JP3907643B2 - Ground motion analysis system, ground motion analysis method, and program - Google Patents

Description

  The present invention relates to a ground motion analysis system, a ground motion analysis method, and a program, and more particularly to a ground motion analysis system, a ground motion analysis method, and a program for evaluating the stability of the ground against a ground motion using a finite element method model. Is.

  Normally, the finite element method used for evaluating the stability of the ground can easily incorporate multiple material properties and complex boundary conditions into the analysis, but it is basically a deterministic analysis method and is applied to ground engineering. In some cases, the material properties of the ground must be ignored and the material properties must be given as definite values.

  In particular, when evaluating the stability of the ground that is the subject of the present invention, the magnitude of the variation of the material is considered to greatly affect the results, and it is necessary to evaluate the stability by reliability analysis based on probability theory. is there.

  Recently, in order to take into account spatial variations in material constants when evaluating the stability of the ground, a Monte Carlo method has been implemented in which analysis is performed by varying the material constants of each element using random numbers. In this method, an analysis case is generated by a combination of material constants in each element. Usually, when performing a probabilistic evaluation, analysis of several thousand cases is necessary, and a huge amount of calculation time and calculation cost are required at present.

  The outline of the stability evaluation of the ground using the conventional Monte Carlo method is shown in FIGS. FIG. 12 is a flowchart showing the procedure of stability evaluation by the Monte Carlo method.

  In FIG. 12, first, a finite element method model (FEM model) of the target ground is created, and the ground physical properties (material constants) are set as fixed values (step S101). Next, dynamic analysis is performed by applying seismic motion (external force) (step S102). In this dynamic analysis, a dynamic analysis using a uniquely determined FEM model is performed, and the earthquake stress of the ground in each case (case 1 to case N) is calculated. This earthquake stress is a time function that changes from moment to moment.

  Next, the stability is evaluated based on the earthquake stress. In this stability evaluation, the acting force of the assumed slip line is determined from the earthquake stress calculated in step S102. In addition, the resistance of the assumed slip line is obtained from the ground condition (ground strength) of the target ground. Then, the slip safety factor Fs is calculated from “resistance force / acting force”. This slip safety factor Fs is a time function that changes from moment to moment, and if it is less than 1.0, the ground may slide during an earthquake. The slip safety factor Fs is also calculated for each case (case 1 to case N).

Moreover, FIG. 13 is a figure which shows the outline | summary of the stability evaluation by a Monte Carlo method.
In FIG. 13, first, the dispersion of physical property values (elastic coefficient, strength, etc.) obtained by ground investigation or the like is modeled by a probability density function, and several hundreds of elements (elements 1 to n) of the FEM model 10 are obtained. Thousands of samplings are performed (step S201). That is, hundreds to thousands of data sets having the same model shape and element division and different physical property value distributions are created. FIG. 13A shows an example of the data distribution of the sampling result.

  Next, hundreds to thousands of dynamic response analyzes and slip margins are calculated for data 1 to data n, and the average and standard deviation of the slip safety factor Fs are calculated by statistical analysis (step S202). , S203). FIG. 13B shows an example of the average μFS of the time history of Fs (slip safety factor) and the standard deviation σFs.

  In order to solve the problem of increase in calculation time and calculation cost in the Monte Carlo method, a probabilistic finite element analysis method using a linear first-order approximation method has been proposed (for example, see Non-Patent Document 1). Here, the proposed method uses a ground coefficient as a random variable, introduces a first-order approximation method to ground motion analysis based on the finite element method, formulates a probabilistic finite element analysis method, and examines the applicability of the method. Therefore, the effectiveness of the first-order approximation method is shown in comparison with the analysis result by the Monte Carlo method.

  The first-order approximation method is a method of approximating a nonlinear function consisting of a plurality of random variables by Taylor expansion and linearizing it by ignoring the second and subsequent terms. As a method for obtaining the expected value and dispersion of displacement and stress.

