KR20080093692A - Behavior analyzing method of pile-bent structure - Google Patents

Abstract

A behavior analysis method of a pile bent structure is provided to analyze the behavior characteristics of a pile bent structure under various load conditions and ground conditions, and particularly to analyze the characteristics of a pile bent structure applied with horizontal load by introducing yield behavior and geometric non-linear behavior of material to analysis method. A behavior analysis method of a pile bent structure comprises the steps of: judging whether the ground reaction force is linear or not; if the ground reaction force is linear, calculating the load and the ground reaction force for linear analysis; calculating the stiffness matrix coefficients and a load vector, and forming a stiffness matrix; judging whether the initial displacement condition is set or not; if the initial displacement condition is not set, calculating an inverse matrix and calculating displacement; judging whether the ground reaction force is linear or not; and if the ground reaction force is linear, calculating axial inner member force and ground resistance.

Description

Behavior analysis method of Pile-Bent structure

1 is a view showing the basic form of the pilot structure of the present invention.

2 is a view showing a model of the pilot structure of the present invention.

Figure 3 is a view showing the stress, strain relationship between concrete and reinforcing bar of the present invention.

Figure 4 is a view showing the behavior of the column in consideration of the P-Δ effect of the present invention.

5 shows the degrees of freedom and stiffness matrix of the beam-column element of the present invention.

Figure 6 shows a beam-column model subjected to the vertical load of the present invention.

7 illustrates a beam-column model subjected to the horizontal load of the present invention.

8 illustrates loads and moments acting on any element of the present invention.

Figures 9a and 9b is a flow chart showing the behavior analysis method of the pilot structure of the present invention.

10 is a diagram showing ground conditions for nonlinear behavior analysis of the present invention.

FIG. 11 is a view showing a pilot material value for nonlinear behavior analysis of the present invention. FIG.

12 is a diagram showing the horizontal behavior during linear analysis.

Figure 13 shows the horizontal behavior during nonlinear analysis.

14 is a view showing the bending moment during linear analysis.

Figure 15 shows the bending moment during nonlinear analysis.

The present invention relates to a method for analyzing the behavior of a pile structure that can analyze the behavior of a pile-bent structure in consideration of pile-ground interaction.

Conventionally, many pile foundations are used as a substructure to support the load of the upper structure, and in most cases, piles are widely applied to group piles using several piles together. The foundation concrete plates connecting the upper part of the group pile are called pile caps or footings, which are usually in contact with the ground, but are often well above the ground when constructing offshore platforms. In the case of urban bridges, there are some restrictions on the use of the site due to pile caps, which are somewhat disadvantageous in terms of air and security due to the staged construction of pile-pile caps and piers.

In addition, the determination of the bearing capacity of the group pile is a very complex problem that has not yet been completely solved. When the piles are installed in close proximity, the stresses transferred to the soil by the piles overlap and the bearing capacity of the piles is reduced. Due to the complex factors of such group piles, the analysis of its behavior is not clear.

Due to industrialization, metropolitanization and compactness of urban areas, various structures are becoming more complex in form and composition. As a result, the design and construction of foundation structures have included more constraints than in the past, requiring analysis and design to reflect them. Recently, in Europe and the United States, the integrated structure and design of superstructure and undercarriage (lower foundation) have been integrated. In the case of bridge foundation, pile-pant structure without pile cap (Cast-) in substructure with conventional group pile and pile cap In-Drilled-Hole Shaft / Column) has recently been studied and some of them have been applied to real structures.

Cast-In-Drilled-Hole Shaft / Column has a pile and pillar without installing a pile cap, unlike the structure consisting of three elements of a pile-pile cap-pillar (pier) It is a structure integrated into a single member. The pilot structure is subjected to considerably large horizontal load due to wind load, temperature load, impact load, earthquake load, etc., and considerable horizontal displacement is expected, so it is necessary to examine the horizontal behavior precisely. However, there is no conventional method capable of analyzing the behavior characteristics of the pile structure, so that accurate analysis cannot be made.

The present invention devised to solve the above problems can analyze the behavior characteristics of the pile-bent structure under various loading conditions and ground conditions. In particular, the P-Δ effect, which is yielding behavior and geometric nonlinear behavior of materials, is introduced into the analysis technique. The purpose of this study is to accurately analyze the characteristics of pile structures subjected to horizontal loads.

