Calculation method, calculation device, and calculation program

Abstract

To provide a calculation method, a calculation device, and a calculation program which determine distribution of a ground contact pressure acting on a foundation bottom surface.SOLUTION: A calculation device 1 defines a virtual surface surrounding a target bottom surface by two first sides which are parallel in a first direction and are positioned outside the target bottom surface, and two second sides which are parallel in a second direction crossing the first direction and are positioned outside the target bottom surface (S1), calculates ground contact pressure distribution of the target bottom surface in the first direction and the second direction (S2 and S3), derives a temporary neutral axis connecting a first point and a second point which are neutral positions of the ground contact pressure distribution in the first direction and the second direction, on the first side and the second side (S4), and repeatedly performs processing of deriving a new first point and second point, from the ground contact pressure of apexes of the virtual surface, and a length between the first point and an apex with a lowest ground contact pressure of the virtual surface and a length between the second point and the apex, and calculates a neutral axis passing through the first point and the second point, and ground contact pressure distribution of the target bottom surface (S5 and S6).SELECTED DRAWING: Figure 10

Description

[Technical field]

[0001] The present invention relates to a calculation method for determining the distribution of ground pressure acting on the bottom surface of a foundation, a calculation device for carrying out such a calculation method, and a calculation program for realizing such a calculation device. [Background technology]

[0002] When earthquake motion acts on a structure, the inertial force in any direction is expressed as inertial action (component force) in two orthogonal directions on a horizontal plane. Until now, inertial forces in two directions have been treated as separate actions in each direction because it is unlikely that they will reach their maximum value at the same time, but it is more realistic to consider cases where inertial forces in two directions act simultaneously. Here, we consider the ground pressure distribution when eccentric actions in two directions are acting.

[0003] Figure 1 is a schematic diagram showing the behavior of concentrated load acting on a two-way eccentric axis. Figure 1(a) shows the case where a vertical force acts within the core in two orthogonal directions, and Figure 1(b) shows the case where a vertical force acts outside the core in two orthogonal directions. The following formula (1) is a basic formula for estimating the ground pressure distribution corresponding to the eccentric action in each direction, and the following formula (2) is a composite formula showing the maximum ground pressure when a vertical force acts off the axis in two orthogonal directions shown in Figure 1(b).

[0004] σ max(min) =N / A±M / Z Formula (1) σ max =(N / L b) (1+6e L / L+6e b / b) Formula (2)

[0005] The problem of calculating the ground pressure distribution is often troublesome because, as shown in Figure 1(b), minbecomes a negative pressure. In reality, negative pressure does not occur and the foundation will rise up. To reflect this in the calculation, the negative ground pressure in equation (2) must be set to 0 and the overall ground pressure must be recalculated. The inventors of this application have presented a rational solution to the case where the eccentric action is in only one direction and the bottom surface of the foundation rises up as described above (see Non-Patent Document 1). [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] Kenzo Ueda and Ryoichi Fukagawa, "A simple method for calculating the contact pressure distribution of a rigid foundation symmetrical with respect to a central axis", Journal of the Japan Society of Civil Engineers, 2003, No. 736, pp. 51-65 [Patent Document 1] Patent No. 4176767 Summary of the Invention [Problem to be solved by the invention]

[0007] However, Non-Patent Document 1 does not propose a reasonable estimation method when the eccentric action occurs in two directions.

[0008] The present invention has been made in consideration of the above circumstances, and has an object to provide a method for calculating the distribution of ground pressure acting on the bottom surface of a foundation, including cases where eccentric action occurs in two directions. [Means for solving the problem]

