JP4828975B2 - Pile foundation analysis device - Google Patents

Description

  The present invention relates to a pile foundation analysis technique.

  Conventionally, joints between piles and foundations (pile caps, etc.) of pile foundation structures have been designed and constructed to approach rigid joints (fixed joints). However, by making the pile head joints rigid, the pile head bending moment at the time of an earthquake increases, and the possibility that the pile head will break during a large earthquake increases. For this reason, in recent years, pile head joint structures have been developed in which the pile head joint is not rigidly joined, such as pin joint or semi-rigid joint. By not making the pile head joint rigid, the pile head bending moment can be reduced, and as a result, advantages such as improvement of the seismic performance of the pile foundation and rationalization of the foundation can be obtained.

  Pile head joint methods that are not currently rigidly developed include specially designed semi-rigid joints by mechanically aiming for a pin structure or by interposing a cushioning material such as rubber between the pile head and the foundation. Some devices use simple devices. Pile head joining methods using special devices are high performance but costly. As a semi-rigid joining method of a pile head that does not use a special device, for example, as disclosed in Patent Document 1, there is basically a joining method in which a foundation is placed on the pile head. Such a pile head joining method is excellent in cost performance and is a practical semi-rigid joining method of pile heads. By adopting a pile head joining method that is not rigidly connected, it is possible to expect benefits such as improving the seismic performance of the pile foundation and rationalizing the foundation as described above, but in order to achieve this, the seismic design of the pile foundation structure At this stage, it is necessary to examine the stress deformation state of the pile in consideration of the rotation of the pile head joint.

  As a method of analyzing the stress deformation state of a pile, a method is to analytically calculate by creating a frame analysis model by replacing the pile with a beam element, the ground with a spring element, and the pile head joint with a rotary spring element. is there. This method can also analyze pile foundations in multi-layered ground. In addition, as another method for analyzing the stress deformation state of the pile, it is assumed that the ground is uniform, but there is a method of analyzing by the beam theory on the single-layer elastic bearing using the pile head fixing degree.

JP 2004-162259 A "Application example of semi-rigid joint of pile heads for ready-made concrete piles", Building Technology, September 2005, pages 162-163

  The analysis using the frame analysis model requires the construction of a frame analysis model and the use of an expensive frame analysis program, and is not suitable for small and medium-scale seismic design. In the method of analysis by the beam theory on single-layer elastic bearing using pile head fixing degree, it is important to set the pile head fixing degree accurately. However, when the pile head is semi-rigid, the pile head fixing degree changes due to the influence of horizontal force, axial force, pile diameter, ground condition, etc. It cannot be set accurately. As described above, structural experiments and numerical analysis require a great deal of labor and cost, and it is the actual situation that general structural designers cannot implement seismic design with high accuracy by this method. Further, in the analysis by the finite element method, an approximate solution can be obtained but a theoretical solution cannot be obtained.

  Accordingly, an object of the present invention is to provide an analysis apparatus that can easily and accurately analyze a pile foundation in consideration of rotation of a pile head.

  According to the first aspect of the present invention, the input means for receiving input of a predetermined analysis condition by the user, the rotational rigidity temporary setting means for temporarily setting the rotational rigidity of the pile head based on the analysis condition, and the analysis condition A fixing degree calculating means for calculating a fixing degree of the pile head with respect to a foundation based on the temporary setting value of the rotating rigidity temporarily set by the rotating rigidity temporary setting means, the analysis condition, and the fixing degree calculation. Based on the fixed degree calculated by the means, a physical quantity calculating means for calculating a physical quantity of a predetermined pile head, the physical quantity calculated by the physical quantity calculating means, a predetermined bending moment and rotation of the pile head Consistency determining means for determining consistency between the M-θ function indicating the relationship of the angle as a function, and when the consistency is affirmed by the consistency determining means, the analysis condition and the fixing degree calculating means Calculated by If the consistency is denied by the analysis result calculation means for calculating a predetermined physical quantity related to the stress deformation state of the pile as an analysis result based on the fixed degree and the consistency determination means, the consistency is positive Re-setting means for resetting the temporary setting value of the rotational stiffness so as to calculate the fixed degree and the physical quantity of the pile head by changing the temporary setting value of the rotational stiffness until it is An analysis device for pile foundations is provided.

  According to the first aspect of the present invention, the user can obtain a theoretical solution based on the pile head fixing degree as an analysis result simply by inputting an analysis condition. An unknown number of pile head fixations is set by introducing the rotational stiffness of the pile heads into the convergence calculation and taking the consistency between the physical quantity calculation results based on the pile head fixation and the M-θ function. Setting conditions and calculation processing can be simplified compared to conventional analysis methods using an element method or the like. Therefore, it is possible to easily and accurately analyze the pile foundation considering the rotation of the pile head.

  According to the second aspect of the present invention, in a pile foundation analyzing apparatus for analyzing a pile foundation in which piles are embedded in a multi-layered ground, an input means for receiving an input of a predetermined analysis condition by a user, and the analysis condition A rotational stiffness temporary setting means for temporarily setting the rotational stiffness of the pile head, a characteristic value calculating means for calculating a characteristic value of the ground and the pile for each layer of the multilayer ground based on the analysis condition, and the multilayer ground An unknown number of equations that define the displacement, rotation angle, shear force and bending moment of the pile based on the beam theory on the elastic bearing according to the part of the pile inside is set by the analysis condition and the rotational stiffness temporary setting means The temporarily set value of the rotational rigidity, the characteristic value calculated by the characteristic value calculating means, a predetermined boundary condition of the pile head, a boundary condition of the pile tip, and a continuous condition between the layers of the multilayer ground , Based on An unknown quantity calculating means, a physical quantity calculating means for calculating a physical quantity of a predetermined pile head based on the equation substituted with the unknown quantity calculated by the unknown quantity calculating means, and the physical quantity calculated by the physical quantity calculating means And the consistency determination means for determining the consistency between the predetermined bending moment and the rotation angle of the pile head and the M-θ function as a function, and when the consistency is affirmed by the consistency determination means On the basis of the equation in which the unknown value calculated by the unknown value calculation means is substituted, at least one of the displacement, rotation angle, shear force, and bending moment of the pile according to the part of the pile in the multilayer ground When the consistency is denied by the analysis result calculation means for calculating the analysis result and the consistency determination means, the temporary setting value of the rotational rigidity is set until the consistency is affirmed. In order to calculate the unknown quantity and the physical quantity of the pile head in a different manner, there is provided a pile foundation analyzing apparatus comprising resetting means for resetting the temporary setting value of the rotational rigidity.