The present invention for achieving the above object, when the vertical load analysis of the pile is required, (A) determining the linearity of the ground reaction force; (B) calculating loads and ground forces for linear analysis if linear; (C) calculating the stiffness coefficients b _i , c _i , d _i and the load vectors f _i and constructing a stiffness matrix; (D) determining whether an initial displacement condition is set; (E) calculating an inverse matrix and calculating displacement if no initial displacement condition is set; (F) determining whether the ground reaction force is linear; And (G) calculating the axial internal member force and the ground resistive force when the ground force is linear.

In addition, when the horizontal load analysis of the pile is required, (a) transmitting the axial internal member force for the horizontal behavior analysis; (b) determining whether the ground reaction force is linear; (c) calculating loads and ground reaction forces for linear analysis if linear; (d) calculating stiffness matrices a _i , b _i , c _i , d _i , e _i and load vectors f _i and constructing a stiffness matrix; (e) determining whether an initial displacement condition is set; (f) calculating an inverse matrix and calculating displacement if no initial displacement condition is set; (g) determining whether the ground reaction force is linear; And (h) calculating bending moments, shear forces, and inclination angles when the ground force is linear.

Preferably, the method may further include calculating the load and the ground reaction force in the q-u curve or the p-y curve when the nonlinear in the step (A) or (b).

The method may further include calculating a stiffness matrix and a load vector in consideration of the initial displacement condition when the initial displacement condition is set in the step (D) or the step (e).

In addition, in the case of (F) or (g), the calculated displacement and the limit displacement may be compared in the case of being nonlinear, and the process may proceed to the next step.

In order to fully understand the present invention, the advantages of the operability of the present invention, and the objects achieved by the practice of the present invention, reference should be made to the accompanying drawings which illustrate preferred embodiments of the present invention and the contents described in the accompanying drawings.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. Like reference numerals in the drawings denote like elements.

1 is a view showing the basic form of the pilot structure of the present invention.

Referring to FIG. 1, the basic type of the pile structure is a plastic hinge near the ground surface of the lower part of the piers using a first type and a pile having a diameter larger than the piers, in which the piers and piles are integrated with the same diameter to form plastic hinges in the ground. It can be divided into the second type to form a.

The feature of the first type is that there is no distinction between piers and piles, so there is no need to consider connection problems other than construction joints. In addition, the maximum bending moment (M _max ) generally occurs at 1 ~ 3 times the depth of the pile diameter below the surface, and when the cross-section diameters are the same, the change of the bending moment is relatively small, causing the plastic hinge to be somewhat wide, resulting in large plastic deformation. Before the destruction of concrete does not occur. However, since the plastic hinge is generated in the ground, it is difficult to determine whether the plastic hinge is formed before the ground excavation when the earthquake load is applied.

The feature of the second type is to increase the diameter of the pile so that the plastic hinge is formed at the bottom of the piers near the ground surface. The seismic response displacement of the bridge is small by designing the pile to be elastically responsive when the earthquake load is applied. However, this type has a relatively short length of plastic hinge for bending moments than other types of piles of the same diameter, resulting in rapid compression failure of concrete. In addition, when plastic deformation occurs due to excessive seismic load action, the ductility decreases, thus exhibiting relatively brittle behavior compared to the first type, and the construction cost is relatively large, which is disadvantageous in terms of economy.

Looking at the basic design method of the pile structure, the equivalent cantilever model (Equivalent Cantilever Model), the equivalent base spring model as a method of modeling the bridge pile foundation in the FHWA (1987) integrated upper and lower Model, and equivalent ground spring model (Equivalent Soil Spring Model) three methods are presented, but generally two methods such as ground spring model, virtual fixed point model as shown in Figure 2 are widely used in the present invention The model was applied.

First, the ground spring model assumes the target ground as a spring and assumes the ground reaction force as a function of pile displacement. The ground reaction force p is calculated by the following equation.

Where p is the ground reaction force (F / L), k is the spring constant (F / L ² ), and y is the displacement of the pile (L).

The reaction force spring constant of the Winkler soil model can be expressed as the product of the soil reaction coefficient (k _s ) and the diameter (width) of the pile.

Where D is the diameter of the pile (L), and k _{s is the} ground reaction coefficient (F / L ³ ).

For non-cohesive ground or normal consolidated clay, k is assumed to increase in proportion to the depth z at the ground surface. In this case, Winkler's reaction force spring constant k is given by Equation 3 below.

Where k ^* denotes a reaction force spring constant that is not dependent on depth.

