all horizontal soil resistance forces (front wall, rear wall, side walls, and wall base) must be equal to the external horizontal load. cancel each other out; The horizontal passive thrust at the front wall end face; The horizontal passive thrust at the rear wall end face; The horizontal frictional resistance of the two side walls; This refers to the horizontal friction force at the bottom of the wall. For the top cable force Horizontal component of force; Vertical force equilibrium equations ( The expression is: The sum of all vertical soil resistance forces (end-face friction, side-wall friction, and wall base reaction) must be equal to the effective vertical load of the structure (self-weight). Subtract the upward vertical component of the cable force Phase equilibrium; The vertical frictional resistance of the front wall end face; The vertical frictional resistance of the rear wall end face; The vertical frictional resistance of the two side walls; This is the vertical reaction force at the base of the wall; For the top cable force The vertical component of the force; For structural transverse loads (foundation self-weight and superstructure loads). Moment balance equations ( ,right The expression for (taking the moment) is: All resistance components relative to the reference point The sum of the resisting moment generated and the overturning moment generated by the external load is zero; They are respectively caused by horizontal force ( The torque generated by (class); They are respectively caused by vertical force ( The torque generated by (class); These are the torques generated by the horizontal frictional force and the vertical reaction force at the bottom of the wall, respectively. External equivalent bending moment (including initial bending moment) and horizontal force right (torque) Furthermore, due to the dynamic changes in the wall-soil contact state (detachment or compression), the above equations are nonlinear, and are solved by combining incremental loading with the Newton-Raphson iterative method. Incremental loading: To improve the convergence of nonlinear problems, the external load is... The loading is divided into several progressively increasing loading steps, gradually increasing from 0 to the target load; each load increment is based on the displacement solution after the previous load convergence as the initial value, gradually approximating the target load condition to ensure the convergence of calculations under large loads. Newton-Raphson iteration: Within each loading step, perform the following sub-steps until convergence (e.g.) Figure 2 (as shown) S51: Calculate the current residual based on the current displacement vector. Calculate the three residuals of the above equilibrium equation. ; S52: Construct the Jacobian matrix, and use the central difference method to calculate the partial derivatives of the residuals with respect to the displacement to form the Jacobian matrix. The Jacobian matrix is ​​the derivative matrix of the residual vector with respect to the displacement vector; in engineering mechanics, it approximately represents the tangent stiffness characteristic of the system; it describes "how the unbalanced force changes with small changes in displacement"; each element in the matrix is ​​a partial derivative; the Jacobian matrix... The expression is: This matrix reflects the degree to which small changes in displacement affect the equilibrium residual; For the structure at the reference depth Horizontal displacement at the location (positive to the right, unit: m); Vertical settlement at the central axis of the structure (downward is positive, unit: m); For the structure around The rotation angle of the axis (clockwise is positive, unit: rad); Indicates horizontal displacement Changes in horizontal unbalanced force The impact; Indicates horizontal displacement The change in the vertical unbalanced force The impact; Indicates horizontal displacement Changes around the reference point Unbalanced overturning moment The impact; Indicates vertical settlement Changes in horizontal unbalanced force The impact; Indicates vertical settlement The change in the vertical unbalanced force The impact; Indicates vertical settlement Changes around the reference point Unbalanced overturning moment The impact; Indicates the basic rotation angle Changes in horizontal unbalanced force The impact; Indicates the basic rotation angle The change in the vertical unbalanced force The impact; Indicates the basic rotation angle Changes around the reference point Unbalanced overturning moment The impact; S53: Solving linear equations using the Gauss-Jordan elimination method Obtain the displacement increment vector ; This represents the displacement increment; The basic reference point (usually the center of rotation) In the horizontal direction ( The displacement increment of the axis; This indicates that the base reference point is in the vertical direction ( The displacement increment (settlement or bulge) of the shaft. This represents the increment of the base's rotation angle (rotation amount) around an axis perpendicular to the ground. For the residual vector, At the current stiffness ( Under what conditions should the required step size be? Only then can the current unbalanced force be just offset. ); S54: Update Displacement: Add the newly calculated "correction step size" to the old displacement to obtain a new displacement that is closer to the true equilibrium state; the expression is: For the new displacement vector; This is the old displacement vector (i.e., the displacement used when calculating the residual in step S1). S55: Convergence determination, calculate the new displacement vector. Then, check the norm of the residual vector. Is it less than the preset convergence threshold? If it is, then the current loading step is considered converged; otherwise, return to step S51 with a new displacement vector. Recalculate the residuals And continue iterating; The final output, after all loading steps are completed and the residuals converge, is the final displacement vector. This refers to the actual displacement of the pile-wall composite anchor foundation.

