JP2007255021A - Design method considering effect of distributional peripheral surface frictional force of pile foundation comprising many pile members - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reflect frictional force working on the peripheral surface of a pile member, in calculation for stability and behavior of a foundation structure. <P>SOLUTION: Strength of distribution peripheral surface frictional force τ<SB>Z</SB>and a range of distributed stratum are set in the same way as general setting of design external force to design a foundation. The effects of action (the action of τ<SB>ZN</SB>) resisting the axial deformation of the whole foundation, action (the action of τ<SB>Zϕ</SB>) resisting the flexural deformation of the whole foundation, and action (the action of τ<SB>Zθ</SB>) resisting the member flexural deformation of each member are reflected in a balanced manner to the components of resultant force of each cross-sectional force of the whole foundation, and a solution of a displacement function of an obtained equation is used for a design calculation expression. The former two action (the action of τ<SB>ZN</SB>and τ<SB>Zϕ</SB>) out of three kinds of action of the distribution peripheral surface frictional force τ<SB>Z</SB>has an effect of reducing the axial force of the pile. In the case of obtaining economical efficiency by reducing the axial force of the pile from the viewpoint of business, an expression reflecting the former two action is used to obtain a simple way of handling. These design methods are useful for the rational and economical design of the pile foundation. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method for designing a pile foundation when peripheral frictional force is applied to a large number of pile members.

A conventional design method for a foundation including a large number of piles pays attention to the one pile, and individually handles members based on a displacement function equation of bending deformation of an independent pile. The basic formula of the bending deformation formula of pile members is the ground reaction force proportional to the horizontal displacement using the horizontal ground reaction force coefficient k _H (Kh, or k _HE ) that distributes the horizontal ground resistance along the pile. Is guided as an independent single member. A design method for applying it to a foundation composed of a large number of pile members is shown in a road bridge specification (Non-Patent Document 1). A typical design method among them is the displacement method. However, the design method of the road bridge specification (Non-Patent Document 1) only takes into account the axial deformation of the pile and the action of the peripheral friction force indirectly.

  A design method other than the displacement method is a frame design method based on a frame model. A general pile foundation has a three-dimensional structure, but the frame model is usually handled in a simplified manner as a two-dimensional model. Done. The deformation model of the frame model for pile members is based on a deformation formula that handles one independent member individually. The deformation formula is applied to each node section provided in a region where the conditions change, and the design is performed by reflecting changes in the members used and the ground conditions.

The frame model of the pile foundation (see FIG. 1) in the road bridge specification (Non-patent Document 2) does not consider the axial deformation of the pile members. To reflect the effect of the axial deformation of the stake member in order that, to organize Loading Test results of pile separately, is allowed to act as the pile head (the concentration) of the axial spring constant K _V or K _VE Yes. This axial spring constant shows a typical value for each type of pile, using a calculation formula that takes into account the material, cross-sectional area and length of the pile.

The effect of the peripheral frictional force of the pile in the frame model of the pile foundation in the Road Bridge Specification (Non-Patent Document 2) cannot be considered in the pile member itself of the frame model, but the (concentrated) axial direction set at the pile head in the value of the spring constant K _V, so that the effect that included experimental results are implied. The method of using this axial spring constant is the same as in the previous displacement method. Therefore, it does not directly reflect the stratum structure of the place where the foundation is installed.

On the other hand, the frame model in the railway bridge structure design standard (Non-Patent Document 3) shown in FIG. 2 considers not only the bending deformation of the pile but also the axial deformation. The effect is handled by the (distribution) design shear ground reaction force coefficient k _SV acting on the circumferential surface of the pile. Then, the pile bottom (distribution) and exerts a design vertical ground reaction force coefficient k _V, a model directly reflects the formation structure.

The evaluation of the effect of frictional force on the surface of pile members with (distributed) shear ground reaction force coefficient k _SV is a calculation formula that treats as a distributed spring coefficient as a deformation formula of members between nodes from the characteristics of the design method of the frame model Is already adopted, and it is adopted from the viewpoint of matching the properties of the coefficient with the ground reaction coefficient that represents the effect of other horizontal and vertical ground.

  Although the peripheral frictional force always works on the pile member in normal ground, the research on the property and how to handle it is not enough, and it cannot be said that it is popular at present. The main factor is that the main structure of a normal pile foundation itself has a multi-frame structure and a high-order indefinite structure. In addition, since the structural body is installed on the ground, it is necessary to reflect the mechanically complex properties of the ground in the calculation when performing stability calculations for ordinary pile foundations.

  In other words, there are two types of complexity factors that reflect the complexity of the structural body of the structure and the complexity of the properties of the ground. is there. Because of these two types of factors, the handling of the peripheral frictional force of the pile has not reached the state where anyone can handle it anywhere, as the level handled by the road bridge specifications.

Ordinary complex nature of the ground has a stable calculation of pile foundation, represented by horizontal subgrade reaction coefficient k _H, etc., the vertical ground reaction force factor k _V and the circumferential surface shear subgrade reaction coefficient k _SV. Among these three types of ground reaction force coefficients, research on how to handle the peripheral frictional force related to the third coefficient k _SV is the most delayed.