As shown in FIG. 2B, the ground spring constant K _i located at the depth z _i is represented by Equation 4 below when the pile length is B _i .

Next, the virtual fixed point model uses the ground spring to model the ground and then the horizontal displacement occurs when the horizontal force E _i acts on the pile structure. The length to the point where horizontal displacement does not occur with respect to the horizontal force is determined as the effective fixed length d _f , and the point fixedly supports the pilot structure.

On the other hand, when considering the nonlinear analysis method of the pile structure, the pile structure may have a relatively large horizontal displacement with respect to the horizontal load due to the characteristics of the structure of the upper and lower structures. Do. The analysis method based on the conventional beam on the elastic foundation is not suitable for the analysis of the horizontal nonlinear behavior of the pile structure. Therefore, in the present invention, the pile and the ground were modeled by the elastoplastic method using the beam-column model, and the load transfer curve that can effectively apply the nonlinear interaction between the pile and the ground was used. . In the case of the vertical load transfer curve, the tip ground is a q-z curve and the main support ground is a t-z curve, and the horizontal load transfer curve is a p-y curve. The yield behavior of the material is based on the correlation of Moment-EI to the nonlinear behavior of the material due to the large horizontal displacement. The application of the P-Δ effect increases the horizontal displacement of the column as the load increases. The P-Δ stiffness matrix was used for the additional second moment in the member due to the P-Δ effect due to the applied axial force.

The material follows Hooke's law up to yield stress and then yields at a constant stress. It is divided into a linear elastic region in which the stress and strain is proportional to the stress-strain curve, and a plastic region, which is a region in which significant yields occur next. Due to the large horizontal displacement in the pile structure, the pile or pier material can move beyond the elastic range and into the firing stage.

In the case of a general single member, as the load gradually increases, the axial force and the bending moment generated in each cross section of the member increase linearly, and the fracture occurs when the applied axial force and the bending moment reach an extreme value. This sectional destruction means the destruction of the material that concrete and rebar can no longer resist external forces.

Concrete has great resistance to compressive stress, while it is vulnerable to tensile stress. Models that define the stress (f) -strain (ε) relationships of compressed concrete have a variety of models, from quadratic parabolic equations to linear linear models. In the present invention, a model expressing the stress-strain relationship of the concrete on the compression side as shown in FIG. 3 (a) is used, and this model is widely used in numerical analysis of concrete structures. Considering the resistance of tension-side concrete, there are two approaches of strength concept that concrete does not resist tensile force after cracking and an energy concept approach that some strength can be resisted after cracking. In the present invention, a model in which the tension stiffening effect of the energy concept is considered is used. This model linearly simplifies the strain softening area after cracking in the stress-strain relationship and assumes that tensile resistance decreases but continues to develop until the strain reaches ε _r .

Unlike concrete, rebar exhibits the same stress-strain relationship on the compressive and tensile sides, and exhibits linear behavior until the yield point is reached. Will behave. In the present invention, as shown in (b) of Figure 3 used a stress-strain relationship represented by two straight lines based on the yield point.

In the present invention, a combination of ε _x = f _x / E, f = Ey / ρ and σ _x = My / I derived from the beam theory is combined with a beam element having a constant curvature (x) due to the bending moment. The correlation between Moment-EI was calculated through the M / EI = x equation. The stress-strain relation curves of concrete and reinforcing bars were applied to reflect the nonlinear behavior of materials.

On the other hand, when the horizontal load acts on the piers, horizontal displacements occur in addition to the bending moments, resulting in additional bending moments due to the vertical loads. This is called the P-Δ effect. Referring to (a) of, it is represented by the following equation (5).

If the bending strength at the bottom of the bridge is M _n, the horizontal force that can resist this bending strength decreases as the horizontal displacement increases, as shown in Equation 6 below.

In addition to the horizontal force reduction, the P-Δ effect also affects the horizontal force-horizontal displacement relationship such that the initial effective stiffness decreases as shown in FIG. 4 (b), so that the rigidity after yielding becomes negative.

Most of the design criteria propose to consider the effect of P-Δ due to short-term ultimate load by applying the moment magnification factor method to the column. However, this design standard has simple advantages, but it does not reflect effectively the factors affecting the ultimate load such as reinforcement ratio and eccentricity, and it tends to underestimate or overestimate the structure.