However, the above proposal is mainly a proposal to verify the effectiveness of the analysis method based on the first-order approximation method. How effective is the linear first-order approximation method in the evaluation of ground stability (dynamic analysis) during an earthquake? There is no mention of how to apply to.
"Hagiwara and Tanaka: Applicability of stochastic finite element method based on linear approximation to ground motion analysis", Bulletin of Wakayama Technical College, No. 27 (1992), pp 67-72

  The present invention has been made to solve such problems. The purpose of the present invention is to introduce a linear first-order approximation method into a portion that requires enormous calculation time in the conventional Monte Carlo method and to evaluate the stability of the ground. Is to provide a ground vibration analysis system, a ground vibration analysis method, and a program that can be effectively performed with a smaller amount of calculation.

The present invention has been made to solve the above-mentioned problems, and the ground vibration analysis system of the present invention generates a finite element method model of the ground to be analyzed and evaluates the stability of the ground. In addition to obtaining the average value of the ground physical properties, the average value finite element method model generating means for generating the finite element method model using the average value of the ground physical properties, the standard deviation value of the ground physical properties, and the ground physical properties A standard deviation value finite element method model generation means for generating a finite element method model using a standard deviation value, an assumed slip line setting means for setting an assumed slip line of the ground to be analyzed, and an external force applied to the ground Using the input ground motion setting means for setting the input ground motion and the finite element method model using the average value of the ground physical properties, using the input ground motion as an external force, the average value for calculating the stress during the earthquake Using a finite element method model using a standard deviation value of the ground physical property, a standard deviation value earthquake stress calculating means for calculating a stress at the time of an earthquake using the input seismic motion as an external force, and the average And an acting force calculating means for calculating an acting force on an assumed slip line by a Monte Carlo method based on the earthquake stress by the value and the earthquake stress by the standard deviation value.
As a result, in the ground vibration analysis by the conventional Monte Carlo method, it is necessary to calculate several hundred to several thousand cases, but in the present invention, there are two cases of the mean value finite element method model and the standard deviation finite element method model. As a result, calculation time and calculation cost can be greatly reduced.

In addition, the ground vibration analysis system of the present invention is based on the ground physical properties of the ground to be analyzed, the earthquake stress by the average value, and the earthquake stress by the standard deviation value. Based on the ground resistance calculation means for obtaining the resistance force, the acting force on the assumed slip line calculated by the action force calculation means, and the resistance force on the assumed slip line calculated by the ground resistance force calculation means A slip safety factor calculating means for obtaining a safety factor Fs (resistance force / acting force) is provided.
Thereby, when evaluating the stability of the ground, the calculation time and the calculation cost can be greatly reduced as compared with the conventional Monte Carlo method. Further, the slip safety factor Fs on the assumed slip line can be easily obtained.

The ground vibration analysis method of the present invention is a ground vibration analysis method for generating a finite element method model of the ground to be analyzed and evaluating the stability of the ground, and obtaining an average value of the ground physical properties, Generate a finite element method model using the mean value finite element method model generation procedure and the standard deviation value of the ground property, and generate the finite element method model using the standard deviation value of the ground property Standard deviation finite element method model generation procedure, assumed slip line setting procedure for setting the assumed slip line of the ground to be analyzed, input seismic motion setting procedure for setting the input seismic motion that gives external force applied to the ground, and the physical properties of the ground Using the finite element method model using the mean value of the above, using the input seismic motion as an external force, the mean value earthquake stress calculation procedure for calculating the stress at the time of the earthquake, and the standard deviation value of the ground property Using a finite element method model, based on the standard deviation value earthquake stress calculation procedure for calculating the stress at the time of the earthquake using the input seismic motion as an external force, the earthquake stress by the average value and the stress at the time of the earthquake by the standard deviation value, And an action force calculation procedure for calculating an action force on an assumed slip line by the Monte Carlo method.
As a result, in the ground vibration analysis by the conventional Monte Carlo method, it is necessary to calculate several hundred to several thousand cases, but in the present invention, there are two cases of the mean value finite element method model and the standard deviation finite element method model. As a result, calculation time and calculation cost can be greatly reduced.