The peripheral frictional force of the pile is calculated as a frictional force that is uniformly distributed between the measurement points based on the axial force difference between the axial force measurement points in the loading test result. Measurement points are set near the main strata boundary and have a considerable section length. When the calculated vertical friction force strength is plotted on the vertical axis and the relative displacement of the pile at the representative point in the middle of the measurement points is plotted on the horizontal axis, the (distribution) shear ground reaction force coefficient k _SV is a graph. Expressed as the slope of

However, even if the shear ground reaction force coefficient k _SV thus obtained is a value representative of the formation, the nonlinearity of the calculation formula obtained under the state where the shear springs are uniformly distributed in the formation, The assumption of the original frictional force that is uniformly distributed between measurement points is difficult to reproduce due to the difference in vertical elastic displacement above and below the formation. Thus, the problem of how to handle the peripheral frictional force is one of the bottlenecks in the development of the pile foundation design method.

  In the design method considering the elastic deformation of the member in the axial direction, when a long pile member is handled, the effect of the elastic deformation appears on the vertical displacement and the overall rotational displacement of the pile head, and the value is larger than the actual value. In order to prevent it, it is necessary to reflect the effect of the peripheral friction force according to the actual situation.

When the frictional force of the peripheral surface of the pile is taken into account by the shear ground reaction force coefficient k _{SV, the} bilinar is handled as a certain upper limit after the strength of the frictional force reaches the upper limit. Although it is reasonable to handle the effect of the peripheral frictional force in two stages, the elastic region and the plastic region, the frictional force itself is of a nature that varies considerably when compared with the evaluation accuracy, and this leads to complicated handling. It is.

  And the effect of the ground acting on the pile is based on the properties measured when there is only one pile, and the effect of the front of the pile group and the internal ground when there are many piles is the design The method has already been made, but its accuracy is not sufficient. For example, in normal foundations, the number of piles in the second and subsequent rows is greater than that in the front row, but the accuracy of reflecting the ground effect inside the pile group is usually worse than how the ground effect in the front is reflected. . This is because it is difficult to conduct many experiments on an actual scale. Even if the pile foundation body is modeled with a frame structure, the accuracy of the coefficient that reflects the effect of the ground is not balanced compared to the calculation accuracy of the frame structure itself.

  The present inventor has already proposed the "Equivalent Single Pile Model Formula", which is described below as an easy-to-handle structural model of the pile foundation body, which is not as complex as the framework model. (See Non-Patent Document 4). After that, these equations are collectively called “equivalent single pile model equations”, and this calculation method treats a large number of pile members as a representative of the displacement function of the center line of the foundation. The bending deformation, axial deformation and shear deformation of the member are taken into account.

  Usually, a single pile member i is subjected to three component cross-sectional forces (Mi, Ni, Qi) of member moment Mi, member axial force Ni, and member shear force Qi. The basic state is shown in FIG. 3 ((a), (b), (c)) with two member elements arranged in parallel. In the cross-sections of a large number of pile members composed of such member elements, in addition to the sum Msb of the member moment Mi, the sum N of the member axial force Ni, and the sum Q of the member shear force Qi, the moments formed by the member axial force Ni There is a sum, which is represented by Maf. In general, the four component cross-sectional forces (Msb, Maf, N, and Q) act on the entire cross-section of a large number of pile members. In the “equivalent single pile model formula”, a large number of members that cause similar deformation are called “member aggregates”. The relationship between the sectional force of the member i and the “member assembly” is expressed by the equations (1) to (4).

  Here, xi is the distance from the center of the assembly to the center of the member i, and Σ represents the sum of n members. The explanation of the symbols used is summarized at the end of the sentence.

  4 types of deformation caused by a large number of members corresponding to each of the four component cross-sectional forces (Msb, Maf, N, Q) are used as basic deformation patterns, and the forms are shown in FIG. 4 ((a), (b ), (C), (d)). These basic deformation patterns are “member bending deformation” for the sum Msb of member moments, “axial deformation” for the sum N of axial forces, and “shear deformation” for the sum Q of shear forces. And follow the conventional name. And the deformation | transformation with respect to the sum Maf of the moment which an axial force makes is called with the new name "overall bending deformation."

  A large number of members that cause such deformation are referred to as “member assemblies”. In ordinary pile foundations and sheet pile foundations, rigid footings and top plates are provided on the heads of vertical members such as piles. Attention is focused on a state in which a large number of pile members undergo deformation that approximates each other due to structural restrictions due to the structural restriction effect exhibited by the rigid footing. When the cross-sectional force of a large number of pile members is expressed by four types of cross-sectional force components, it can be handled by a simplified model as the cross-sectional force of one equivalent member. The modeling state is shown in FIG. 5 ((a), (b)).

  A model having a rigid footing at the upper end of the “member assembly” is called a “group pile model”. This model has the same form as an ordinary pile foundation. Select a displacement function that represents four basic deformation patterns, and based on the four types of sectional force and the four types of displacement function of the foundation centerline, one member that is equivalent to the displacement and sectional force of the entire foundation The general term for the simplified expression is "Equivalent Single Pile Model". The main points of guidance of this formula and typical calculation formulas will be described below.

  FIG. 6 shows the overall coordinates (X, Z) and the local coordinates (ξ, ζ), and FIG. 7 shows the sectional force of the member element and its assumed direction. The displacement position of the arbitrary point i of the structure after deformation is defined as (ui, wi), and the position is represented by four types of displacement functions and coordinates reflecting the basic deformation pattern of the basic body center line. The vertical displacement wno, the horizontal displacement uo, the member rotational displacement θmo and the total rotational displacement φ are selected as the four types of displacement functions of the base center line point o, and the rotational angle of the member i is represented by (φ + θmi). The state before and after the deformation of the “group pile model” and the display content of the displacement function are shown in FIG. 8 ((a), (b)).