Accordingly, the present invention reflects the P-Δ effect by using a geometric stiffness matrix capable of performing geometric nonlinear behavior similar to the actual behavior. In the numerical analysis of beam-column using the general finite element method, a 6 × 6 stiffness matrix is obtained from the relation between the member force and displacement of the magnetic induction of the beam-column element of FIG. Here, K _E is an elastic stiffness matrix, and K _G is a geometric stiffness matrix showing the P-Δ effect.

When the stiffness matrix of FIG. 5 is separated and divided into axial force, shear force, and bending moment, simultaneous equations as shown in Equations 7 to 9 are obtained.

By establishing a moment equilibrium equation and substituting Equations 7 to 9, the following Equation 10 can be derived.

The geometric stiffness matrix calculated by the finite element analysis has the same meaning as the P-Δ effect in the beam-column theory.

On the other hand, looking at the pile analysis model applied to the analysis method described above, it can be described by dividing the pile model receiving a vertical load and the pile model receiving a horizontal load.

First, when looking at the pile model subjected to the vertical load, since the pile is used as the foundation of the structure it serves to transfer the upper load to the lower support ground through the main surface resistance and the end support. In this case, most of the structural load acts as a load on the pile head. Such vertical load-bearing piles can be modeled as finite nodes connected by a series of springs, as shown in FIG. Each node is connected by a spring representing the axial stiffness of the pile, the value of which is AE / h. A is the cross-sectional area of the member, E is the modulus of elasticity and h is the length of the element. The external load Q and the ground spring S can be seen to be located at all nodes.

Where i = node number, u _i = displacement at node i, h = length of the element, AE _i = modulus of elasticity of the element between nodes (i) and (i-1) of the beam-column element The product of the cross sectional area, Q _i = the load acting on the node i, S _i = the spring coefficient of the ground resisting at the node i of the beam-column element, T _i = Internal axial force between the nodes (i) and (i-1) of the beam-column element.

Equilibrium condition of axial force (x direction) at any node i is

From the load-displacement relationship of each spring, the member force at each node i is given by Equations 12 and 13 below.

By substituting Equations 12 and 13 into Equation 11 and arranging them by the same coefficient, a governing equation for node i as in Equation 14 can be obtained.

Where b _i = (AE) _i / h, c _i = [-(AE) _i- (AE) _{i + 1} ] / hS _i , d _i = (AE) _{i + 1} / h, f _i = -Q _i means

In order to apply the above numerical method, the pile is divided into N nodes, and the coefficients b _i , c _i , d _i and f _i of Eq. 14 are calculated from i = 1 to N to form a determinant such as Equation 15 below. This can be expressed simply as Equation 16. Where A is the stiffness matrix, u is the displacement vector, and f is the load vector. Equation 16 may calculate u, which is the displacement of the pile, by calculating the inverse matrix A ⁻¹ , and calculate the axial force of the member by applying Equations 12 and 13 through the calculated displacement.

On the other hand, when looking at the pile model receives a horizontal load, the pile may be caused by a large horizontal load and moment on the head due to external forces such as wind or earthquake. In this case, the horizontal resistance is generally weaker than the vertical direction, so excessive horizontal displacement can occur and cause great damage to the structure. A pile subjected to such a horizontal load may exhibit behavior characteristics using a discrete element model as shown in FIG. 7. The actual pile member can be represented by a series of sections of length h representing rigid body behavior. Each section is joined by an elastic hinge to transmit shear, axial, and bending moments. The flexural stiffness at each node can be expressed by dividing the bending moment by the angle of rotation, or by the product of the modulus of elasticity and the cross section moment.

External load Q and linear ground spring S can be placed at all nodes. Since the force and rotational restraint conditions acting on any node i cannot directly act on the node, it can be replaced by the equivalent load and elastic spring on both adjacent nodes. The axial internal member force, T, which is calculated during the analysis of piles under congratulations, generates an additional bias, T _i (-y _{i -1} + y _i ), and was considered in the analysis.

Through the above, the process of obtaining the governing equation of pile is as follows.

First, the moment equilibrium at O ₁ in the element (i-1) is calculated as shown in FIG. 8. In the element (i-1), the moment equilibrium in O ₁ is given by Equation 17 below.

In a similar way the moment equilibrium in (i) is

Second, the equilibrium of force at the node i is expressed by Equation 19.

를 의미하며, 이 식을 다시 정리하면 아래 수학식 20과 같다.here,

This equation is rearranged as shown in Equation 20 below.

Third, the load-displacement relationship and the median differential equation are applied at node i. The relationship between the displacement and the moment is shown in Equation 21, and the second derivative of the displacement may be applied to the central difference equation as shown in Equation 22.

