Torsion response prediction method and torsion response prediction apparatus

Abstract

To provide a torsion response prediction method and a torsion response prediction device capable of easily evaluating torsion response caused by foundation input motion of a building located on irregular ground.SOLUTION: Calculating respective impedance ratios α γ = (γ 1 * Vs1) / (γ 2 * Vs2) of the stratum structures 1 and 2, where Vs1 and Vs2 are respective shear wave velocities of the stratum structures 1 and 2, and γ 1 and γ 2 are respective wet densities of the stratum structures 1 and 2, and calculating an area ratio β = A1 / (A2 + 2A1) from respective basic cross-sectional areas A1 and A2 of the stratum structures 1 and 2; A response analysis of a one dimensional soil column model is performed with respect to each of the layer structures 1 and 2, maximum displacements D1 and D2 of the grounds of the layer structures 1 and 2 are calculated, a difference in ground displacement Δ D = D1 - D2 is obtained, and a rotation angle θ max of the building caused by a base input motion is calculated using the following equation θ max = = p * (Δ D·L) q·α γ / β using preset coefficients p and q with a base length L of the building.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a torsional response prediction method and a torsional response prediction device that can easily evaluate the torsional response caused by foundation input motion of a building located on irregular ground. [Background technology]

[0002] Regarding the seismic behavior of buildings built on uneven ground (irregular ground) in the supporting layer, detailed analysis using the finite element method is common. Furthermore, research on the seismic behavior of buildings built on irregular ground has disclosed, for example, a method for analyzing the bias of horizontal force borne by heterogeneous foundations using three-dimensional finite element method analysis (see Non-Patent Document 1). [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Narita, N., Yasui, Y., Kaneko, O.: Effect of torsional response of hybrid foundations combining pile foundations and spread foundations on inertia forces of buildings during earthquakes, Journal of Structural and Mechanical Engineering, Architectural Institute of Japan, Vol. 83, No. 743, pp. 101-109, 2018.1 Summary of the Invention [Problem to be solved by the invention]

[0004] However, if we try to analyze the behavior of a building on irregular ground during an earthquake using the finite element method, it takes a huge amount of time to analyze.

[0005] The present invention has been made in view of the above, and aims to provide a torsional response prediction method and a torsional response prediction device that can easily evaluate the torsional response caused by foundation input motion of a building located on irregular ground. [Means for solving the problem]

[0006] In order to solve the above-mentioned problems and achieve the object, the torsional response prediction method according to the present invention is a method for predicting the torsional response of a building located across a first geological structure having an uneven portion and a second geological structure having no uneven portion, the torsional response prediction method being a method for predicting the torsional response of a building caused by a foundation input motion to the building, the method comprising: defining shear wave velocities of the first and second geological structures as Vs1 and Vs2, respectively; defining wet densities of the first and second geological structures as γ1 and γ2, respectively; defining impedance ratios α of the first and second geological structures as γ1 and γ2, respectively; γ = (γ1 × Vs1) / (γ2 × Vs2), calculate the area ratio β = 2A1 / (A1 + A2) from the cross-sectional areas A1 and A2 of the foundations of the first and second geological structures, perform a response analysis of a one-dimensional earth column model for each of the first and second geological structures, calculate the maximum displacements D1 and D2 of the ground for each layer structure 1 and 2, determine the ground displacement difference ΔD = D1 - D2, set this as the foundation length of the building, and use the preset coefficients p and q to calculate the rotation angle θmax of the building due to the foundation input motion using the following equation: θmax == p × (ΔD L) q α γ / β is used for calculation.

[0007] The torsional response prediction device according to the present invention is a torsional response prediction device having an analysis unit that predicts a torsional response of a building that is located across a first geological structure having an uneven portion and a second geological structure that does not have an uneven portion, the analysis unit defining shear wave velocities of the first and second geological structures as Vs1 and Vs2, wet densities of the first and second geological structures as γ1 and γ2, and impedance ratios α of the first and second geological structures as γ = (γ1 × Vs1) / (γ2 × Vs2), calculate the area ratio β = 2A1 / (A1 + A2) from the cross-sectional areas A1 and A2 of the foundations of the first and second geological structures, perform a response analysis of a one-dimensional earth column model for each of the first and second geological structures, calculate the maximum displacements D1 and D2 of the ground for each layer structure 1 and 2, determine the ground displacement difference ΔD = D1 - D2, set this as the foundation length of the building, and use the preset coefficients p and q to calculate the rotation angle θmax of the building due to the foundation input motion using the following equation: θmax == p × (ΔD L) q α γ / β is used for calculation. [Effects of the Invention]