  Expressions (5) and (6) represent the displacement (ui, wi) of the arbitrary point i by four types of displacement functions (uo, wno, φ, θmo). These two formulas are approximate assumptions of three items (1. Linear proportionality of member center axis strain (φ is constant in the cross section), etc., due to the structural restriction effect exhibited by rigid footing, and 2. Distance between members 2. Invariance (uo≈ui) 3. Considering the approximation of the rotation angle of the member (θmo≈θmi), this is the most basic expression when the entire foundation is simplified and expressed. This is the starting point for the induction of the “single-pile model equation.” The relationship between the four types of cross-sectional forces and displacement functions derived from equations (5) and (6) is expressed by equations (7) to (10). Is done.

  Here, E is Young's modulus, G is the shear elastic constant, Ag is the total cross-sectional area, Ip is the sum of the member cross-sectional secondary moments, and Ig is the sum of the cross-sectional secondary moments formed by each member with respect to the center of the assembly. . The differential in the Z-axis direction is represented by ′.

  In a cross section of a structure similar to the “group pile model” formed by a large number of pile materials and a rigid top plate, the relationship of Expression (7) to Expression (10) is established regardless of the form. This is called “commonness of displacement field” in the “equivalent single pile model formula”. The basic equation of the “equivalent single pile model equation” is a second-order simultaneous differential equation using four types of displacement functions, and is expressed by equations (11) to (14).

  Here, q is the sum in the cross section of the horizontal distribution external force qi shown in FIG.

An expression (15) expressed as the sum of ground reaction forces proportional to the horizontal displacement uo in the term of the sum q of the horizontal distributed external force in the inner expression (14) of the basic equation of the “equivalent single pile model expression” (15) ) Is substituted into Equation (16), which is an equation for handling ordinary pile foundations. The basic equations of the “elastic spring support model” are four formulas of formula (11) to formula (13) and formula (16). The general solution of this basic equation is expressed by equations (17) to (20). This general solution includes equations (21) to (24) as balance condition equations (characteristic equations), and coefficients of the solution. The relational expressions (25) to (28) are attached.

Where Kh is a representative horizontal ground reaction coefficient, B is a reference width in which the horizontal ground reaction coefficient is distributed, a is a correction coefficient for Kh and B, and coefficients A _{1 to} D ₄ are 12 integral constants. is there. However, it is a case where Ψ <1 (see Expression (28)).

  Formulas (17) to (20) of the general solution of the “elastic spring support model” are general solutions when the “group pile model” is supported by the elastic spring, and various similar basic forms installed in the ground This is a basic formula when applied as a simple design method. These “Equivalent Single Pile Model Equations” are simple expressions, but the axial deformation and shear deformation of the members are considered simultaneously.

The first example of applying the “equivalent single pile model formula” to various similar basic forms is the case where the term of the distributed horizontal external force q is 0, returning to formula (14). If the solution in that case is calculated | required, it can apply to the structure where only the pile foundation main body protrudes on the ground, a multi-column type foundation, or a column member. On the other hand, in addition to the term of distributed external force q, an example of developing an “equivalent single pile model formula” as a model in which an axial linear frictional force acts on both side surfaces of a member main body for a steel pipe sheet pile foundation is already in the present invention. (See Non-Patent Document 5).

  In this way, it is possible to develop a balance formula between the cross-sectional force and the acting force with different combinations of the types of external forces working according to the characteristics of the type and form of the foundation for the “group pile model”. This is called “stress field expansibility”.

  The two characteristics of "displacement field commonality" and "stress field deployment" are the grounds that "equivalent single pile model formula" can be applied to various similar types of foundations.

  Fig. 9 is a simplified representation of a conventional calculation system assembled for individual members as an individual single pile format system, and the main development items predicted by the "Equivalent Single Pile Model Formula" are frameworks. This is shown in contrast to the case of systematizing the simplified design method as an equivalent single pile type system.

  The present invention is a model in the case where the peripheral frictional force acts on the pile members of the “group pile model”, and becomes the fourth model following the three types of models described above. This is shown in FIG. 9 considering the peripheral frictional force. Assuming the types and forms of existing foundations, the above four types of models are the basic model types necessary for design calculation. Once these basic models are in place, as shown in FIG. 9, after that, including the combination of models of different materials and types, consideration of the plastic region of members and materials and dynamic design methods, etc. Deployment can be done with procedures similar to existing methods.

The present invention simultaneously satisfies the two problems of simply expressing a foundation structure and expressing the complex nature of the ground simply and clearly, and is the basis for developing a new design method. .
Road Bridge Specification / Explanation IV Substructure Chapter 12 Pile Foundation Design, pp. 373-375, 378-397, March 2002. Road Bridge Specification / Explanation V Seismic Design Chapter 12 Response values and allowable values of pier foundation, pp. 215, March 2002. Railroad structure design standards and explanations Foundation structures and earth pressure structures Chapter 10 Pile foundations, pp. 219, October 1999. Hiroshi Maehara, Tsunekazu Nakata: New calculation method for group pile foundation, bridge and foundation, pp. 8-12, 1996-2. Hiroshi Maehara, Tsunekazu Nakata: Consideration on design method of sheet pile foundation, bridge and foundation, pp. 32-37, 1996-3. Steel Pipe Pile Association: Design and construction of steel pipe pile foundation, road bridge specification (March 2002 version) revision, 3.4.3 Design method, pp. 20, April 2002.