By applying Equation 22 to Equation 21, a polynomial like Equation 23 can be obtained.

By calculating the nodes (i-1) and (i + 1) in a similar manner, the following equations (24) and (25) can be obtained.

Fourth, the moment terms of Equations 17 and 18 are replaced with Equations 24 and 25, and the shear force V is calculated.

Finally, the coefficient of the governing equation is estimated. Substituting the calculated shear force equations (26) and (27) into equation (20) yields equation (28) below.

After multiplying both sides of Equation 28 by -h ³ , a finite-differential governing equation such as Equation 29 can be obtained.

Where a _i = F _{i -1} -0.25hR _{i -1} , b _i = -2 (F _i + F _{i -1} ) -h ² T _{i -1} , c _i = (F _{i -} 1 + 4F _i + F _{i + 1} ) + h ³ S _i +0.25 h (R _i-1 + R _{i + 1} ) + h ² (T _i-1 + T _i ), d _i = -2 (F _i + F _{i + 1} ) -h ² T _i , e _i = F _{i +1} -0.25hR _{i +1} , f _i = h ³ Q _i -0.5h ² (c _i-1 -c _{i + 1} ).

In order to apply the above numerical method to the pile, the pile was divided into a total of N nodes in the same manner as in the previous case, and the coefficients a _i , b _i , c _i , d _i , e _i and f Calculate _i The coefficients of Equation 29 are automatically determined at all nodes because they are independent of the horizontal displacement (w _i ) of the pile, and the number of polynomials including the virtual nodes is one (N + 2) at each end point. This polynomial can be represented by a determinant such as Equation 30 or simply as Equation 31. Where A is the stiffness matrix, w is the displacement vector, and f is the load vector. In Equation 31, the horizontal displacement of the pile may be calculated by multiplying both sides by the inverse matrix A ⁻¹ .

The behavior analysis method of the present invention can be largely divided into the analysis portion of the pile receiving a vertical load and the analysis portion of the pile receiving a horizontal load. The deflection and the internal member force of the pile can be obtained through the analysis of the pile under vertical load, and the calculated internal member force affects the analysis results of the pile under horizontal load. The load transfer curve of the ground can be considered both linear and nonlinear. When considering the nonlinearity of the material, the elastic modulus of the material is first calculated and then repeated calculation is performed until the displacement of the pile converges in the analysis of the calculated pile as shown in FIGS. 9A and 9B.

9A and 9B are flowcharts illustrating a method for analyzing behavior of a pilot structure of the present invention.

9A and 9B, the type is selected for the behavior analysis of the pile (S100). More specifically, one type of pile analysis is to be selected: vertically loaded pile analysis, horizontally loaded pile analysis, and vertically and horizontally loaded pile analysis. If vertical load analysis is required, first, it is determined whether the ground reaction force is linear (S110). If the determination result is linear, calculate the load and ground reaction force for the linear analysis (S120). However, in the nonlinear case, the load and the ground force are calculated from the qu curve (S130). After that, the stiffness matrices b _i , c _i , d _i and the load vectors f _i are calculated to form the stiffness matrices (S140). Thereafter, it is determined whether the initial displacement is set (S150). If the initial displacement is not set, the inverse matrix is calculated and the displacement is calculated (S160). If the initial displacement is set in step S150, the stiffness matrix and the load vector are calculated in consideration of the initial displacement (S170), and then the process proceeds to step S160. Then, it is determined whether the ground reaction force is linear (S180), and in the case of nonlinearity, the calculated displacement and the limit displacement are compared (S190). If it is not satisfied, the process proceeds to step S110, and if it is satisfied, the axial internal member force and ground resistance force are calculated (S195). On the other hand, if the ground reaction force is determined to be linear in the step S180 immediately proceeds to step S195.