[0027] (6) Output the actual displacement and corresponding deformation analysis results, back-calculate the resistance sharing ratio of each soil and rock layer, and conduct a stability assessment. Summarize the resistance values ​​obtained after the convergence of the Newton-Raphson iteration (already calculated in S5); let the total resistance vector be... Its components include horizontal force With vertical force Total resistance expression: Resistance sharing ratio calculation: Define the proportion (i.e., the sharing ratio) of each component (end face, side wall, wall base) in the total resistance; taking the horizontal direction as an example: End face horizontal resistance sharing ratio: Sidewall horizontal resistance sharing ratio: Horizontal resistance sharing ratio at the base of the wall: Similarly, the vertical resistance sharing ratio of the end face can be calculated. Vertical resistance sharing ratio of sidewalls Vertical resistance sharing ratio at the base of the wall ; Based on the back-calculated sharing ratio and displacement results, a stability evaluation function is constructed, including: Safety Margin Assessment: Stability can be assessed by calculating the resistance reserve factor or load level factor; let the maximum allowable displacement threshold be... The calculated actual displacement is Displacement safety factor The expression is: ;like If so, it is assumed that the foundation meets the deformation stability requirements under the current load conditions.

[0028] This invention first obtains the geometric parameters, soil-rock layering parameters, and external load parameters of the pile-wall composite foundation. Second, it establishes a Winkler foundation model and reduces the normal subgrade coefficient and tangential shear stiffness coefficient of the wall-soil interface according to a preset mud cake reduction factor, generating corrected foundation parameters. Next, it sets the initial displacement vector of the foundation reference point, calculates the horizontal displacement distribution of the diaphragm wall in the depth direction based on the rigid body displacement mode and the assumption that the soil is not tensile, and determines the contact state of the wall-soil interface. Then, it calculates the horizontal resistance, vertical frictional resistance, and corresponding resisting bending moment of the diaphragm wall end face and sidewalls by piecewise integration based on the contact state. Finally, it establishes a system of overall equilibrium equations including horizontal force balance, vertical force balance, and moment balance, and solves the equations using a numerical method combining incremental loading and the Newton-Raphson iteration method to obtain and output the actual displacement of the foundation reference point. This invention quantifies construction defects by introducing a mud cake reduction coefficient and combining it with a dynamic contact separation judgment mechanism. This solves the problems of low deformation prediction accuracy and dangerous results caused by neglecting the mud cake gradient weakening effect and wall-soil contact nonlinearity in the prior art. It significantly improves the deformation analysis accuracy and engineering design safety of pile-wall composite anchor foundations under large overturning bending moments.