  The second aspect of the present invention is based on a novel idea of applying a beam theory on an elastic bearing to a multi-layer ground and introducing a rotational rigidity of a pile head to derive a theoretical solution. According to the second aspect of the present invention, the user can obtain the theoretical solution based on the equation defined based on the beam theory on the elastic bearing for the rotational rigidity of the pile head joint as the analysis result simply by inputting the analysis conditions. The rotational stiffness of the pile head joint is set by convergence between the physical quantity calculated based on the beam theory on the elastic bearing and the M-θ function of the pile head joint. As compared with the conventional analysis method using a method or the like, it is possible to simplify the setting of conditions and calculation processing. Therefore, the analysis of the pile foundation in consideration of the rotation of the pile head, in particular, the analysis of the pile foundation for the multilayer ground can be performed easily and accurately.

  In the second aspect of the present invention, the pile foundation analyzing apparatus analyzes for each of a plurality of groups of piles, and the physical quantity calculating means is the equation in which the unknown number calculated by the unknown number calculating means is substituted. Calculated as a physical quantity of the pile head by multiplying the value calculated based on the analysis condition and the correction coefficient calculated based on the equation in which the unknown number calculated by the unknown number calculation unit is substituted, The analysis result calculation means is calculated based on the equation in which the unknown value calculated by the unknown value calculation means is substituted, and the displacement, rotation angle, and shear force of the pile according to the part of the pile in the multilayer ground. Further, it is possible to employ a configuration in which a value obtained by multiplying at least one of the bending moment by the correction coefficient is calculated as the analysis result.

  In the first and second aspects of the present invention, the physical quantity calculating means calculates a rotation angle of the pile head as the physical quantity of the pile head, and the consistency determining means is the pile head calculated by the physical quantity calculating means. Consistency is determined based on the rotational stiffness of the pile head calculated based on the rotational angle of the pile and the M-θ function, and the temporary setting value, and the resetting means is calculated by the physical quantity calculating means It is possible to adopt a configuration in which the rotational rigidity calculated based on the rotation angle of the pile head thus made and the M-θ function is reset as the temporary setting value.

  In the first and second aspects of the present invention, the M-θ function can be a hyperbolic function defined by the initial rotational stiffness and maximum resistance moment of the pile head calculated by the analysis conditions. .

  In addition, according to the third aspect of the present invention, there is provided a pile foundation analysis program that causes a computer to function as each of the above-described means.

  According to the present invention, it is possible to easily and accurately analyze a pile foundation in consideration of rotation of a pile head.

<Analyzer configuration>
FIG. 1 is a block diagram showing an example of an analysis apparatus (computer system) according to an embodiment of the present invention. The analysis apparatus of the present invention can be executed by a general-purpose computer system as shown in FIG. 1 includes a CPU 101 that executes an analysis program to be described later, a RAM 102 that temporarily stores data and programs processed by the CPU 101, a ROM 103 that stores data and programs executed by the CPU 101, and an OS (operation system). ) And a program such as an analysis program described later, and a hard disk 104 storing data such as parameters input by the user as analysis conditions. It goes without saying that other types of storage means can be adopted as these storage means.

  An input interface (hereinafter referred to as I / F) 105 is an interface for accepting user input of predetermined analysis conditions necessary for analysis of pile foundations, processing instructions, and the like, to which input devices such as a mouse and a keyboard are connected. . A display I / F 106 is an interface for displaying a GUI screen and an analysis result when a user inputs analysis conditions on the display 107.

<M-θ relationship by hyperbolic function>
In the present embodiment, two methods are proposed, when the ground is handled as a uniform ground and when it is handled as a multi-layered ground. Both methods use a function indicating the rotational properties (M-θ relationship) of the pile head joint. Various functions have been proposed. In this embodiment, the function is defined by a hyperbolic function based on the initial rotational rigidity and maximum resistance moment of the pile head. By defining the M-θ relationship of the pile head with a hyperbolic function, the M-θ relationship of the pile head can be more easily set for analysis, and according to the experiment conducted by the inventors, The M-θ relationship is accurately reproduced. FIG. 2 is an explanatory diagram of the M-θ relationship of the pile head based on the hyperbolic function.

In FIG. 2, Formula 1-1 is a basic formula showing a function of the M-θ relationship of the pile head in the present embodiment, and is a hyperbolic function having the initial rotational stiffness K ₀ and the maximum resistance moment M _{max of} the pile head as parameters. is there. The initial rotational rigidity K ₀ is calculated by the equation 1-2 in FIG. As shown in FIG. 3A, the initial rotational rigidity K ₀ is obtained by an elastic theory by regarding the pile cap concrete constituting the foundation as a semi-infinite elastic body. The maximum resistance moment _Mmax is assumed to be equal to the maximum eccentric moment due to the axial force N of the pile, and is calculated by Equation 1-3 in FIG.

<Analysis method 1>
First, an example of an analysis method when handling the ground as a uniform ground will be described. In the analysis method 1, the pile head fixing degree α is introduced into the beam theory on the elastic bearing to obtain the stress deformation state of the pile in consideration of the rotation of the pile head joint. FIG. 3B is a diagram showing an outline of the bending moment distribution of the pile according to the pile head fixing degree α and the depth of the ground.

  The pile head fixing degree α is 1.0 when the pile head joint is completely fixed (pile head rigid joint), and 0.0 when the pile head pin joint is used. [Alpha] is a value between 0.0 and 1.0. The calculation formula of the physical quantity regarding the stress deformation state of the pile using the pile head fixing degree α can be expressed by Formula 2-1 to Formula 2-6 in FIG. If the pile head fixing degree α can be set appropriately, the stress deformation state of the pile considering the rotation of the pile head can be calculated by these equations. Equations 2-1 to 2-6 in Fig. 4 are equations assuming that the ground is uniform in the depth direction and the pile length is infinitely long. In this case as well, the analysis method 1 of the present embodiment can be applied.

Here, the pile head fixing degree α and the rotational stiffness (secant stiffness) K _θ of the pile head joint have a relationship of Equation 3-1 in FIG. Accordingly, the rotational stiffness K _θ corresponding to the horizontal force H acting on the pile is obtained from the M-θ relationship of the pile head joint by the hyperbola function described above, and this is substituted into Equation 3-1, so that the pile head fixing degree α Can be determined appropriately. However, as shown in the M-θ relationship of the pile heads by the hyperbolic function, the M-θ relationship of the pile head joints shows non-linear properties. Therefore, in order to obtain the rotational rigidity K _θ according to the horizontal force H, convergence is required. Calculation is required. Hereinafter, an example of the analysis program of the analysis method 1 will be described with reference to FIG. FIG. 6 is a flowchart showing an example of an analysis program based on the analysis method 1, which is executed by the CPU 101.