[0008] According to the present invention, it is possible to easily evaluate the torsional response caused by foundation input motion of a building located on irregular ground. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a diagram showing an example of a target model to which a torsional response prediction method according to the present embodiment is applied. [Figure 2] FIG. 2 is a flowchart showing the procedure for torsional response analysis processing according to this embodiment. [Figure 3] Figure 3 shows the contents of several models for buildings with mixed foundations, which are pile foundations in the case of uneven ground in the supporting layer, and spread foundations in the case of uneven ground structures. [Figure 4] FIG. 4 is a diagram comparing the rotation angle predicted by this embodiment with the rotation angle obtained by conventional response analysis. [Figure 5] FIG. 5 is a block diagram showing the configuration of a torsional response prediction device 40 according to this embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0010] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings. This embodiment is for easily predicting the torsional response (rotation angle θ of the building) of a building caused by foundation input motion of the building on irregular ground.

[0011] <Outline of torsional response prediction> Fig. 1 is a diagram showing an example of a target model to which the torsional response prediction method according to this embodiment is applied. In the target model shown in Fig. 1, the support layer of a building 30 resting on a foundation 3 is located on ground with an uneven portion 20. That is, the building 30 is located across a geological structure 1 (first geological structure) in which the base 10 is located deep, and a geological structure 2 (second geological structure) in which the base 10 is located shallow. Within the foundation 3, an area 3b separated by a boundary 3c is located on the geological structure 1, and an area 3a is located on the geological structure 2.

[0012] Conventionally, when determining the torsional response (rotation angle θ) of a building on irregular ground due to input motion to its foundation, the target model shown in FIG. 1 is created, and an earthquake response analysis is performed on the entire target model to determine the displacement responses y1 and y2 of nodes 31 and 32 at the ends of the foundation, which are taken as the foundation length L of building 30, and the rotation angle θ is determined as (y1 - y2) / L. However, in this embodiment, earthquake response analysis is not performed on the entire target model, but is instead performed simply by using a one-dimensional earthquake response analysis of the stratum structures 1 and 2.

[0013] 2 is a flowchart showing the torsional response analysis procedure according to this embodiment. As shown in FIG. 2, first, the shear wave velocities Vs1 and Vs2 (m / s) of the geological structures 1 and 2 and the wet densities γ1 and γ2 (t / m 3 ) from the impedance ratio α of the geological structure 1 and 2 γ =(γ1×Vs1) / (γ2×Vs2) is calculated (step S101).

[0014] Furthermore, the area ratio β from the base cross-sectional area A1 on the stratum 1 and the base cross-sectional area A2 on the stratum 2 = 2A1 / (A1+A2) is calculated (step S102).

[0015] Thereafter, a response analysis of the one-dimensional earth column model is performed for each of the layer structures 1 and 2, the maximum ground displacements D1 and D2 of each of the layer structures 1 and 2 are calculated, and the ground displacement difference ΔD (=D1-D2) is determined (step S103).

[0016] Then, using the foundation length L (m) of the building and the preset coefficients p and q, the rotation angle θmax of the building due to the foundation input motion is calculated using the following equation (1) (step S104), and this process is terminated. θmax==p×(ΔD·L) q α γ / β (1)

[0017] <Example of torsional response prediction> Next, an example of calculating the rotation angle θmax of a building due to foundation input motion for various models using this embodiment will be described. FIG. 3 is a diagram showing the contents of multiple models for a building on mixed foundations, with pile foundations for stratum structure 1 and spread foundations for stratum structure 2, on ground with uneven supporting layers. As shown in FIG. 3, three patterns of models M1 to M3 with different ratios of pile foundation area to spread foundation area were used, and the shear wave velocity Vs1 of the surface layer of stratum structure 1 was changed to 80, 100, 133, 200, and 267 (m / s). When Vs1 of stratum structure 1 was changed to 80, 100, 133, 200, and 267 (m / s), the ground period of stratum structure 1 was 1, 0.8, 0.6, 0.4, and 0.3 s, respectively.

[0018] Therefore, in this response analysis, the input earthquake motion was set to a sine wave, and the periods of the sine wave when the shear wave velocity Vs1 was 80, 100, 133, 200, and 267 (m / s) were set to 1, 0.8, 0.6, 0.4, and 0.3 s, and the amplitude level was set so that the maximum value of the pseudo-velocity response spectrum for each waveform was 16 cm / s.

[0019] When a response analysis was performed on a one-dimensional soil column model of layer structures 1 and 2 when one sine wave was input, the ground displacement difference ΔD (m) when the shear wave velocity Vs1 was 80, 100, 133, 200, and 267 (m / s) was 0.027, 0.0187, 0.0096, 0.0031, and 0.001 m, respectively.