[0009] In order to solve the above problems, the calculation method disclosed in the present application is a calculation method for calculating the ground pressure distribution of the bottom surface on which a structure is constructed, and includes the steps of: defining a virtual surface surrounding the target bottom surface with two first sides that are parallel to a first direction included in a plane including the target bottom surface to be calculated for the ground pressure distribution and are located outside the target bottom surface, and two second sides that are parallel to a second direction included in the plane including the target bottom surface, intersect with the first direction, and are located outside the target bottom surface; calculating the ground pressure distribution of the target bottom surface in the first direction; and calculating the ground pressure distribution of the target bottom surface in the second direction. The method is characterized by carrying out the steps of: deriving a virtual neutral axis connecting a first point on the first side that is a neutral position of the ground pressure distribution in a first direction, and a second point on the second side that is a neutral position of the ground pressure distribution in a second direction; deriving new first and second points based on a predetermined derivation formula from the ground pressure of the vertex of the imaginary surface and the length from the vertex where the ground pressure of the imaginary surface is the lowest to the first point and the length from the vertex to the second point; and calculating the ground pressure distribution of the target bottom surface using a straight line passing through the first and second points that converges by repeatedly deriving the first and second points as the neutral axis.

[0010] Furthermore, the calculation device disclosed in the present application is a calculation device that calculates the ground pressure distribution of a bottom surface on which a structure is constructed, and includes a means for defining a virtual surface surrounding the target bottom surface with two first sides that are parallel to a first direction included in a plane including the target bottom surface to be subjected to the calculation of the ground pressure distribution and are located outside the target bottom surface, and two second sides that are parallel to a second direction included in the plane including the target bottom surface, intersect with the first direction, and are located outside the target bottom surface, a means for calculating the ground pressure distribution of the target bottom surface in the first direction, a means for calculating the ground pressure distribution of the target bottom surface in the second direction, and the first sides The present invention is characterized in that it comprises a means for deriving a virtual neutral axis connecting a first point which is a neutral position of the ground pressure distribution in a first direction and a second point on the second side which is a neutral position of the ground pressure distribution in a second direction, a means for deriving new first and second points based on a predetermined derivation formula from the ground pressure of the vertex of the imaginary surface and the length from the vertex where the ground pressure of the imaginary surface is the lowest to the first point and the length from the vertex to the second point, and a means for calculating the ground pressure distribution on the target bottom surface using a straight line passing through the first and second points which converges by repeatedly deriving the first and second points as the neutral axis.

[0011] Furthermore, the calculation program disclosed in the present application is a calculation program that causes a computer to calculate the ground pressure distribution of the bottom surface on which a structure is constructed, and includes the steps of: defining a virtual surface that surrounds the target bottom surface with two first sides that are parallel to a first direction included in a plane including the target bottom surface that is the subject of calculation of the ground pressure distribution and are located on the outside of the target bottom surface, and two second sides that are parallel to a second direction included in the plane including the target bottom surface, intersect with the first direction, and are located on the outside of the target bottom surface; calculating the ground pressure distribution of the target bottom surface in the first direction; and calculating the ground pressure distribution of the target bottom surface in the second direction. The method is characterized by executing the steps of: deriving a virtual neutral axis connecting a first point on the first side that is a neutral position of the ground pressure distribution in a first direction and a second point on the second side that is a neutral position of the ground pressure distribution in a second direction; deriving new first and second points based on a predetermined derivation formula from the ground pressure of the vertex of the imaginary surface and the length from the vertex where the ground pressure of the imaginary surface is the lowest to the first point and the length from the vertex to the second point; and calculating the ground pressure distribution of the target bottom surface using a straight line passing through the first and second points that converges by repeatedly deriving the first and second points as the neutral axis. Effect of the Invention

[0012] The calculation method disclosed in the present application has excellent advantages, such as making it easy to calculate the distribution of ground pressure acting on the bottom surface of the foundation. [Brief description of the drawings]