  As described above, the frictional force of the ground normally acts on the peripheral surface of the pile member in the vertical direction. However, reflecting the effect in the calculation of stability and behavior of the foundation structure according to the structure of the ground is performed in Non-Patent Document 3 in the field of civil engineering structures, it is complicated, and the circumferential frictional force It is necessary to be able to reflect the characteristics of this in practical design in a simple way.

The basic requirements for practical design of foundation structures are as follows.
1) The calculation of the structure is not as complicated as the frame analysis by the frame model.
2) The main effects of mechanically complex ground properties can be reflected in the calculation.
3) There is little disparity in the accuracy of how to handle both the structure and the ground.
4) The basic behavior of the entire foundation and each component can be expressed concisely.
5) It can be widely applied to structures of similar type.

The peripheral frictional force of the pile is calculated as a frictional force that is uniformly distributed between the measuring points of the axial force. The value does not correspond exactly to the relative displacement of the station itself. Therefore, the peripheral friction force is not the (distributed) shear ground reaction force coefficient k _SV of the pile peripheral surface but the distributed friction force τ _Z, and the strength and distribution range of this friction force τ _Z are the same as general design external force. Set and design the foundation.

There are four types of basic deformation patterns caused by a large number of members: “axial deformation”, “overall bending deformation”, “member bending deformation”, and “shear deformation”. Of these, the peripheral friction force τ _Z of the pile works on three basic deformation patterns other than “shear deformation”, and works to reduce the deformation. FIG. 10 ((a) shows a model of the manner in which the peripheral surface friction force τ _Z acts on the three basic deformation patterns on which the peripheral surface friction force works by dividing it into three types (τ _ZN , τ _Zφ , τ _Zθ ). ), (B), (c), (d)).

  FIG. 10 is an expression according to the form in which the working method of the peripheral friction force is divided into three types of action patterns with respect to the basic deformation pattern when a large number of pile members are captured at once. In an ordinary pile foundation, the state of the lower half of FIG. 10 occurs in a state where it is synthesized at the base of the pile below the footing.

  In the conventional way of handling the way of working the peripheral frictional force on one independent pile member, only two directions of pushing or pulling are considered for one member. On the other hand, when a large number of pile members are captured at once, the state in which the peripheral frictional force acts on a large number of pile members is modeled by dividing them into three types of action patterns against those of the basic deformation pattern. Instead of handling the work individually, treat them all together at the same time.

FIG. 10 specifically explains the patterns of the action of the three types of peripheral surface frictional forces (τ _ZN , τ _Zφ , τ _Zθ ). The center of the length of the member is the boundary of the deformation direction. With respect to the “member bending deformation” in (a), the surface is _expanded and contracted by bending the member for each member, and the peripheral frictional force τ _Zθ acts on the surface of each member in the opposite direction to the expansion and contraction. .

For (b) “overall bending deformation”, the direction of the axial force varies depending on the position of the member, and the member expands and contracts accordingly. The circumferential frictional force τ _Zφ acts as a couple across the entire cross section of the foundation in the opposite direction to the expansion and contraction. And for the “axial deformation” of (c), the circumferential frictional force τ _ZN acts in the opposite direction to the direction in which the entire foundation is compressed (or pulled).

In order to express the difference in working method of the peripheral friction force τ _Z with respect to the three types of basic deformation patterns formed by a large number of member elements based on FIG. A specific model is shown for each function.

  The member elements i and j on the opposite sides of the center of the foundation are modeled by modeling the three types of action patterns of the peripheral frictional force for each basic deformation pattern as shown in FIGS. (A), (b), (c)).

The peripheral surface friction force τ _ZN shown in FIG. 11 acts on the acting force N in the same direction (pushing or pulling direction). The circumferential frictional force τ _Zφ shown in FIG. 12 differs depending on the position of the member with respect to the acting force Maf and acts on the entire foundation as a couple. (A) of FIG. 13 represents the state which the expansion-contraction of an area arises on the surface of the member with the bending deformation of the member with respect to cross-sectional force Msb. (B) and (c) show a state in which the peripheral frictional force τ _Zθ acting on the surface causing expansion and contraction acts on the surface of the member when the cross section is circular. The frictional force τ _Zθ is different in the working direction on the front surface and the back surface of the member. FIG. 11 to FIG. 13 are diagrams expressing three types of working methods of the peripheral frictional force by modeling them individually.

Next, the action of the three types (τ _ZN , τ _Zφ , τ _Zθ ) of the peripheral surface friction force τ _{Z on} the three types of cross-sectional force components (N, Maf, Msb) of a large number of members, Expressed in a balanced formula. FIG. 14 shows the displacement field of the model in that case along with the assumed direction of the cross-sectional force in FIG. For the displacement, the original position is indicated by a broken line, and the position after the positive displacement is indicated by a solid line. Note that the assumed direction of bending moment in FIG. 7 is opposite to the forward direction of rotation.

11 and 14, the balance of the peripheral friction force τ _ZN with respect to the total axial force _N , the balance of the peripheral friction force τ _Zφ with respect to the sum Maf of the moments formed by the member axial force from FIGS. 12 and 14, and FIG. 13. From FIG. 14 and FIG. 14, the balance of the peripheral friction force τ _Zθ with respect to the sum Msb of the member bending moments is individually summarized, and the balance of the shear force Q is also taken into account in consideration of the distributed horizontal external force q. Are the equations (29) to (32). These four equations are balanced equations for the cross-sectional force of the “member _assembly ” when the distributed frictional force τ _Z (τ _ZN , τ _Zφ , τ _Zθ ) works.