  In S <b> 1, user input of predetermined analysis conditions relating to a pile foundation to be analyzed, a horizontal force acting on a building supported by the pile foundation, and a ground on which the pile is embedded is received, and the input analysis conditions are input to the hard disk 104. Save the file. In this embodiment, a case where a plurality of piles are grouped and analyzed will be described. This corresponds to the case where the axial force and the bending stiffness of the pile are different depending on the pile placement site. Pile grouping can be a group of piles that can be considered to have the same bending rigidity and axial force. Of course, this grouping is not necessary if all stakes can be considered equally.

FIG. 7 is a diagram showing an example of parameters input by the user as analysis conditions. First, as common parameters, the total horizontal force H _all acting on building pile foundation is analyzed to support, the Young's modulus of the ground that the pile is embedded E _g, the horizontal subgrade reaction coefficient k _h threshold and this There are threshold values 1 and 2 for determining consistency between a calculation result based on a pile head displacement threshold value δ and a pile head fixing degree α, which are parameters to be calculated, and a pile head M-θ relationship based on a hyperbolic function.

The pile head displacement threshold δ is set to, for example, about several mm to 1 cm. Next, the outer diameter D and inner diameter d (0 in the case of a solid pile), Young's modulus E, sectional secondary moment I, the number n of piles in the group, and piles are connected as parameters for each group. There are Young's modulus E _p of pile cap concrete, Poisson's ratio ν, and axial force N of pile. Of these, general parameters can be set to default values.

Returning to FIG. 6, in S <b> 2, the initial rotational stiffness K ₀ of the pile head is calculated for each group and stored in the hard disk 104. The initial rotational stiffness K ₀ is calculated by the equation 1-2 by reading out the outer diameter D and inner diameter d of the pile inputted in S1, the Young's modulus E _p of the pile cap concrete joined to the pile, and the Poisson's ratio ν.

In S3, the maximum resistance moment M _max of the pile head is calculated for each group and stored in the hard disk 104. The maximum resistance moment M _max is calculated by reading the outer diameter D of the pile and the axial force N of the pile input in S1, and using Equation 1-3.

In S 4, the horizontal ground reaction force coefficient k _h is calculated for each group and stored in the hard disk 104. The horizontal ground reaction force coefficient k _h is calculated from the pile head displacement threshold value δ input in S1 and based on this and the reference value k _{h0 according to} the expression 3-3-1. The reference value k _h0 can be appropriately set by the designer according to the Young's modulus E _{g of the} ground. In the present embodiment, the reference value k _h0 is calculated by an expression 3-3-3 as an example of calculation. Thus, the horizontal subgrade reaction coefficient k _h in this embodiment reads the outer diameter D of the Young's modulus E _g, pile head displacement threshold δ and piles of ground input in S1, is calculated by the equation 3-3-1.

In S5, rotational rigidity is temporarily set for each group. Specifically, the initial rotational stiffness K ₀ calculated in S2 is set as the value of the rotational stiffness K _θ1 temporarily set for each group. In S6 sets the horizontal subgrade reaction coefficient k _h calculated in S4 as the value of the horizontal subgrade reaction k _h1 provisionally set for each group.

In S 7, the ground and pile characteristic value β is calculated for each group and stored in the hard disk 104. The characteristic value β is calculated from the horizontal ground reaction force coefficient k _h set in S6 and the pile outer diameter D, Young's modulus E, and cross-sectional secondary moment I input in S1, and calculated by Expression 2-7. In S8, the pile head fixing degree α is calculated for each group and stored in the hard disk 104. The pile head fixing degree α is obtained by reading the rotational stiffness K _θ 1 set in S5, the characteristic value β calculated in S7, and the Young's modulus E and the secondary moment I of the cross-section input in S1, and calculating by the formula 3-1. .

In S <b> 9, the horizontal force H acting on a single pile is calculated for each group and stored in the hard disk 104. The horizontal force H is calculated by Expression 3-4-1 and Expression 3-4-2. First, the rotational stiffness K _θ1 set in S5, the characteristic value β calculated in S7, the outer diameter D of the pile input in S1, the Young's modulus E, the secondary moment I of the section, and the number n are read out. The total horizontal force H _all is distributed to each group by 4-2, and the horizontal force H ′ for each group is calculated. Next, the horizontal force H ′ is calculated by dividing the horizontal force H ′ by the number of piles in the group according to Equation 3-4-1.

  In S 10, the pile head displacement y is calculated for each group and stored in the hard disk 104. The pile head displacement y is obtained by reading the horizontal force H calculated in S9, the pile head fixing degree α calculated in S8, the characteristic value β calculated in S7, and the Young's modulus E and the secondary moment I of the cross section input in S1. Calculated according to Equation 2-3.

Step S11 for each of the groups to recalculate the horizontal subgrade reaction coefficient k _h, it is stored in the hard disk 104 as a horizontal subgrade reaction coefficient k _h2. The horizontal ground reaction force k _h2 has a different calculation formula depending on whether or not the pile head displacement y calculated in S10 is larger than the pile head displacement threshold value δ input in S1. When the value is equal to or less than the pile head displacement threshold value δ, the value is calculated by Expression 3-3-1. Note that these equations are exemplary, calculation of horizontal subgrade reaction coefficient k _h is not limited to this. In addition, parameters necessary for calculation are read from the hard disk 104.

In S12, a predetermined physical quantity of the pile head is calculated. In the present embodiment, the physical quantity is the rotation angle θ _α of the pile head, and is calculated for each group and stored in the hard disk 104. The rotation angle θ _α reads the horizontal force H calculated in S9, the pile head fixing degree α calculated in S8, the characteristic value β calculated in S7, and the Young's modulus E and the secondary moment I of the cross section input in S1. Calculated according to Equation 2-2.

In S13 to S15, S12 calculated rotation angle theta _alpha performs processing relating to consistency determination of whether to match the M-theta relationship pile head according to hyperbolic functions. First, calculate the rotational stiffness K _theta and a M-theta relationship pile head by the rotation angle theta _alpha and hyperbolic functions calculated in S12, S13, it is stored in the hard disk 104 as a K _.theta.2. K _θ2 is calculated from the initial rotational stiffness K ₀ calculated in S2, the maximum resistance moment M _max calculated in S3, and the rotation angle θ _α calculated in S12, and is calculated by Expression 3-2-1.

In S14, the horizontal ground reaction force coefficient k _h1 and horizontal ground reaction force coefficient k _h2 and the matching threshold value 1 input in S1 are read out for each group, and the horizontal ground reaction force coefficient k _h1 and horizontal ground reaction force coefficient k _h2 are obtained. Is determined to be approximate. If all groups are approximated, the process proceeds to S15, and if any group is not approximated, the process proceeds to S17. For example, in the case of k _h1 / k _h2 <matching threshold 1, it is determined that the approximation is made, and the matching threshold 1 is set to about 0.95, for example.