[0029] like Figure 3 As shown, a second aspect of the present invention provides a deformation analysis system for a pile-wall composite anchor foundation, used to implement the above-mentioned analysis method, comprising: The parameter acquisition module is used to acquire the geometric parameters of the pile-wall composite foundation (including the dimensions of the pile cap and diaphragm wall, and the thickness of each soil layer), the layered parameters of the soil and rock mass (including the subgrade coefficient and shear stiffness of each soil layer), and the external load parameters (including the magnitude and angle of the cable force, the self-weight of the structure, and the initial bending moment), providing a basic data source for subsequent mechanical modeling. The model construction and correction module is used to establish a Winkel foundation model based on the geometric parameters and soil-rock layering parameters, and to reduce the normal subgrade coefficient and tangential shear stiffness coefficient of the wall-soil interface in the Winkel foundation model according to the preset mud cake reduction coefficient, thereby generating corrected foundation parameters, and thus quantifying the weakening effect of mud cake effect on interface force transmission performance during construction. The contact state determination module is used to set the initial displacement vector of the foundation reference point, calculate the horizontal displacement distribution of the diaphragm wall in the depth direction based on the initial displacement vector and the corrected foundation parameters, and determine the contact state of the wall-soil contact surface based on the assumption that the soil is not tensile, so as to accurately eliminate soil areas that fail due to tension when calculating resistance; the displacement vector includes the horizontal displacement of the reference point, vertical settlement and foundation rotation angle; The resistance calculation module is used to calculate the horizontal resistance, vertical frictional resistance and resisting bending moment of the diaphragm wall end face and side wall based on the contact state determination result by performing piecewise integration on the reaction force micro-elements of the diaphragm wall end face, side wall and bottom wall, thereby quantifying the constraint effect of the foundation soil on the foundation deformation. The equilibrium equation construction and iterative solution module is used to establish a complete set of equilibrium equations including horizontal force equilibrium, vertical force equilibrium, and moment equilibrium. It employs a numerical algorithm combining incremental loading and the Newton-Raphson iterative method to solve for the displacement increment by constructing the Jacobian matrix until the residual converges, thus obtaining the actual displacement of the foundation reference point. The iterative solution module is specifically configured as follows: Execute an incremental loading loop to apply the external load in multiple loading steps; Within each loading step, Newton-Raphson iteration is performed, the Jacobian matrix is ​​constructed through numerical difference, and the displacement increment is solved using Gaussian elimination until the residual converges. The resistance inversion and safety assessment module is used to output the actual displacement and corresponding deformation analysis results obtained from the solution in a formatted manner, and further calculate the resistance sharing ratio provided by each soil layer to the foundation. Based on the resistance sharing ratio, the stability of the pile-wall composite anchor foundation under different load conditions is evaluated, providing a quantitative basis for the design and stability assessment of the pile-wall composite anchor foundation.

[0030] It should be noted that the pile-wall composite anchor foundation deformation analysis system provided in this embodiment can be a computer program (including program code) running on a computer device. For example, the pile-wall composite anchor foundation deformation analysis system is an application software; the pile-wall composite anchor foundation deformation analysis system can be used to execute the corresponding steps in the above-described method provided in the embodiments of this application.

[0031] This application also provides a computer-readable storage medium storing a computer program that is executed by a processor to implement... Figure 1 The methods provided in each step are detailed in the implementation methods provided in the above steps, and will not be repeated here.

[0032] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for deformation analysis of pile-wall composite anchor foundations, characterized in that, Includes the following steps: S1: Obtain the geometric parameters, soil and rock layering parameters, and external load parameters of the pile-wall composite foundation; S2: Based on the geometric parameters and soil-rock layering parameters, a Winkel foundation model is established, and the normal subgrade coefficient and tangential shear stiffness coefficient of the wall-soil interface in the Winkel foundation model are reduced according to the preset mud cake reduction coefficient to generate the corrected foundation parameters. S3: Set the initial displacement vector of the basic reference point, calculate the horizontal displacement distribution of the diaphragm wall in the depth direction based on the initial displacement vector and the corrected foundation parameters, and determine the contact state of the wall-soil contact surface based on the assumption that the soil is not tensile. S4: Based on the contact state determination result, the horizontal resistance, vertical frictional resistance and the resisting bending moment of the diaphragm wall end face, side wall and bottom are calculated by segmenting and integrating the reaction force micro-elements of the diaphragm wall end face, side wall and bottom of the wall. S5: Establish a set of overall equilibrium equations that include horizontal force balance, vertical force balance and moment balance, and use a numerical algorithm that combines incremental loading and Newton-Raphson iteration method to solve for displacement increment by constructing Jacobian matrix until residual convergence, and obtain the actual displacement of the foundation reference point. S6: The actual displacement and corresponding deformation analysis results obtained from the solution are formatted and output, and the resistance sharing ratio provided by each soil layer to the foundation is further calculated. Based on the resistance sharing ratio, the stability of the pile-wall composite anchor foundation under different load conditions is evaluated.