[0020] Figure 4 shows a comparison of the rotation angle θmax predicted by equation (1) and the rotation angle θmax calculated by conventional response analysis. The coefficient p in equation (1) is 4.86 × 10 -4, and the coefficient q is set to 0.97. As shown in Fig. 4, in the case of model M3, although the rotation angle θmax is large, it can be seen that the prediction results using equation (1) and the conventional response analysis results correspond closely to each other.

[0021] <Outline of the torsional response prediction device> FIG. 5 is a block diagram showing the configuration of torsional response prediction device 40 according to the present embodiment. As shown in FIG. 5, torsional response prediction device 40 includes input unit 41, display unit 42, storage unit 43, and control unit 44. Input unit 41 is an input interface for inputting various types of information. Display unit 42 is a display output interface for displaying and outputting various types of information. Storage unit 43 is a storage device such as a nonvolatile memory that stores at least analysis target information DA, which is a model of the analysis target and parameter values. Control unit 44 is a control unit that controls the entire torsional response prediction device 40 and includes analysis unit 45. Control unit 44 stores programs corresponding to analysis unit 45 in a storage device such as a nonvolatile memory, and loads these programs into memory and executes them on a CPU to execute the corresponding processes.

[0022] The analysis unit 45 calculates the rotation angle θmax of the building caused by the foundation input motion using the equation (1) for the target model, and outputs and displays the result on the display unit .

[0023] In this embodiment, the torsional response caused by foundation input motion of a building located on irregular ground can be easily predicted using only the conditions of the ground and foundation and the results of one-dimensional response analysis of the ground, without creating a detailed analytical model.

[0024] Note that the configurations illustrated in the above embodiments and modifications are merely functional schematics and are not necessarily physically configured as shown. In other words, the distribution and integration of each device and component is not limited to that illustrated, and all or part of them can be functionally or physically distributed and integrated in any unit depending on various usage situations, etc. [Explanation of symbols]

[0025] 1,2 Geological structure 10 Foundation 20 Unland area 30 Buildings 31,32 nodes 40 Torsional response predictor 41 Input section 42 Display section 43 Storage section 44 Control Unit 45 Analysis Department DA analysis target information θmax rotation angle Vs1, Vs2 shear wave velocities γ1, γ2 wet density A1, A2 basic cross-sectional area

Claims

1. 1. A torsional response prediction method for predicting a torsional response of a building caused by a foundation input motion to the building located across a first geological structure having an uneven portion and a second geological structure having no uneven portion, comprising: The shear wave velocities of the first and second geological structures are Vs1 and Vs2, and the wet densities of the first and second geological structures are γ １ , γ ２ The impedance ratios α of the first and second geological structures are γ =(γ １ × Vs1) / (γ ２ × Vs2) and Each base cross-sectional area A of the first and second geological structures １ , A ２ Therefore, the area ratio β = 2A １ / (A １ +A ２ ) is calculated, A response analysis of the one-dimensional earth column model was performed for each of the first and second geological layers, and the maximum displacement D of the ground of each layer structure 1 and 2 was calculated. １ , D ２ Calculate the ground displacement difference ΔD = D １ -D ２ Seeking The rotation angle θmax of the building caused by the foundation input motion is calculated using the following equation, with the foundation length of the building as L and the preset coefficients p and q: θmax==p×(ΔD・L) ｑ ·a γ / b A torsional response prediction method, characterized in that the torsional response is calculated using

2. A torsional response prediction device having an analysis unit that predicts a torsional response of a building caused by a foundation input motion to the building located across a first geological structure having an uneven portion and a second geological structure having no uneven portion, The analysis unit The shear wave velocities of the first and second geological structures are Vs1 and Vs2, and the wet densities of the first and second geological structures are γ １ , γ ２ The impedance ratios α of the first and second geological structures are γ =(γ １ × Vs1) / (γ ２ × Vs2) and Each base cross-sectional area A of the first and second geological structures １ , A ２ Therefore, the area ratio β = 2A １ / (A １ +A ２ ) is calculated, A response analysis of the one-dimensional earth column model was performed for each of the first and second geological layers, and the maximum displacement D of the ground of each layer structure 1 and 2 was calculated. １ , D ２ Calculate the ground displacement difference ΔD = D １ -D ２ Seeking The rotation angle θmax of the building caused by the foundation input motion is calculated using the following equation, with the foundation length of the building as L and the preset coefficients p and q: θmax==p×(ΔD・L) ｑ ·a γ / b A torsional response prediction device characterized by calculating using

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