In S15 the rotational stiffness K _.theta.1 and rotational stiffness K _.theta.2 reads the matching threshold 2 input in S1, it is determined whether or not the rotational stiffness K _.theta.1 and rotational stiffness K _.theta.2 are close. If it is approximated in all groups, the process proceeds to S16 because the consistency is affirmed. If not approximated in any group, the process proceeds to S17 because the consistency is denied. For example, it is determined that the approximation is approximated when K _θ1 / K _θ2 <matching threshold 2 and the matching threshold 2 is set to about 0.95, for example.

In S16, a physical quantity related to the stress deformation state of the pile is calculated based on the pile head fixing degree α calculated in S12. This is the analysis result. As physical quantities to be calculated, pile head bending moment M _α , pile head rotation angle θ _α , pile head displacement y, and maximum bending moments M _gmax and M _gmax in the underground are shown in equations 2-1 to 2-6. L _m and first dissimilarity depth L ₀ , and parameters necessary for the calculation are appropriately read from the hard disk 104. The user who is a structural designer examines the analysis result, and if the analysis result satisfies the design criteria, the design will be completed. Conversely, if you are not satisfied, you will be redesigned.

Next, in S17, the horizontal ground reaction force coefficient and rotational rigidity are reset. Here, for each group, the value of the horizontal ground reaction force coefficient k _h2 is set to k _h1 and the value of the rotational stiffness K _θ2 is set to the rotational stiffness K _θ1 , and the process returns to S7. Thereafter, the processes of S7 to S15 and S17 are repeated until it is determined that the approximation is made in S15. That is, convergence calculation is performed until the calculation result by the pile head fixing degree α matches the pile head M-θ relationship by the hyperbolic function.

  Thus, in the analysis method 1, the user can obtain a theoretical solution based on the pile head fixing degree as an analysis result only by inputting the analysis conditions. An unknown number of pile head fixations is set by introducing the rotational stiffness of the pile heads into the convergence calculation and taking the consistency between the physical quantity calculation results based on the pile head fixation and the M-θ function. Setting conditions and calculation processing can be simplified compared to conventional analysis methods using an element method or the like. Therefore, it is possible to easily and accurately analyze the pile foundation considering the rotation of the pile head.

In the analysis program shown in FIG. 6, the pile head rotation angle θ _α is calculated based on the pile head fixing degree α in S12, but the pile head bending moment M _α may be calculated. In this case, the rotational rigidity _{Kθ2 in} S13 may be obtained from Equation 3-2-2.

<Other examples of analysis method 1>
The analysis program of FIG. 6 has a processing for changing the horizontal subgrade reaction coefficient k _h. This is because the horizontal elastic deformation of the ground is not necessarily linear, and the elastic property varies depending on the amount of horizontal displacement, and a more accurate analysis is possible. However, when the analysis accuracy is not so high, the horizontal elastic deformation of the ground is regarded as linear, and the horizontal ground reaction force coefficient k _h can be set to a fixed value.

In addition, in the analysis program of FIG. 6, the consistency between the pile head rotation angle θ _α calculated based on the pile head fixing degree α and the M-θ relation of the pile head by the hyperbolic function was determined by the rotational stiffness K _θ. It can also be determined by moment. Hereinafter, an example of an analysis program employing these will be described with reference to FIG.

  In S21, user input of predetermined analysis conditions relating to the pile foundation to be analyzed, the horizontal force acting on the building supported by the pile foundation, and the ground on which the pile is embedded is received, and the input analysis conditions are stored in the hard disk 104. Save the file. In this embodiment, a case where a plurality of piles are grouped and analyzed will be described.

  The parameters that the user inputs as analysis conditions are basically the same as those shown in FIG. 7, but in the case of this analysis program, the pile head displacement threshold δ and the matching threshold 1 are not required.

In S 22, the initial rotational stiffness K ₀ of the pile head is calculated for each group and stored in the hard disk 104. This is the same processing as S2 in FIG. In S 23, the maximum resistance moment M _max of the pile head is calculated for each group and stored in the hard disk 104. This is the same processing as S3 in FIG. In S 24, the horizontal ground reaction force coefficient k _h is calculated for each group and stored in the hard disk 104. Although the process is the same as S4 in FIG. 6, in this example, since the horizontal elastic deformation of the ground is not considered to be non-linear, the horizontal ground reaction force coefficient k _h is calculated from the reference value k _h0 of Equation 3-3-3. Set as follows.

k _h = k _h0
In S25, the rotational rigidity is provisionally set for each group. In particular, it sets an initial rotational stiffness K ₀ calculated in S22 as the value of rotational stiffness K _theta provisionally set for each group.

  In S 26, the ground and pile characteristic value β is calculated for each group and stored in the hard disk 104. This is the same processing as S7 in FIG. In S27, the pile head fixing degree α is calculated for each group and stored in the hard disk 104. This is the same processing as S8 in FIG. In S <b> 28, the horizontal force H acting on a single pile is calculated for each group and stored in the hard disk 104. This is the same processing as S9 in FIG.

In S29 and S30, a predetermined physical quantity of the pile head is calculated. In the present embodiment, the physical quantities are the pile head rotation angle θ _α and the pile head bending moment M _α . First, in S 29, the rotation angle θ _{α of the} pile head is calculated for each group and stored in the hard disk 104. The rotation angle θ _α reads the horizontal force H calculated in S28, the pile head fixing degree α calculated in S29, the characteristic value β calculated in S26, and the Young's modulus E and the secondary moment I of the cross section input in S1. Calculated according to Equation 2-2. In S 30, the pile head bending moment M _α is calculated for each group and stored in the hard disk 104. Bending moment M _alpha reads the pile head fixed degree alpha and characteristic values calculated in S26 beta calculated in the horizontal force H and S29 calculated in S28, the calculated by the equation 2-1.

In S31 and S32, processing related to consistency determination as to whether or not the rotation angle θ _α calculated in S29 and the bending moment M _α calculated in S30 match the M-θ relationship of the pile head by a hyperbolic function is performed. In S <b> 31, the pile head bending moment M _f is calculated from the rotation angle θ _α calculated in S <b> 29 and the pile head M-θ relationship based on the hyperbolic function, and stored in the hard disk 104. The bending moment M _f is calculated by the equation 1-1 by reading out the initial rotational stiffness K ₀ calculated in S22, the maximum resistance moment M _max calculated in S23, and the rotation angle θ _α calculated in S29.

In S32, the pile head bending moment M _α , the pile head bending moment M _f and the matching threshold value 2 input in S1 are read out, and it is determined whether or not the pile head bending moment M _α and the pile head bending moment M _f are approximate. judge. If it is approximated in all groups, the process proceeds to S33 because the consistency is affirmed, and if not approximated in any group, the process proceeds to S34 because the consistency is denied. For example, it is determined that the approximation is approximated when M _α / M _f <matching threshold 2 and the matching threshold 2 is set to about 0.95, for example.