  Here, Ui is the circumference of the pile member i, ri is the radius, xe is the distance from the center of the assembly to the center of the outer edge member, and the symbol || represents the absolute value.

  In FIG. 14, the assumed direction of the bending moment does not match the positive direction of rotation. The distribution of the peripheral frictional force τzφ within the entire cross section of interest can be divided into two types: a uniform distribution (FIG. 15) and a case where the peripheral surface friction force τzφ is proportional to the distance from the center of the base to the center of the member (FIG. 16). The two types of influences on are shown in equation (30). FIG. 15 assumes a case where there is an influence of the adhesive strength of the formation, and FIG. 16 assumes a case where the influence of the adhesive strength is small.

In order to simplify the expression of the equation, the coefficients F _A , F _G , F _T , F _P , and F _K are defined as in Expression (33) to Expression (37), and the peripheral friction force τ _Z (τ _ZN , Τ _Zφ , τ _Zθ ) are balanced force equations (29) to (32) of the cross-sectional force component, and four types of displacement functions (wno, φ, uo, θmo) of the structure center line are used. What is expressed is a basic equation that takes into account the peripheral frictional force of the pile, and is a simultaneous differential equation of equations (38) to (41).

When the general solution of equation (41) is obtained from equation (38) of this simultaneous differential equation, it is expressed by equations (42) to (45). These formulas (42) to (45) are general calculation formulas for a foundation composed of a large number of underground vertical members on which circumferential frictional force acts. The internal expressions (44) and (45) are accompanied by expressions (46) to (50) as relational expressions of coefficients in the solution. Here, eight coefficients A ₁ to B ₂ and E ₁ to E 4 are integral constants.

  Formulas (42) to (45) and accompanying formulas (46) and (46) are used as general solution formulas for a general-purpose simple design method for a foundation composed of a large number of vertical members on which the peripheral surface frictional force of the present invention works. (50).

As a practical and simpler formula, the conventional frictional force τ _Zθ acting on member bending deformation is used in accordance with the conventional practice of consideration for member bending moment as a safety consideration in design. Ignored expression. The equations are expressed by equations (51) to (54), and equations (53) and (54) are accompanied by equations (55) to (62). Here, the twelve coefficients A ₁ to B ₂ and C 1 to D 4 in the equations (51) to (54) are integral constants.

The present invention, the "expression of the equivalent single pile model" that target multiple stake member expands when the skin friction is working, three way acts as a distribution skin friction tau _Z (tau _ZN , τ _Zφ , τ _Zθ ) are modeled separately, and these three types of functions are formulated.
Expressions (51) to (54) are obtained by taking out two types (τ _ZN , τ _Zφ ) of working parts as the main workings of the distributed circumferential frictional force _τz .

  The integral constants included in the general solution equations (17) to (20), equations (42) to (45), and practical solution equations (51) to (54) are associated with each equation. The number of conditional expressions and the number of unknowns (integral constants) are equal to each other from the balance conditional expression (characteristic expression), the relational expression of the coefficients in the solution, and the boundary condition expressions given above and below the structure (four expressions each above and below). Then, specific values are determined.

  When the displacement function of the general solution is specifically determined, the displacement at an arbitrary point is obtained from the equations (5) and (6), the sectional force of the entire foundation is obtained from the equations (7) to (10), and the member sectional force is obtained from the equation. It is specifically obtained from an expression expressing the expression (4) in reverse from (1).

  The general solution equations (42) to (45) considering the three types of working methods of the peripheral friction force are used when the influence of the peripheral friction force is strictly calculated.

In addition, when not expecting the effect of reducing the displacement of the pile head and the overall rotation, but only expecting the effect of reducing the axial force due to the peripheral frictional force of the pile, the balanced equations (29) and (30) and from the coefficients of equation (33) and (34), is represented by a linear function of Z for each member forces N and Maf was coefficients _EA g · _{F a} and _EI g · _{F G,} it is a simple leverage .

  In terms of how to evaluate the ground, the peripheral frictional force acting on ordinary ground can be handled at the same time in a simple and clear manner, in addition to how to handle both horizontal and vertical ground reaction forces. It will encourage the examination and research of problems related to the peripheral friction force. In particular, the low peripheral surface friction force is expected everywhere as long as it is not soft ground, and attention is paid to the effective use of the effect.

  In addition, one of the issues of the peripheral frictional force of the pile is the pile that the three parties work together by adding the vertical spring effect of the support layer and the peripheral frictional force to the elastic effect of the pile body. There is a problem concerning the elucidation of the vertical spring effect of the head. Until now, there has been insufficient research to clarify its characteristics. According to the method of the present invention that can easily handle the state in which the circumferential friction force is uniformly distributed in a predetermined section, this research is facilitated, which is useful for advancing research in this direction.

  In the practical aspect of how to handle the peripheral friction force, the strength and distribution of the peripheral friction force are handled in the same manner as other design loads, and the distribution state is clear in the method of the present invention. The effect of setting the circumferential friction force with a uniform distribution occurs as a linear decrease in the axial force of the pile, which has the advantage that it can be clearly understood and utilized.