[0013] [Figure 1] FIG. 13 is a schematic diagram showing the behavior of a concentrated load acting on a bidirectional eccentric shaft. [Diagram 2] FIG. 11 is an explanatory diagram showing an example of an analysis of ground pressure distribution. [Diagram 3] FIG. 11 is an explanatory diagram showing an example of an analysis of ground pressure distribution. [Figure 4] FIG. 4 is an explanatory diagram of an analysis model showing an example of a relationship between parameters of a response value for each eccentric shaft. [Diagram 5] FIG. 11 is an explanatory diagram showing the movement state of the neutral axis under a load condition. [Figure 6]FIG. 13 is an explanatory diagram conceptually illustrating an example of grid ground pressure at a node of interest. [Figure 7] This is a calculation procedure that excludes the defined negative value range. [Figure 8] FIG. 2 is an explanatory diagram conceptually illustrating the procedure of the calculation method disclosed in the present application. [Figure 9] FIG. 2 is a block diagram showing an example of a hardware configuration of a computing device disclosed in the present application. [Figure 10] 1 is a flowchart illustrating an example of a calculation process executed by a calculation device disclosed in the present application. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] This application discloses a method for calculating partial ground pressure at the bottom of a foundation supporting a structure. The calculation method disclosed in this application is based on the force balance condition based only on the compression state, and focuses on the fact that the neutral axis position that occurs when the center of gravity of the bottom changes with the movement of a vertical force. In other words, the calculation method disclosed in this application is capable of finding the position of the neutral axis where the ground pressure becomes zero due to an eccentric load when an eccentric load acts on the bottom of the foundation, and further, of finding the ground pressure distribution at the bottom of the foundation.

[0015] The calculation method disclosed in this application takes into consideration a foundation structure with a single foundation bottom surface consisting of a combination of rectangular shapes, and proposes a simple and rational method for estimating ground pressure distribution when the foundation is subjected to eccentric actions in two directions and part of it rises up.

[0016] 2 and 3 are explanatory diagrams showing an analysis example of the ground pressure distribution. The symbols shown in FIG. 2 are as follows.

[0017] N: Total vertical force acting on the bottom of the foundation d L ,d b (e L ,e b ): The distance from the compression edge or center of gravity to the point where the vertical force N is applied, counted for each axis M x ,M y : Bending moment acting on each axis y L ,y b : Distance from the opposite edge of compression to the neutral axis σ xmax ,σ ymax : Maximum contact pressure of the compression edge on the X and Y axes σ xmin ,σ ymin : Minimum contact pressure at the opposite edge of compression σ e :Average ground pressure (=N / A=dz =1) σ M (-σ M ): The contact pressure at the compressed edge and the opposite edge that occurs due to the effect of bending moment g,ρ: Distance from 0 point to center of gravity, center of gravity to neutral axis α o ,x i : Rotation angle, distance from center of gravity axis Y to point of interest d z (Δd z ): original length and its distortion σ x (σ xz ): Ground pressure increment at the point of interest

[0018] The proposed method is explained by enlarging the relationship between the response value and the displacement on the X-axis in Fig. 3, which is the case where a vertical force is applied away from the center of gravity of the solid bottom shown in Fig. 2. i Regarding the displacement at a distant position, the following equation (3) holds due to the similarity of triangles. σ x The stress-strain relationship can be expressed by the following equation (4). On the other hand, the external force M x and the response value σ x From this relationship, the following equation (5) holds. Substituting equation (4) into equation (5) gives the following equation (6). In equation (6), the second term on the left side is the second moment I of the base. If equation (6) is expressed in terms of I, it can be rearranged as in equation (7) below. If equation (5) is transformed into equation (8) below and made equal to the right side of equation (7), the following equation (9) is obtained. Equation (9) is M x Due to the influence of i The ground pressure σ x Therefore, in equation (9), σ e Adding (=N / A) gives the ground pressure σxz is calculated as the following formula (10). On the other hand, from the X-axis, y i The displacement at a position distant by a distance can be derived in the same way as equation (3). In this case, equations (4) to (10) can also be derived, so the following equation (11) is finally established. By combining these, the following proposed equation (12) is established.