In S33, a physical quantity related to the stress deformation state of the pile is calculated based on the pile head fixing degree α calculated in S27. This is the same processing as S16 in FIG. 6, and this is the analysis result. In S34, a rotational rigidity resetting process is performed. Here, the rotational stiffness K _θ is read out from the initial rotational stiffness K ₀ calculated in S22, the maximum resistance moment M _max calculated in S23, and the bending moment M _f calculated in S31. calculate. The calculated rotational stiffness _Kθ is stored in the hard disk 104, and the process returns to S27.

Thereafter, the processes of S27 to S32 and S34 are repeated until it is determined that the approximation is made in S32. That is, convergence calculation is performed until the calculation result by the pile head fixing degree α matches the pile head M-θ relationship by the hyperbolic function. In the analysis program of FIG. 8, the bending moment M _f is calculated in S31, but the pile head rotation angle θ _f can also be calculated from the bending moment M _{α according} to Formula 1-1. In this case, performs approximation determination that pile head rotation angle theta _alpha calculated at the pile head rotation angle theta _f and S29 in S32, calculates the rotational stiffness K _theta from pile head rotation angle θf by the S34 Formula 3-2-1 Will do.

<Analysis method 2>
Next, a case where the ground is handled as a multilayer ground will be described. FIG. 9 is an explanatory diagram of a pile foundation in the multilayer ground to be analyzed by the analysis method 2. Analysis method 2 is based on the new idea of applying the beam theory on elastic bearings to multi-layered ground and introducing the rotational rigidity of the pile head to this to derive the theoretical solution. By setting the boundary conditions in consideration, the stress deformation state of the pile considering the rotation of the pile head is analyzed with high accuracy.

In the example of FIG. 9, the ground is a k-layer multilayer ground, and piles are continuous in the multilayer ground. The thickness L indicates the thickness (depth) of each layer, and x indicates the depth from the upper end of each layer. Assuming that the characteristics of the ground are uniform in each layer, the characteristic value β of the ground and the pile is set for each layer. When the beam theory on elastic bearings is applied to the multi-layer ground, the stress deformation state of the pile cannot be expressed by a simple calculation formula using the pile head fixing degree α as in Analysis Method 1. From theory, it can be expressed by a general solution by an equation such as Equation 4-1 in FIG. In Formula 4-1, i indicates a layer number, which are 1, 2, and 3 in order from the upper layer, and the lowest layer is k. Incidentally, the horizontal subgrade reaction coefficient k _h in this example is a fixed value (in this example using Equation 4-3.).

The horizontal displacement, rotation angle, bending moment and shear force of the pile at an arbitrary depth x _i in each layer can be expressed by Equation 4-1. In Equation 4-1, the unknown C is the number of layers k × 4. In the case of a three-layer ground, there are 12 unknowns C. In calculating the unknown C, if a conditional expression for the number of layers k × 4 can be set, it can be calculated as a simultaneous equation. Therefore, the continuous condition of the pile, the boundary condition of the pile tip and the pile head are set as conditional expressions.

Equation 4-1 represents the physical quantity of the stress deformation state of the piles in each layer, but since the piles are continuous through each layer, equations 5-1-1 to 5-1 in FIG. -4 can be set. In addition, although the case where a load does not act on the underground part of a pile is illustrated here, ground displacement is introduced into the term of the pile displacement y _i (x _i ) in Formula 5-5-1, and the balance condition is set. It is also possible to consider the case where a load acts on the underground part.

  Next, as a boundary condition of the tip of the pile, for example, when the tip of the pile is a free condition, the bending moment and the shearing force are 0, and Equations 5-2-1A and 5-2-1B in FIG. Can be set. Moreover, when the tip of the pile is set as a fixing condition, the displacement and the rotation angle are 0, and the boundary conditions shown in Expression 5-2-2A and Expression 5-2-2B in FIG. 11 can be set. Furthermore, when the tip of the pile is a pin condition, the displacement and the bending moment are 0, and the boundary conditions shown in Equations 5-2-3A and 5-2-3B in FIG. 11 can be set.

Next, the boundary conditions of the pile head, can set an expression 5-3-1 of Figure 11 from the rotational stiffness K _theta of pile head joint as boundary conditions for the bending moment of pile head joint. When the pile head joint is a rigid joint, [θ _i (x _i )] _{xi = 0} = 0 in Equation 5-3-1, and in the case of a pin joint, [M _i (x _i ) / EI] _{xi = 0} = 0.

Moreover, in addition to Formula 5-3-1, Formula 5-3-2 or Formula 5-3-3 in FIG. 11 can be set as the boundary condition of the pile head. Formula 5-3-2 is set from the viewpoint that the shear force of the pile head is equal to the horizontal force, and the reference horizontal force H _ζ of the pile unit is a parameter set in advance on the program side in order to derive the unknown C It is. Equation 5-3-3 specifies the pile head displacement, and the reference pile head displacement y _ζ is a parameter set in advance on the program side when the unknown C is derived.

Either the reference horizontal force H _{ζ or the} reference pile head displacement y _ζ may be set, but only one of them is set, and the reference horizontal force H _ζ is set to about 100 kN, for example, and the reference pile head displacement y _ζ is About 1 cm is set. When the reference horizontal force H _ζ is set, the boundary conditions of the pile head are expressed by Equations 5-3-1 and 5-3-2. On the other hand, when the reference pile head displacement y _ζ is set, the boundary conditions of the pile head are expressed by Equations 5-3-1 and 5-3-3. In consideration of the analysis accuracy, it is desirable to set the reference pile head displacement y _ζ .

  FIG. 13 is a flowchart showing an example of an analysis program based on the analysis method 2, which is executed by the CPU 101. In S101, the pile foundation to be analyzed, the horizontal force acting on the building supported by the pile foundation, and the user input of the predetermined analysis conditions relating to the ground where the pile is buried are received, and the input analysis conditions are stored in the hard disk 104. Perform the save process. In this example as well, a case where a plurality of piles are grouped and analyzed will be described.

FIG. 14 is a diagram showing an example of parameters input by the user as analysis conditions. First, common parameters include the total horizontal force H _all acting on the building supported by the pile foundation to be analyzed, and the matching threshold.

As for the parameters for each group, the outer diameter D, inner diameter d, Young's modulus E, secondary moment I of the cross section, number of piles n in the group, pile cap concrete Young to be joined to the pile, as in the example of FIG. There is a coefficient E _p , a Poisson's ratio ν, and an axial force N of the pile. The parameters relating to the ground are set for each layer, and include the Young's modulus E _{g of the} ground and the thickness L of the layer. The subscript indicates the layer number.