  The rational pile foundation design method takes into account the elastic deformation of the pile body, but from the viewpoint of both the computational rationality to prevent large deformation as the pile length increases and the economical use of the pile material It is necessary to consider the action of the peripheral friction force. In that case, unlike the conventional method, the method of the present invention can set the strength and distribution of the peripheral frictional force according to the structure of the ground, and the effect can be handled by a simple calculation method. It is an effective way to pursue sex.

  Furthermore, it is possible to perform foundation design calculation by matching the ground handling method between the calculation of the ultimate bearing capacity of the pile and the stability calculation of the foundation.

Examples and Comparative Examples FIG. 17 to FIG. 21 show the case of 24 (4 rows × 6) cast-in-place piles as an example (a) when the peripheral surface friction force works, and (f) when there is no friction ( It is shown by contrast as b). The pile head has a depth of 0 m.

  The cast-in-place pile has a diameter of 1.5 m and a length of 37.5 m, and is calculated by dividing the base ground below the footing into five layers.

  The upper three layers are landfills in the first and second layers, and the third layer is an alluvial layer consisting of a sand layer and a silty clay layer. Although the second layer is a landfill board, it is a layer in which the N value continues around 10 to 20 in a portion deeper than 8 m from the ground surface. The 4th and 5th layers are divergent and thin sandy layers, gravel-mixed sand layers, silty sand layers and silty clay layers, and the 4th layer is an alternating layer with an N value of about 20-30. The fifth layer is an alternating layer having a support layer portion with an N value of about 35-50.

  Since this support layer is a thin alternate layer, a pile of about 11 m is embedded. Only the fifth layer is considered for the peripheral frictional force when calculating the ultimate bearing capacity of the pile.

The second layer has a thickness of about 11 m and the fourth layer has a thickness of about 9 m, and it is considered that the peripheral frictional force is acting. Therefore, the effect of the peripheral frictional force acting on the intermediate layer is examined. The total of the initial peripheral friction force acting on the pile does not exceed the vertical load Vo. Since the layer thickness of the second and fourth layers is large, the circumferential area of the pile is large, and the initial set value τ _ZO of the peripheral friction force τ _Z is as small as 29.4 KN / m ² (= 3.0 tf / m ² ). The value of When this value is applied to the peripheral surfaces of the second and fourth layer piles, the amount is almost equivalent to the average axial force (2,736KN / piece). Consider without acting. In addition, the function of the frictional force _τZθ with respect to the bending deformation of the member was ignored, and the calculation was performed using the practical solutions (51) to (54).

The peripheral friction force τ _Z was applied to the second layer and the fourth layer, and the calculated actual action values (τ _ZN , τ _Zφ ) were set to τ _ZN = τ _Zφ = τ _ZO / 2, respectively. This is assumed in this way because almost half of the maximum pile reaction force is the average axial force for level 1 equivalent seismic loads.

In the section in which the circumferential frictional force τz works, there is a reduction in axial force by (τ _Z × circumferential length) per unit section. Work contributing tau _ZN and tau _Zfai this axial force reduction is considered homogeneous in the compression zone of ground. The sum of the axial forces decrease is axial force decrease due tau _Z. The situation is examined by comparative calculation.

Since the value of the set friction force tau _Z This comparison calculation is not large, the distribution of tau _Zfai considering the viscous nature of the ground was uniform distribution of FIG 15. In addition, since it is difficult to make all distributions uniform, there is a correction that reduces the magnitude of the acting friction force to 1/10 in the range where the vertical displacement is less than 1 mm in the primary trial calculation value. went.

  FIG. 17 compares the vertical displacement distributions of the calculation results, and illustrates the first and fourth rows at both ends of the pile and the center of the foundation. Since the range in which the peripheral friction is applied is relatively wide, the maximum vertical displacement of the pile head is reduced from 6.3 mm to 4.5 mm (71%). The distribution of (b) is a straight line, but in (a), the influence of the peripheral surface friction appears and the gradient of the distribution map changes to form a curve. In (b), correction is made to reduce the applied frictional force to 1/10 within a range where the vertical displacement is less than 1 mm.

  FIG. 18 is a comparative diagram of the result of the total axial force N, and FIG. 19 shows the distribution of the moment Maf (total bending moment) and the total moment (Maf + Msb) generated by the axial force. The total axial force N (Fig. (18)) and the moment Maf (Fig. (19)) formed by the axial force are constant from top to bottom when there is no friction. The values decrease linearly with the same slope in the second layer and fourth layer where the is working. This represents the contents of the balance force balance equations (29) and (30). That is, changes in the sectional force N and Maf are expressed by a linear function of Z.

The influence of the horizontal external force is also considered as a couple of axial force moments in Maf, and the peripheral friction force reduces the moment Maf due to the couple of axial forces. This is clearly shown in FIG. The phenomenon that the couple of axial force moments is reduced by the peripheral frictional force _τZφ is a phenomenon that cannot be expressed simply even if a constant frictional force is applied to the conventional frame analysis. However, the method of the present invention is simply represented in FIG.

The total axial force N is reduced by about 40%, and the moment Maf generated by the axial force is reduced by about 50% by the peripheral frictional force. Although the value of the actual acting friction force (τ _ZN , τ _Zφ ) is as small as 14.7 KN / m ² (= 1.5 tf / m ² ), if the working area is so large, the effect is very large. Show.

  In FIG. 19, the difference in graph between the total moment (Maf + Msb) and the moment Maf formed by the axial force is the member bending moment Msb. (B) shows the horizontal axis of (a) doubled. The distribution form itself of the member moment Msb is hardly changed. However, considering the friction, the absolute value of the moment Maf at the pile head is slightly increased, but the absolute value of the member moment Msb at the pile head changes accordingly. The amount of change may be about 10% when viewed from the member moment Msb.