[0019]

number

[0020] An example of an analysis of a hollow polygonal bottom surface will now be described. Figure 4 is an explanatory diagram of an analytical model showing an example of the relationship between the response value parameters for each eccentric shaft. Calculations were performed using the analytical model of the hollow polygonal bottom surface shown in Figure 4. In the calculations for the analytical model, the position of the neutral axis that satisfies the balance conditions for each eccentric shaft was calculated using the minimum input parameters shown in the upper part of Table 1 below, and the corresponding ground pressure of the two-dimensional bottom surface was calculated and shown in the lower part of Table 1. The ground pressure σ min ≧0. Furthermore, the calculation results were substituted into equation (12) and the three-dimensional ground pressure distribution is shown in Table 2 below.

[0021] [Table 1]

[0022] [Table 2]

[0023] Contact pressure σ at the opposite edge of compression c We will explain the correspondence between positive and negative σ c If is a positive value, it is determined that the entire bottom surface of the foundation is in compression and in contact with the ground. σ cIf is not a positive value, a negative value range will appear, and if it is not allowed, the calculation element will be changed or the following action will be taken. In other words, since no tensile force acts between the ground and the bottom surface unless some kind of ingenuity is used, it is determined that the bottom surface is in a state of being separated from the ground and rising up. The calculation method described in this application for such a floating situation will be explained.

[0024] FIG. 5 is an explanatory diagram showing the movement of the neutral axis under load conditions. FIG. 6 is an explanatory diagram conceptually showing an example of the grid contact pressure at the node of interest. FIG. 7 shows the procedure for calculation to exclude the defined negative area. c In order to find the equilibrium condition using only the compressive force, first determine the position of the neutral axis calculated using the following formulas (13) and (14) on the line from point C to point D and the line from point C to point B as shown in Figures 5 and 7, and calculate, and the values ​​α = 1.775 m and β = 2.784 m are obtained. If points α and β are connected with a straight line, it will result in an irregularly shaped pentagonal base (the dummy area in Figure 7 is ignored). The ground pressure of α and β is calculated using formula (15) to be σα = -7.05 kN / m 2 ,σβ=-6.33. The initial solution α and β are defined by equations (13) and (14). When n=1, L and σD in equation (13) and b and σB in equation (14) are variables. The variables are the following equation (15) which is the overlap of equations (10) and (11). Equation (15) is an extended equation that extends the conventional method proposed in the calculation method disclosed in this application. Note that equation (15) is expanded in a compound manner with positive and negative signs so that the ground pressure at the edge opposite to the compression can also be evaluated. In addition, simple overlapping results in overlapping average ground pressures, so this is subtracted.

[0025]

number

[0026] Applying equation (15), the ground pressure at the assumed neutral axis position is calculated as σα = -7.05 kN / m 2 , σβ=-6.33 km / m 2This is because, in equation (12), point C σα = σβ = -77.42 kN / m 2 It shows a tendency to converge to zero compared to the initial value. In other words, if the ground pressure of the neutral axis at a slight increase or decrease distance (α+Δα, β+Δβ) obtained by applying formula (13) and formula (14) from the ground pressure at both ends of the line segment is 0 ≠ σα, 0 ≠ σβ, an iterative calculation is performed as shown in Figure 7 to approach zero infinitesimally. The simulation results showed that a practical ground pressure was obtained after several iterative calculations. Table 3 below shows the specifications of the contact surface obtained as a result of convergence.

[0027] [Table 3]

[0028] The calculation method disclosed in the present application described above allows the ground pressure distribution and uplift of a rigid foundation consisting of a combination of rectangular shapes to be easily and quickly carried out by the proposed simulation. In addition, even if the ground pressure distribution of the unidirectional eccentric shaft shows a trapezoidal distribution, the calculation method disclosed in the present application may result in a negative value range (tensile force) when combined. Furthermore, the calculation method disclosed in the present application is expected to be useful for design sites where ensuring the safety of buildings is the top priority.

[0029] Fig. 8 is an explanatory diagram conceptually showing the procedure of the calculation method disclosed in the present application. In addition to the above explanation, Fig. 8 is disclosed to facilitate understanding.

[0030] The calculation method disclosed in the present application can be realized, for example, by being implemented in a calculation device using a computer. In the following, a specific embodiment for implementing the calculation method disclosed in the present application will be described with reference to an example.