2. The deformation analysis method for a pile-wall composite anchor foundation according to claim 1, characterized in that: The geometric parameters in step S1 include the pile cap parameters, diaphragm wall parameters, and soil layer thickness; Foundation parameters: including foundation length ,width ,high Diaphragm wall parameters: including diaphragm wall length ,width Soil layer thickness: Cohesive soil layer thickness Thickness of strongly weathered rock layers Thickness of moderately weathered rock layers ; The layered parameters of the soil and rock mass include the subgrade coefficient and the wall base stiffness; the subgrade coefficient includes the passive subgrade coefficient of each soil layer. Horizontal shear stiffness of sidewalls Vertical shear stiffness of sidewalls The wall base stiffness includes the horizontal stiffness of the bottom surface of the moderately weathered rock layer. and vertical stiffness ; External load parameters include top cable force Angle between the cable tension and the horizontal plane Structural self-weight Initial bending moment .

3. The deformation analysis method for a pile-wall composite anchor foundation according to claim 2, characterized in that: In step S2, the Winkler foundation model expression is: in, For the foundation reaction force; The subgrade coefficient is further subdivided according to the direction of force: [The rest of the text is incomplete and requires further context.] normal subgrade coefficient at the end face of the soil layer , No. Horizontal shear stiffness of the sidewalls of the soil layer , No. Vertical shear stiffness of the sidewalls of the soil layer ; The relative displacement at that point is based on the body displacement assumption; under the assumption of rigid body displacement, the horizontal displacement... and vertical displacement This is the displacement that triggers the foundation reaction force.

4. The deformation analysis method for a pile-wall composite anchor foundation according to claim 3, characterized in that: The corrected first step in step S2 normal subgrade coefficient at the end face of the soil layer Horizontal shear stiffness of sidewalls Vertical shear stiffness of sidewalls The expressions are as follows: ， in, This is the mud skin reduction factor.

5. A method for deformation analysis of a pile-wall composite anchor foundation according to any one of claims 2-4, characterized in that: The initial displacement vector mentioned in step S3 includes the horizontal displacement, vertical settlement, and foundation rotation of the reference point; Horizontal displacement of diaphragm wall in the depth direction The calculation formula is: in, Stiffness-weighted reference depth; For reference depth Horizontal displacement at the location; The depth of the current calculation point; Based on the corner.

6. A method for deformation analysis of a pile-wall composite anchor foundation according to any one of claims 2-4, characterized in that: In step S3, the state of the wall-soil contact surface is determined by the horizontal displacement of the diaphragm wall in the depth direction. Decision; the judgment rule is: when At that time, it is determined that the front wall end face of the diaphragm wall at that depth is under compression with the soil, activating the horizontal passive thrust and vertical frictional resistance in that area; when At that depth, it is determined that the end face of the diaphragm wall at that depth is under compression with the soil, thus activating the normal passive earth pressure and vertical frictional resistance in that area. when When the wall moves away from the soil at that depth, the soil is separated, and the normal resistance and vertical frictional resistance fail simultaneously.

7. The method for deformation analysis of a pile-wall composite anchor foundation according to claim 6, characterized in that, Step S4 includes: For the front wall, when At that time, calculate its horizontal passive thrust. and vertical frictional resistance Horizontal passive thrust The expression is: ; By horizontal passive thrust The generated resisting bending moment The expression is: ; Vertical frictional resistance The expression is: ; Vertical frictional resistance The generated resisting bending moment The expression is: ; For the back wall, when At that time, calculate its horizontal passive thrust. and vertical frictional resistance ; Horizontal passive thrust The expression is: ; By horizontal passive thrust The generated resisting bending moment The expression is: ; Vertical frictional resistance The expression is: ; Vertical frictional resistance The generated resisting bending moment The expression is: ; Calculate the lateral horizontal frictional resistance of the two side walls of the diaphragm wall. and lateral and vertical frictional resistance Lateral horizontal frictional resistance The expression is: ; Lateral horizontal friction The generated resisting bending moment The expression is: ; Lateral and vertical frictional resistance The expression is: ； Lateral and vertical frictional resistance The expression for the resisting overturning moment is: 。 8. The deformation analysis method for a pile-wall composite anchor foundation according to claim 7, characterized in that: The equilibrium equations in step S5 include the horizontal force equilibrium equations: , The horizontal passive thrust at the front wall end face; The horizontal passive thrust at the rear wall end face; The horizontal frictional resistance of the two side walls; This refers to the horizontal friction force at the bottom of the wall. For the top cable force Horizontal component of force; Vertical force equilibrium equations: , The vertical frictional resistance of the front wall end face; The vertical frictional resistance of the rear wall end face; The vertical frictional resistance of the two side walls; This is the vertical reaction force at the base of the wall; For the top cable force The vertical component of the force; For structural transverse load; Moment equilibrium equation: These are the torques generated by the horizontal force; These are the torques generated by the vertical force; These are the torques generated by the horizontal frictional force and the vertical reaction force at the bottom of the wall, respectively. This is the external equivalent bending moment.