Returning to FIG. 13, in S <b> 102, the initial rotational stiffness K ₀ of the pile head is calculated for each group and stored in the hard disk 104. This is the same processing as S2 in FIG. In S 103, the maximum resistance moment M _max of the pile head is calculated for each group and stored in the hard disk 104. This is the same processing as S3 in FIG.

In S104, rotational rigidity is temporarily set for each group. Specifically, the initial rotational stiffness K ₀ calculated in S102 is set as the value of the rotational stiffness K _θ1 temporarily set for each group. In S <b> 105, the ground and pile characteristic value β is calculated for each group for each layer and stored in the hard disk 104. The characteristic value β is calculated by Expression 4-2 in FIG. k _h is calculated by Equations 4-3 and 4-4 in FIG. Other necessary parameters are read from the hard disk 104 in the same manner as in the analysis method 1.

In S <b> 106, the unknown C in Expression 4-1 is calculated and stored in the hard disk 104. The unknown C is derived from Expressions 5-1-1 to 5-3-1 and Expression 5-3-2 or Expression 5-3-2 in FIG. As described above, when the reference horizontal force H _ζ is set, Expression 5-3-2 is used, and when the reference pile head displacement y _ζ is set, Expression 5-3-3 is used. Further, the rotational stiffness K _theta in Formula 5-3-1 utilizes reads the rotational stiffness K _.theta.1.

In S107, the correction coefficient G is calculated. In the present embodiment, a pile head rotation angle θ ₁ (0) is calculated as a physical quantity in S108, which will be described later, and processing for determining consistency with the M-θ relationship of the pile head using a hyperbolic function is performed. The correction coefficient G is a coefficient for correcting the value of the pile head rotation angle θ ₁ (0).

In this embodiment, the unknown C is calculated using the reference horizontal force H _ζ or the reference pile head displacement y _ζ. However, when the pile is analyzed in a plurality of groups, the characteristics of the piles in the group units are different. Therefore, it is necessary to redistribute the horizontal force acting on the pile head derived from the reference horizontal force H _ζ or the reference pile head displacement y _{ζ in} units of groups.

That is, the reference horizontal force H _ζ or the reference pile head displacement y _ζ is a provisional value for deriving the unknown C, and the analysis result is corrected by the correction coefficient G according to the total horizontal force H _all input by the user. However, when the grouping of the piles is not performed, it is possible to obtain the analysis result directly without using the correction coefficient G by setting the reference horizontal force H _ζ = H _all / n (the number of piles). .

FIG. 17 is a flowchart illustrating an example of the calculation process of the correction coefficient G. FIG. 12 shows a calculation formula used to calculate the correction coefficient G. The correction coefficient G is an equation of the equation 4-1 in which the analysis condition (mainly the reference horizontal force H _ζ or the reference pile head displacement y _ζ ), the unknown C calculated in S106 and the characteristic value β calculated in S105 are substituted. (Mainly, calculation of horizontal force equivalent to the reference horizontal force H _ζ or pile head displacement equivalent to the reference pile head displacement y _ζ ).

In FIG. 17, in step S _< b> 201, the horizontal stiffness K _H of the pile head for each group is calculated and stored in the hard disk 104. The horizontal rigidity _KH is calculated from the equation 6-1 in FIG. In Expression 6-1, either one of the reference horizontal force H _ζ and the reference pile head displacement y _ζ is set on the program side, but the other is an unknown. Therefore, the value not set is calculated based on the equation 4-1 to which the unknown C calculated in S106 and the characteristic value β calculated in S105 are substituted. -2 for each group.

Next, in S 202, the total horizontal rigidity K _all is calculated and stored in the hard disk 104. The total horizontal stiffness K _all is the horizontal stiffness of the pile head exerted by all the piles, and is calculated by the equation 6-3-1 in FIG. Supplementally, integrating the value obtained by multiplying the horizontal stiffness K _H of the group to the pile the number of each group the number of groups.

Next, in S <b> 203, the horizontal force H in units of piles is calculated for each group and stored in the hard disk 104. The horizontal force H is calculated by Expression 6-4 by reading out the horizontal stiffness K _H calculated in S201, the total horizontal stiffness K _all calculated in S202, and the total horizontal force H _all input by the user in S101 as analysis conditions. .

In step S204, the correction coefficient G is calculated for each group and stored in the hard disk 104. The correction coefficient G is calculated by reading the horizontal force H calculated in S203 and the reference horizontal force H _ζ (a value set on the program side or a value derived by Expression 6-2-1) and by Expression 6-5. Thus, the correction coefficient G calculation process ends.

Returning to FIG. 13, in S <b> 108, a predetermined physical quantity of the pile head is calculated. In the present embodiment, the physical quantity is the rotation angle θ ₁ (0) of the pile head, and is calculated for each group and stored in the hard disk 104. The rotation angle θ ₁ (0) is calculated by substituting the unknown C calculated in S106 and the characteristic value β calculated in S105 into Equation 4-1.

In S109 and S110, a process related to consistency determination is performed as to whether or not the rotation angle θ ₁ (0) calculated in S108 matches the M-θ relationship of the pile head by a hyperbolic function. First, the rotational stiffness K _theta and a M-theta relationship pile head according to hyperbolic functions calculated by the equation 3-2-1, for each group as K _.theta.2 rotation angle theta ₁ calculated in S108 in S109 (0) Save to the hard disk 104. Although the process is the same as S13 in FIG. 6, the correction angle G is multiplied by the rotation angle θ ₁ (0).

S110 in the rotational stiffness K _.theta.1 and rotational stiffness K _.theta.2 reads the matching threshold input in S1, it is determined whether or not the rotational stiffness K _.theta.1 and rotational stiffness K _.theta.2 are close. If it is approximated in all groups, the process proceeds to S111 because the consistency is affirmed, and if not approximated in any group, the process proceeds to S112 because the consistency is denied. Similar to S15 in FIG. 6, for example, it is determined that the approximation is approximated when K _θ1 / K _θ2 <matching threshold, and the matching threshold is set to about 0.95, for example.

  In S111, the pile horizontal deformation as the stress deformation state of the pile is obtained by changing the depth x for each layer in Equation 4-1 in which the unknown C calculated in S107 and the characteristic value β calculated in S105 are substituted for each group. A displacement, a rotation angle, a bending moment, and a shearing force are calculated, and a value obtained by multiplying these by a correction coefficient G is calculated as an analysis result and stored in the hard disk 104.

  The calculation result is displayed on the display 107. FIG. 15 is a diagram showing a display example. In FIG. 14, the entire range of the depth x is targeted, but it goes without saying that the analysis result may be calculated for a specific depth x. The user who is a structural designer examines the analysis result, and if the analysis result satisfies the design criteria, the design will be completed. Conversely, if you are not satisfied, you will be redesigned.