[0031] <Hardware configuration of the computing device> FIG. 9 is a block diagram showing an example of a hardware configuration of the computing device 1 disclosed in the present application. Figure 9The computing device 1 illustrated in the example is realized by using a personal computer, a client computer connected to a server computer, or other various computers. The computing device 1 includes various mechanisms such as a control unit 10, a storage unit 11, an input unit 12, a display unit 13, and a communication unit 14.

[0032] The control unit 10 is a processor such as a CPU (Central Processing Unit) that executes processes for controlling the entire device, and includes various circuits such as an information processing circuit, a timer circuit, and a register circuit.

[0033] The storage unit 11 is a circuit configured using non-volatile memories such as a hard disk, a RAID (Redundant Array of Inexpensive Disks), and a flash memory, and volatile memories such as various RAMs (Random Access Memories), and stores various information. The storage unit 11 stores programs such as a basic program (OS: Operating System) and an application program (application program) that runs on the basic program. As the application program, various programs such as a calculation program 110 for realizing the calculation device 1 disclosed in the present application are stored.

[0034] The input unit 12 is a device such as a keyboard, a mouse, etc. The display unit 13 is a device such as a liquid crystal display.

[0035] The communication unit 14 is a device that connects to a communication network such as the Internet, a Wide Area Network (WAN), a Local Area Network (LAN), a dedicated communication network, etc. The computing device 1 can access other devices connected to the communication network via the communication unit 14.

[0036] A computer having the various configurations exemplified above operates as a calculation device 1 by reading various programs such as the calculation program 110 stored in the memory unit 11 under the control of the control unit 10 and executing various procedures contained in the various programs.

[0037] In the present application, for convenience of explanation, an embodiment in which the calculation device 1 is realized using one computer is exemplified, but the calculation device 1 may be realized using multiple computers. Specifically, a part or all of the contents of the database stored in the storage unit 11 may be stored in a computer such as a database server grounded on a communication network, and the calculation device 1 may be configured as a whole by appropriately accessing the contents from a main computer. In addition, the calculation program 110 may be executed by a server computer, and the man-machine interface such as the input unit 12 and the display unit 13 may be executed by a client computer, thereby configuring the calculation device 1 as a whole.

[0038] <Processing by the software of the calculation device 1> Next, a description will be given of the calculation process of the calculation device 1 disclosed in the present application. Fig. 10 is a flowchart showing an example of the calculation process executed by the calculation device 1 disclosed in the present application. The control unit 10 of the calculation device 1 executes a calculation program 110 stored in the storage unit 11 to perform the calculation method.

[0039] The control unit 10 defines a virtual surface surrounding the target bottom surface by two first sides that are parallel to a first direction included in a plane including the target bottom surface for which the ground pressure distribution is to be calculated and are located outside the target bottom surface, and two second sides that are parallel to a second direction included in the plane including the target bottom surface, intersect with the first direction, and are located outside the target bottom surface (step S1).

[0040] The control unit 10 calculates the ground pressure distribution of the target bottom surface in the first direction (step S2), and calculates the ground pressure distribution of the target bottom surface in the second direction (step S3).

[0041] The control unit 10 derives a provisional neutral axis connecting a first point on the first side that is a neutral position of the ground pressure distribution in the first direction and a second point on the second side that is a neutral position of the ground pressure distribution in the second direction (step S4).

[0042] The control unit 10 derives new first and second points based on a predetermined derivation formula from the ground pressure of the vertex of the imaginary surface, and the length from the vertex where the ground pressure of the imaginary surface is the lowest to the first point and the length from the vertex to the second point (step S5).

[0043] The control unit 10 calculates the ground contact pressure distribution of the target bottom surface by using a straight line passing through the first point and the second point, which converges by repeating the derivation of the first point and the second point, as a neutral axis (step S6).