9. A method for deformation analysis of a pile-wall composite anchor foundation according to any one of claims 2-4, characterized in that, Step S5 includes: Based on the resistances and moments calculated in step S4, a three-dimensional residual equation is constructed that includes horizontal force balance, vertical force balance, and moment balance. ; External load The loading process is divided into several smaller loading steps, gradually increasing from 0 to the target load; each step uses the converged solution of the previous step as the initial value. Within each loading step, based on the current displacement vector Calculate the three residuals of the equilibrium equation. ; This is an unbalanced force in the horizontal direction; This is an unbalanced force in the vertical direction; To circumvent the reference point Unbalanced overturning moment force; The partial derivatives of the residuals with respect to displacement are calculated using the central difference method, forming the Jacobian matrix. ; Solving the linear equations using the Gauss-Jordan elimination method To obtain the displacement increment ; ,in, The displacement increment of the base reference point in the horizontal direction; This represents the vertical displacement increment of the base reference point; This represents the increment of the base's rotation angle about an axis perpendicular to the ground. For the residual vector, ; Displacement increment Adding it to the old displacement vector yields a new displacement vector that more closely approximates the true equilibrium state. The expression is: ; Check the norm of the residual vector Is it less than the preset convergence threshold? If it is, then the current loading step is considered converged; otherwise, use a new displacement vector. Recalculate the residuals And continue iterating; Once all loading steps are complete and the residuals converge, the final displacement vector is output. This refers to the actual displacement of the pile-wall composite anchor foundation.

10. A deformation analysis system for pile-wall composite anchor foundations, characterized in that, The method for performing deformation analysis of pile-wall composite anchor foundations as described in any one of claims 1-9 includes: The parameter acquisition module is used to acquire the geometric parameters, soil and rock layering parameters, and external load parameters of the pile-wall composite foundation. The model construction and correction module is used to build a Winkel foundation model based on the geometric parameters and soil-rock layering parameters, and to reduce the normal subgrade coefficient and tangential shear stiffness coefficient of the wall-soil interface in the Winkel foundation model according to the preset mud cake reduction coefficient, so as to generate the corrected foundation parameters. The contact state determination module is used to set the initial displacement vector of the foundation reference point, calculate the horizontal displacement distribution of the diaphragm wall in the depth direction based on the initial displacement vector and the corrected foundation parameters, and determine the contact state of the wall-soil contact surface based on the assumption that the soil is not tensile. The resistance calculation module is used to calculate the horizontal resistance, vertical frictional resistance and resisting bending moment of the diaphragm wall end face and side wall based on the contact state determination result by performing piecewise integration on the reaction force micro-elements of the diaphragm wall end face, side wall and bottom wall. The equilibrium equation construction and iterative solution module is used to establish a set of overall equilibrium equations that include horizontal force equilibrium, vertical force equilibrium, and moment equilibrium. It adopts a numerical algorithm that combines incremental loading and the Newton-Raphson iterative method to solve for the displacement increment by constructing the Jacobian matrix until the residual converges, and obtains the actual displacement of the foundation reference point. The resistance inversion and safety assessment module is used to output the actual displacement and corresponding deformation analysis results obtained from the solution in a formatted manner, and further calculate the resistance sharing ratio provided by each soil layer to the foundation. Based on the resistance sharing ratio, the stability of the pile-wall composite anchor foundation under different load conditions is evaluated.

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