  The member moment Msb converges to 0 at a deeply embedded portion. In this example, the member moment Msb is 0 at a depth of less than 20 m. In the deeper part, only the axial deformation occurs in the pile. This deep part is a part where both the total axial force N and the moment Maf formed by the axial force are reduced to a small value.

  FIG. 20 shows the axial force of the piles for each pile row. The compression side is the pile row 4 and the drawing side is the pile row 1. In this example, the pulling force itself is not generated. The axial force of the pile in FIG. 20B is constant because it does not consider friction. In the pile row 4 on the compression side in FIG. 20A, the axial force N is reduced by about 45% due to the overlap effect of the total axial force N and the moment Maf formed by the axial force. However, on the extraction side, the reduction effect of N and Maf cancels out and is almost the same as the original value.

The fact that the maximum compression axial force is reduced to about ½ means that the initial set value τ _ZO of the peripheral surface friction force τ _Z and the distribution range are compared with the average axial force almost half of the maximum pile reaction force. This is because the acting frictional force is set as τ _ZN = τ _Zφ = τ _ZO / 2. As described above, according to the design method of the present invention, the influence of the peripheral frictional force can assume its main effect at the initial setting stage, and the handling method is simple and clear.

  FIG. 21 compares the horizontal displacement of the piles. The horizontal displacement of the pile head has decreased from 3.9 mm to 3.5 mm (90%). The point above the depth of 0 m is obtained by adding the rotational horizontal displacement of the footing to the pile head displacement. The rotation angle of the footing is reduced to 70% like the vertical displacement. As for the effect on the superstructure, the effect of this rotation angle is greater than the amount of decrease in vertical and horizontal displacement.

  Thus, according to the method of the present invention, it is easy to verify the effect of the peripheral friction force initially assumed, and considering the peripheral friction force of the pile, it is simple that there is an effect of reducing the axial force of the pile as set. Can be handled by calculation formula. Therefore, the pile material design can be made more economical by appropriately estimating the peripheral frictional force for good ground.

In this example, the actual working friction force was set to be small, but according to the design guideline for steel pipe soil cement piles (Non-Patent Document 6), the design maximum peripheral surface friction force is shown in FIG. 22 ((a) sandy soil, (b) viscous viscosity. (Sat) The maximum value is 200 KN / m ² for both sandy and cohesive soils, which is 13.6 times the value of this example (14.7 KN / m ² ). According to FIG. 22, the peripheral frictional force can be sufficiently expected even in the formation where the N value is around 10, and when the action area is large, the maximum axial force of the pile is about ½ as in this example.

In this example, the actual action values (τ _ZN , τ _Zφ ) of the peripheral surface friction force are set to the same value, but there are various ways of using them depending on the condition of the action load. For example, the load at the time of an earthquake at level 2 does not change much in the value of the vertical force Vo compared to the load at level 1, but the horizontal force Ho and the moment Mo change greatly. _Assuming that the maximum allowable value of the circumferential frictional force τ _Z is τ _ZSA, τ _ZSA is adopted as τ _Z in this case. Greater skin friction is also tau _ZN the working frictional force acting in the intermediate layer as tau _{ZSA / 2,} there is a case where the frictional force tau _ZN to digest the axial force caused by vertical forces Vo. Since the balance equation (29) disappears deeper than that, the function as τ _Zφ = τ _ZSA remains while τ _Z = τ _ZSA is working. The _{fact that} the value of τ _Zφ suddenly changes from τ _ZSA / 2 to τ _ZSA does not match the actual situation, so the vertical force Vo and other sharing ratios are roughly set for the maximum axial force at the final load and maximized. It is conceivable to share the allowable value τ _ZSA .

This is the ultimate load condition, but in the case of strong winds that occur frequently and during earthquakes of level 1, the allowable peripheral friction force τ _ZA and the initial friction force τ _ZO equivalent to the average axial force are used as a guide. In consideration of the axial force contribution ratio of the external force load, the usage of the actual action values (τ _ZN , τ _Zφ ) of the peripheral surface friction force is devised. Deciding how to use the actual action values (τ _ZN , τ _Zφ ) of the peripheral frictional force is a new research subject for ground evaluation, but it can be handled considering the above as a guideline for operation. .

  When the ground is not soft, cast-in-place piles and steel pipe soil cement piles with pile lengths exceeding 20 m can be economically designed by considering the effect of peripheral friction, and the longer the pile length, the more effective It is thought to grow. Furthermore, the effect becomes very large if it is devised to appropriately evaluate the ground for temporary loads such as seismic loads.