[0044] The present invention is not limited to the above-described embodiment, and can be implemented in various other forms. Therefore, the embodiment is merely illustrative in all respects and should not be interpreted as being restrictive. The scope of the present invention is defined by the claims, and is not limited in any way by the text of the specification. Furthermore, all modifications and changes within the equivalent scope of the claims are within the scope of the present invention. [Explanation of symbols]

[0045] 1 computing device 10 Control section 11 Storage section 110 Calculation Program 12 Input section 13 Display section 14 Communications Department

Claims

1. A method for calculating the ground pressure distribution on the bottom surface on which a structure is constructed, comprising the steps of: A step of defining a virtual surface surrounding the target bottom surface with two first sides that are parallel to a first direction included in a surface including the target bottom surface that is the subject of calculation of the ground pressure distribution and are located outside the target bottom surface, and two second sides that are parallel to a second direction included in the surface including the target bottom surface, intersect with the first direction, and are located outside the target bottom surface; Calculating a ground contact pressure distribution on a target bottom surface in a first direction; Calculating a ground contact pressure distribution on the target bottom surface in a second direction; A step of deriving a provisional neutral axis connecting a first point on the first side that is a neutral position of the ground pressure distribution in the first direction and a second point on the second side that is a neutral position of the ground pressure distribution in the second direction; deriving new first and second points based on a predetermined derivation formula from the ground contact pressure of the vertex of the imaginary surface, and the length from the vertex at which the ground contact pressure of the imaginary surface is minimum to the first point and the length from the vertex to the second point; A step of calculating the ground pressure distribution on the target bottom surface by using a straight line passing through the first point and the second point, which converge by repeatedly deriving the first point and the second point, as a neutral axis; A calculation method comprising:

2. A calculation device for calculating a ground pressure distribution on a bottom surface on which a structure is constructed, A means for defining a virtual surface surrounding the target bottom surface with two first sides that are parallel to a first direction included in a surface including the target bottom surface that is the subject of calculation of the ground pressure distribution and that are located outside the target bottom surface, and two second sides that are parallel to a second direction included in the surface including the target bottom surface, intersect with the first direction, and that are located outside the target bottom surface; A means for calculating a ground contact pressure distribution on a target bottom surface in a first direction; A means for calculating a ground contact pressure distribution on a target bottom surface in a second direction; A means for deriving a provisional neutral axis connecting a first point on a first side that is a neutral position of a ground pressure distribution in a first direction and a second point on a second side that is a neutral position of a ground pressure distribution in a second direction; a means for deriving new first and second points based on a predetermined derivation formula from the ground contact pressure of the vertex of the imaginary surface and the length from the vertex at which the ground contact pressure of the imaginary surface is minimum to the first point and the length from the vertex to the second point; A means for calculating a ground contact pressure distribution on a target bottom surface by using a straight line passing through the first point and the second point, which converge by repeatedly deriving the first point and the second point, as a neutral axis; 16. A computing device comprising:

3. A calculation program for causing a computer to calculate the ground pressure distribution of the bottom surface on which a structure is constructed, On the computer, A step of defining a virtual surface surrounding the target bottom surface with two first sides that are parallel to a first direction included in a surface including the target bottom surface that is the subject of calculation of the ground pressure distribution and are located outside the target bottom surface, and two second sides that are parallel to a second direction included in the surface including the target bottom surface, intersect with the first direction, and are located outside the target bottom surface; Calculating a ground contact pressure distribution on a target bottom surface in a first direction; Calculating a ground contact pressure distribution on the target bottom surface in a second direction; A step of deriving a provisional neutral axis connecting a first point on the first side that is a neutral position of the ground pressure distribution in the first direction and a second point on the second side that is a neutral position of the ground pressure distribution in the second direction; deriving new first and second points based on a predetermined derivation formula from the ground contact pressure of the vertex of the imaginary surface, and the length from the vertex at which the ground contact pressure of the imaginary surface is minimum to the first point and the length from the vertex to the second point; A step of calculating the ground pressure distribution on the target bottom surface by using a straight line passing through the first point and the second point, which converge by repeatedly deriving the first point and the second point, as a neutral axis; A computing program characterized by executing the above.

Images