Next, in S112, rotational rigidity resetting processing is performed. Here, the value of the rotational stiffness K _θ2 is set to the rotational stiffness K _θ1 for each group, and the process returns to S106. Thereafter, the processes of S106 to S110 and S112 are repeated until it is determined that the approximation is made in S110. That is, the convergence calculation is performed until the calculation result of the unknown C matches the M-θ relationship of the pile head by the hyperbolic function.

  Thus, in the analysis method 2, the user can obtain a theoretical solution based on an equation (Equation: 4-1) defined based on the beam theory on the elastic bearing as an analysis result simply by inputting the analysis conditions. The unknown C in the equation defined by the beam theory on elastic bearings (Formula: 4-1) is calculated by introducing the rotational stiffness of the pile head joint into the boundary condition of the pile head. The rotational stiffness of the pile head joint is determined by the convergence calculation. The consistency between the physical quantity calculated based on the beam theory equation (formula: 4-1) on the elastic bearing and the M-θ function of the pile head joint Therefore, it is possible to simplify the setting of conditions and the arithmetic processing compared to the conventional analysis method using the finite element method or the like. Therefore, the analysis of the pile foundation in consideration of the rotation of the pile head, in particular, the analysis of the pile foundation for the multilayer ground can be performed easily and accurately.

In the analysis program of FIG. 13, the pile head rotation angle θ ₁ (0) is calculated in S108, but the pile head bending moment M ₁ (0) can also be calculated from Equation 4-1. In this case, the rotational stiffness K _{θ2 of} S109 may be obtained from Equation 3-2-2, but the pile head bending moment M ₁ (0) is multiplied by the correction coefficient G.

Further, although the horizontal ground reaction force coefficient k _h is fixed in the analysis program of FIG. 13, more accurate analysis can be performed by changing the horizontal ground reaction force coefficient k _h as in the analysis program of FIG. 6. In this case, the horizontal subgrade reaction coefficient k _h of each layer can be changed according to the representative value of the displacement of the pile (the maximum value, an intermediate depth of the displacement, the top displacement, etc.).

<Another example of analysis method 2>
In the analysis program of FIG. 13, the consistency between the calculation result of the unknown C and the M-θ relationship of the pile head by the hyperbolic function is determined by the rotational stiffness K _θ , but it can also be determined by the pile head bending moment. Hereinafter, an example of the analysis program will be described with reference to FIG.

  S121 is the same process as S101 described above, and accepts user input of predetermined analysis conditions regarding the pile foundation to be analyzed, the horizontal force acting on the building supported by the pile foundation, and the ground where the pile is buried. Then, the input analysis conditions are stored in the hard disk 104. In this example as well, a case where a plurality of piles are grouped and analyzed will be described.

In S 122, the initial rotational stiffness K ₀ of the pile head is calculated for each group and stored in the hard disk 104. This is the same processing as S102 in FIG. In S123, the maximum resistance moment M _max of the pile head is calculated for each group and stored in the hard disk 104. This is the same processing as S103 in FIG. In S124, the rotational rigidity is lowered for each group. Specifically, the initial rotational stiffness K ₀ calculated in S122 is set as the value of the rotational stiffness K _θ temporarily set for each group. In S125, the ground and pile characteristic value β is calculated for each group for each layer and stored in the hard disk 104. This is the same processing as S105 in FIG.

  In S126, the unknown number C in Expression 4-1 is calculated and stored in the hard disk 104. This is the same processing as S106 in FIG.

In S127, the correction coefficient G is calculated. This is the same processing as that of S107 in FIG. 13 (FIG. 17). In S128 and S129, a predetermined physical quantity of the pile head is calculated. The physical quantities are the pile head rotation angle θ ₁ (0) and the pile head bending moment M ₁ (0). First, in S128, the rotation angle θ ₁ (0) of the pile head is calculated for each group and stored in the hard disk 104. The rotation angle θ ₁ (0) is calculated by substituting the unknown C calculated in S126 and the characteristic value β calculated in S125 into Equation 4-1.

In S129, the bending moment M ₁ (0) of the pile head is calculated for each group and stored in the hard disk 104. The bending moment M ₁ (0) of the pile head is calculated by substituting the unknown C calculated in S126 and the characteristic value β calculated in S125 into Equation 4-1.

In S130 and S131, it is related to consistency determination whether or not the rotation angle θ ₁ (0) calculated in S129 and the bending moment M ₁ (0) calculated in S130 match the M-θ relationship of the pile head by a hyperbolic function. Perform processing. First, in S 130, the pile head bending moment M _f is calculated for each group from the rotation angle θ ₁ (0) calculated in S 128 and the M-θ relationship of the pile head using a hyperbolic function, and stored in the hard disk 104. The bending moment M _f is calculated by the equation 1-1 by reading out the initial rotational stiffness K ₀ calculated in S122, the maximum resistance moment M _max calculated in S123, and the rotation angle θ ₁ (0) calculated in S128. . However, the rotation angle θ ₁ (0) is multiplied by the correction coefficient G.

In S131, the bending moment M ₁ (0) calculated in S129, the bending moment M _f calculated in S130, and the alignment threshold value input in S121 are read, and the value obtained by multiplying the bending moment M ₁ (0) by the correction coefficient G is It is determined whether or not the bending moment M _f is approximate. If it is approximated in all groups, the process proceeds to S132 because consistency is affirmed, and if it is not approximated in any group, the process proceeds to S133 because consistency is denied. For example, it is determined that approximation is made when M ₁ (0) / M _f <matching threshold, and the matching threshold is set to about 0.95, for example.

  In S132, the pile horizontal deformation as a state of stress deformation of the pile is obtained by changing the depth x for each layer in Equation 4-1 in which the unknown C calculated in S126 and the characteristic value β calculated in S125 are substituted for each group. A displacement, a rotation angle, a bending moment, and a shearing force are calculated, and a value obtained by multiplying these by a correction coefficient G is calculated as an analysis result and stored in the hard disk 104. This is the same processing as S111 in FIG.

In S133, a rotational rigidity resetting process is performed. Here, the rotational rigidity _Kθ is recalculated, stored in the hard disk 104, and the process returns to S126. And rotational stiffness K _theta initial rotational stiffness K ₀ calculated in S122, reading and maximum resistance moment M _max calculated in S123, and a bending moment M _f calculated in S130, is calculated by the equation 3-2-2.

Thereafter, the processes of S126 to S131 and S133 are repeated until it is determined that the approximation is made in S131. That is, the convergence calculation is performed until the calculation result of the unknown C matches the M-θ relationship of the pile head by the hyperbolic function. In the analysis program of FIG. 16, the bending moment M _f is calculated in S130. However, the pile head rotation angle θ _f may be calculated from the bending moment M ₁ (0) calculated in S129 by Equation 1-1. it can. In this case, in S131, an approximate determination is made between the pile head rotation angle θ _f and the value obtained by multiplying θ ₁ (0) calculated in S128 by the correction coefficient G, and in S133, the pile head rotation angle θ is calculated by Expression 3-2-1. _The rotational rigidity _Kθ is calculated from _f .