Explanatory drawing of the pile foundation model of a road bridge specification. Explanatory drawing of the pile foundation model of design standard, such as a railway structure. Explanatory drawing which shows three types of cross-sectional force and deformation | transformation of a member element. Explanatory drawing which shows four types of cross-sectional force and deformation | transformation of a member assembly. Explanatory drawing which models many members into one equivalent member. Explanatory drawing of a global coordinate and a local coordinate. Explanatory drawing of the cross-sectional force and assumed direction of a member element. Explanatory drawing of the display content of a deformation model and a displacement function. System diagram of the design method. Explanatory drawing of the state which a circumferential surface friction force works according to three types of deformation components. Explanatory drawing of the distributed frictional force with respect to axial deformation. Explanatory drawing of the distributed frictional force with respect to the deformation | transformation by the moment which axial force makes. Explanatory drawing of the expansion-contraction state and distributed frictional force of the surface by member bending deformation. Explanatory drawing of the assumption direction of the displacement field and section force of member elements i and j. Explanatory drawing of the state where distributed frictional force (tau) _Zphi is uniformly distributed. Explanatory drawing of the state in which distributed friction force becomes τ _Zφ in proportion to the distance from the center. Comparison chart of vertical displacement distribution. Comparison diagram of total axial force distribution N. The comparison figure of distribution of moment Maf which axial force makes, and all moments. The comparison figure of axial force distribution of a pile. Comparison diagram of horizontal displacement distribution of pile and horizontal displacement and inclination of footing. Relationship diagram between peripheral friction force and N value (steel pipe soil cement pile).

Explanation of symbols

Mi: bending moment of the sectional force of the member i,
Ni: axial force of the sectional force of the member i,
Qi: Shear force of the sectional force of the member i,
Msb: Sum of member moments of cross-sectional force of member assembly,
Maf: sum of moments formed by member axial forces of the member assembly,
N: Sum of member axial forces of the member assembly,
Q: Sum of member shear force of member assembly,
Ag: total cross-sectional area of the member assembly,
Ip: the sum of the moments of section of the members of the member assembly,
Ig: Sum of moments of section formed by the member section with respect to the center of the assembly,
E, G: Young's modulus of member, shear elastic modulus,
xi: distance between the member assembly center line and the center of the member i,
Σ: represents the sum of all n members,
X, Z, ξ, ζ: global coordinate system and local coordinate system,
ui, wi: Displacement components of the arbitrary point i in the X-axis and Z-axis directions (ui≈uo),
uo, wno: the displacement component in the X-axis and Z-axis directions of the point o of the aggregate center line,
φ: rotation angle of the entire cross section due to the overall bending deformation,
θmo, θmi: The amount excluding the angle φ by the rotation angle due to the influence of bending deformation of the member at the center line point o and the arbitrary point i (θmi≈θmo),
Δ: micro amount of variable,
': Differential in the Z-axis direction,
Vo, Mo, Ho: Vertical force, moment, horizontal force, acting force on the bottom of the footing,
qi, q: horizontal distribution external force and its sum in all cross sections (q = Σqi),
a: correction coefficient for Kh and B,
B: Reference width of the surface on which the horizontal ground reaction force acts,
Kh: Typical horizontal ground reaction force coefficient of the stratum,
k _H , k _HE : horizontal ground reaction force coefficient,
k _V : vertical ground reaction force coefficient,
k _SV : Shear ground reaction force coefficient of pile circumference,
K _V , K _VE : Axial spring constant of the pile head,
Ui, ri: circumference of member i, radius,
xe: the distance between the member assembly center line and the center of the outer member,
τ _Z : peripheral frictional force of the pile working at depth Z,
_τZN : peripheral frictional force acting on axial displacement wno,
τ _Zφ : peripheral frictional force acting on displacement due to the overall rotation angle φ,
τ _Zθ : peripheral frictional force acting against deformation due to member rotation angle (φ + θmo),
τ _ZO : Initially set peripheral surface friction force equal to or less than the friction force corresponding to the vertical force Vo,
τ _ZA : Permissible circumferential frictional force of the pile,
τ _ZSA : Maximum allowable peripheral friction force of the pile,
ω: the parameter of the angle in the derivation or solution of the equation,
α: α = β (1 + Ψ) ^1/2 or r ^1/4 cos (ω / 2),
β: β = (aKhB / 4EIp) ^1/4 or r ^1/4 sin (ω / 2),
η: η = β (1−Ψ) ^1/2 and Ψ <1,
Ψ: Ψ = (aKhB · EIp) ^1/2 / 2GAg,
F _A : F _A = Στ _ZN Ui / EAg,
F _G : F _G = Στ _Zφ Ui | xi | / EIg
or Στ _Zφ Uixi ² / xeEIg,
F _T : F _T = πΣτ _Zθ · ri ³ / EIp,
F _P : F _P = GAg / EIp,
F _K : F _K = aKhB / GAg,
k ₁ : k ₁ = (1−F _K / r ^1/2 ) α,
k ₂ : k ₂ = (1 + F _K / r ^1/2 ) β,
p: p = F _T + F _K ,
r: r = (F _P + F _T ) F _K and p ² −4r <0,
cosω = p / 2r ^1/2 and sinω = (4r−p ² ) ^1/2 / 2r ^1/2

Claims (2)

A design method of pile foundation consisting of a number of stake member, resilient spring in the support model, three deformation component (axial deformation distribution skin friction tau _Z acting on the stake member are a number of member groups causes, It is divided into three kinds of working methods (τ _ZN , τ _Zφ , τ _Zθ ) based on total bending deformation and member bending deformation, and a design calculation formula is obtained from a balance formula for each resultant force of each sectional force component A pile foundation design method consisting of a large number of pile members. A design method of pile foundation consisting of a number of stake member, resilient spring in the support model, three deformation component (axial deformation distribution skin friction tau _Z acting on the stake member are a number of member groups causes, It is divided into three types of working methods (τ _ZN , τ _Zφ , τ _Zθ ) based on total bending deformation and member bending deformation, and each of the two types of working methods (τ _ZN , τ _Zφ ) A design method for pile foundations consisting of a large number of pile members, characterized in that a design calculation formula is obtained from the balance formula for each resultant force.

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