After that, it is determined whether the horizontal load analysis step is additionally required at the time of analysis (S200). If the horizontal load analysis step is not necessary, the procedure ends, and if necessary, transmits the axial internal member force for horizontal behavior analysis (S205). After that, it is determined whether the ground reaction force is linear (S210). If the determination result is linear, calculate the load and ground reaction force for the linear analysis (S220). However, in the nonlinear case, the load and the ground force are calculated from the py curve (S230). After that, the stiffness coefficients a _i , b _i , c _i , d _i , e _i and the load vectors f _i are calculated to form a stiffness matrix (S240). Thereafter, it is determined whether the initial displacement is set (S250). If the initial displacement is not set, the inverse matrix is calculated and the displacement is calculated (S260). If the initial displacement is set in step S250, the stiffness matrix and the load vector are calculated in consideration of the initial displacement (S270), and then the process proceeds to step S260. Then, it is determined whether the ground reaction force is linear (S280), and in the case of nonlinearity, the calculated displacement and the limit displacement are compared (S290). If dissatisfied with this, the process proceeds to step S210, and if satisfactory, the bending moment, the shear force and the inclination angle are calculated (S295). On the other hand, if the ground reaction force is determined to be linear in the step S280 immediately proceeds to step S295 and ends.

The present invention relates to an analysis method that can analyze the behavior of a pile-bent structure considering the pile-ground interaction, and introduces the P-Δ effect, which is the nonlinear behavior of the material and the geometrical nonlinear behavior, into the analysis technique. It is possible to analyze the characteristics of the pilot structure receiving relatively accurately. In the case of the conventional behavior analysis method, there is a disadvantage that the upper and lower integrated analysis on the vertical and horizontal loads is not performed, but the present invention can consider this. Even if the horizontal load is small, the structure shows a difference in the behavior due to the P-Δ effect.In addition, the bending moment (P-Δ effect), which occurs when the horizontal displacement occurs, is introduced in the analysis technique, and more accurate behavior analysis is possible than in the conventional analysis technique. Do. In addition to the material characteristics of the pile, the nonlinearity of the ground to the horizontal load can be considered, so that the soil-structure interaction can be considered.

In order to understand the nonlinear horizontal behavior of the pile structure considering the integrated analysis of upper and lower parts, the linear and nonlinear analyzes were compared by applying the property values of FIGS. 10 and 11. The results of linear and nonlinear analysis according to the ground layer are shown in FIGS. 12 and 13 for horizontal displacement and 14 and 15 for bending moment.

In the analysis of the vertical and horizontal behavior of the pile, the verification results of the conventional method and the present analysis method, and the difference between the nonlinear analysis and the linear analysis result can be confirmed. It can be seen that it gives a more accurate value in the behavior analysis of.

Although the present invention has been described with reference to one embodiment shown in the drawings, this is merely exemplary, and those skilled in the art will understand that various modifications and equivalent other embodiments are possible therefrom. . Therefore, the true technical protection scope of the present invention will be defined by the technical spirit of the appended claims.

The present invention can analyze the behavior characteristics of the pile structure under various loading conditions and ground conditions, and in particular, the P-Δ effect of the horizontal load by introducing the P-Δ effect, which is the yielding behavior and the geometric nonlinear behavior of the material, is analyzed. The characteristics of can be analyzed relatively accurately.

Claims (5)

If the vertical load analysis of the pile is necessary, (A) determining whether the ground reaction force is linear; (B) calculating loads and ground forces for linear analysis if linear; (C) calculating the stiffness coefficients b _i , c _i , d _i and the load vectors f _i and constructing a stiffness matrix; (D) determining whether an initial displacement condition is set; (E) calculating an inverse matrix and calculating displacement if no initial displacement condition is set; (F) determining whether the ground reaction force is linear; And (G) calculating the axial internal member force and the ground resistance force when the ground force is linear. If the horizontal load analysis of the pile is necessary, (a) transmitting an axial internal member force for horizontal behavior analysis; (b) determining whether the ground reaction force is linear; (c) calculating loads and ground reaction forces for linear analysis if linear; (d) calculating stiffness matrices a _i , b _i , c _i , d _i , e _i and load vectors f _i and constructing a stiffness matrix; (e) determining whether an initial displacement condition is set; (f) calculating an inverse matrix and calculating displacement if no initial displacement condition is set; (g) determining whether the ground reaction force is linear; And (h) calculating the bending moment, shear force, and inclination angle when the ground reaction force is linear; The method according to claim 1 or 2, If the non-linear in step (A) or (b) step of calculating the load and the ground force in the q-u curve or p-y curve further comprises the step of analyzing the behavior of the pilot structure. The method according to claim 1 or 2, Comprising a step of calculating the stiffness matrix and the load vector in consideration of the initial displacement conditions when the initial displacement conditions are set in step (D) or (e). The method according to claim 1 or 2, The method of analyzing the behavior of the pilot structure to compare to the calculated displacement and the critical displacement when the non-linear in the step (F) or (g) to proceed to the next step.

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