<Another example of analysis method 2>
In the programs shown in FIG. 13 and FIG. 16, it is assumed that the pile diameter, the second moment of inertia and the Young's modulus of the pile are uniform regardless of the part of the pile. It may be different. Therefore, by setting the pile diameter, cross-sectional second moment and Young's modulus of each pile individually for each layer and calculating the numerical values related to them, it is possible to perform analysis corresponding to the case where these differ depending on the part of the pile. The

It is a block diagram which shows the example of the analyzer which concerns on one Embodiment of this invention. It is explanatory drawing of the M-theta relationship of the pile head based on a hyperbolic function. (A) is an explanatory view of a method of calculating the initial rotational stiffness K _0, (b) is a diagram showing an outline of a bending moment distribution of piles in accordance with the depth of the pile head fixed degree α and ground. It is a figure which shows the calculation formula used for the analysis method 1. FIG. It is a figure which shows the calculation formula used for the analysis method 1. FIG. It is a flowchart which shows the example of the analysis program performed by the analyzer which concerns on one Embodiment of this invention. It is the figure which showed the parameter which a user inputs as analysis conditions. It is a flowchart which shows the other example of the analysis program performed by the analyzer which concerns on one Embodiment of this invention. It is explanatory drawing of the pile foundation in the multilayer ground used as the analysis object of the analysis method 2. FIG. It is a figure which shows the calculation formula used for the analysis method 2. FIG. It is a figure which shows the calculation formula used for the analysis method 2. FIG. It is a figure which shows the calculation formula used for the analysis method 2. FIG. It is a flowchart which shows the example of the other analysis program performed by the analyzer which concerns on one Embodiment of this invention. It is the figure which showed the parameter which a user inputs as analysis conditions. It is a figure which shows the example of a display of an analysis result. It is a flowchart which shows the other example performed by the analyzer which concerns on one Embodiment of this invention. It is a flowchart which shows the example of the calculation process (S107, S127) of the correction coefficient G.

Claims (6)

Input means for receiving input of predetermined analysis conditions by the user;
Based on the analysis conditions, rotational rigidity temporary setting means for temporarily setting the rotational rigidity of the pile head,
Based on the analysis condition and the temporary setting value of the rotational rigidity temporarily set by the rotational rigidity temporary setting means, a fixing degree calculating means for calculating the fixing degree of the pile head with respect to the foundation,
Based on the analysis condition and the fixed degree calculated by the fixed degree calculating means, a physical quantity calculating means for calculating a physical quantity of a predetermined pile head,
Consistency determining means for determining consistency between the physical quantity calculated by the physical quantity calculating means, and an M-θ function indicating a relationship between a predetermined bending moment and a rotation angle of the pile head as a function;
When consistency is affirmed by the consistency determination unit, based on the analysis conditions and the degree of fixation calculated by the degree-of-fixation calculation unit, a predetermined physical quantity related to the stress deformation state of the pile is used as an analysis result. An analysis result calculation means for calculating,
When consistency is denied by the consistency determination unit, the rotational rigidity of the pile stiffness is calculated in order to calculate the fixing degree and the physical quantity of the pile head by changing the temporary setting value of the rotation rigidity until consistency is affirmed. Resetting means for resetting the temporary setting value;
A pile foundation analyzing device characterized by comprising: In the pile foundation analysis device that analyzes the pile foundation with piles embedded in the multi-layer ground,
Input means for receiving input of predetermined analysis conditions by the user;
Based on the analysis conditions, rotational rigidity temporary setting means for temporarily setting the rotational rigidity of the pile head,
Based on the analysis conditions, characteristic value calculation means for calculating the characteristic value of the ground and the pile for each layer of the multilayer ground,
An unknown number of equations defining the displacement, rotation angle, shearing force and bending moment of the pile based on the beam theory on the elastic bearing according to the site of the pile in the multilayer ground, the analysis condition, and the rotational stiffness provisional setting A provisional set value of the rotational rigidity set by the means, the characteristic value calculated by the characteristic value calculating means, a predetermined pile head boundary condition, a pile tip boundary condition, and each layer of the multilayer ground An unknown number calculating means for calculating based on the continuous condition;
A physical quantity calculating means for calculating a physical quantity of a predetermined pile head based on the equation in which the unknown value calculated by the unknown quantity calculating means is substituted;
Consistency determining means for determining consistency between the physical quantity calculated by the physical quantity calculating means, and an M-θ function indicating a relationship between a predetermined bending moment and a rotation angle of the pile head as a function;
When consistency is affirmed by the consistency determination means, based on the equation into which the unknown number calculated by the unknown number calculation means is substituted, the displacement of the pile according to the part of the pile in the multilayer ground, An analysis result calculation means for calculating at least one of a rotation angle, a shear force and a bending moment as an analysis result;
When consistency is denied by the consistency determination means, the rotational rigidity provisional value is calculated in order to calculate the unknown and the pile head physical quantity by changing the rotational rigidity provisional value until consistency is affirmed. Resetting means for resetting the setting value;
A pile foundation analyzing device characterized by comprising: The pile foundation analysis device performs analysis for each of a plurality of groups of piles,
The physical quantity calculation means is the equation in which the analysis condition and the unknown value calculated by the unknown value calculation means are substituted into a value calculated based on the equation in which the unknown value calculated by the unknown quantity calculation means is substituted. A value obtained by multiplying the correction coefficient calculated based on and as a physical quantity of the pile head,
The analysis result calculation means is calculated based on the equation in which the unknown value calculated by the unknown value calculation means is substituted, and the displacement, rotation angle, and shear force of the pile according to the part of the pile in the multilayer ground. The pile foundation analysis apparatus according to claim 2, wherein a value obtained by multiplying at least one of the bending moment by the correction coefficient is calculated as the analysis result. The physical quantity calculation means calculates a rotation angle of the pile head as a physical quantity of the pile head,
The consistency determination means is based on the pile head rotation stiffness calculated by the physical quantity calculation means, the pile head rotation stiffness calculated based on the M-θ function, and the temporary setting value. Judging gender,
The resetting means resets the rotational rigidity calculated based on the rotation angle of the pile head calculated by the physical quantity calculating means and the M-θ function as the temporary setting value. The pile foundation analysis device according to any one of claims 1 to 3.   The M-θ function is a hyperbolic function defined by an initial rotational stiffness and a maximum resistance moment of a pile head calculated according to the analysis conditions. Pile foundation analysis device.   The pile foundation analysis program which makes a computer function as each means of any one of Claims 1 thru | or 5.

Images