Further, the ground vibration analysis method of the present invention is based on the ground physical properties of the ground to be analyzed, the earthquake stress by the average value, and the earthquake stress by the standard deviation value. Based on the ground resistance calculation procedure for determining the resistance force, the acting force on the assumed slip line calculated by the above-mentioned action force calculating procedure, and the resistance force on the assumed slip line calculated by the above-mentioned ground resistance calculating procedure. And a slip safety factor calculation procedure for obtaining a safety factor Fs (resistance force / acting force).
Thereby, when evaluating the stability of the ground, the calculation time and the calculation cost can be greatly reduced as compared with the conventional Monte Carlo method. Further, the slip safety factor Fs on the assumed slip line can be easily obtained.

  In addition, the computer program of the present invention generates a finite element method model of the ground to be analyzed and calculates the average value of the ground physical properties to the computer in the ground vibration analysis system for evaluating the stability of the ground. The average value finite element method model generation procedure for generating a finite element method model using the average value of the ground, and the standard for generating the finite element method model using the standard deviation value of the ground physical property while obtaining the standard deviation value of the ground physical property Deviation value finite element method model generation procedure, assumed slip line setting procedure for setting the assumed slip line of the ground to be analyzed, input seismic motion setting procedure for setting the input seismic motion that gives external force applied to the ground, and the physical properties of the ground Using a finite element method model using an average value, using the input seismic motion as an external force, an average value earthquake stress calculation procedure for calculating an earthquake stress, and the ground physical properties Using a finite element method model using a standard deviation value, using the input seismic motion as an external force, a standard deviation value calculating a stress at the time of an earthquake, an earthquake stress calculation procedure based on the average value, and an earthquake stress and the standard deviation value This is a program for executing an action force calculation procedure for calculating an action force on an assumed slip line by the Monte Carlo method based on an earthquake stress.

In the ground vibration analysis system and ground vibration analysis method of the present invention, the input ground motion that gives the external force applied to the ground is set, the stress during the earthquake is calculated based on the finite element method model using the average value of the ground physical properties, Moreover, the stress at the time of earthquake is calculated based on the finite element method model using the standard deviation value of ground physical properties. And based on the stress at the time of the earthquake by the average value and the stress at the time of the earthquake by the standard deviation value, the acting force on the assumed slip line is calculated by the Monte Carlo method.
As a result, in the ground vibration analysis by the conventional Monte Carlo method, it is necessary to calculate several hundred to several thousand cases, but in the present invention, there are two cases of the mean value finite element method model and the standard deviation finite element method model. As a result, calculation time and calculation cost can be greatly reduced.

In the ground vibration analysis system and ground vibration analysis method of the present invention, the resistance force of the ground at the assumed slip line is calculated from the ground physical properties of the ground to be analyzed, and the acting force and resistance force at the assumed slip line are calculated. Based on this, the slip safety factor Fs (resistance force / action force) is obtained.
Thereby, when evaluating the stability of the ground, the calculation time and the calculation cost can be greatly reduced as compared with the conventional Monte Carlo method. Further, the slip safety factor Fs on the assumed slip line can be easily obtained.

  Next, the best mode for carrying out the present invention will be described with reference to the drawings.

[Description of the outline of stability evaluation according to the present invention]
In the present invention, for the stability evaluation of the ground, by introducing a linear first-order approximation method into a dynamic analysis portion that is performed by applying ground motion (external force), the calculation case of several thousand cases and the standard are obtained. The total number of cases for obtaining the deviation is two cases.

  FIG. 1 is a flowchart showing an outline of a stability evaluation procedure in the ground vibration analysis system according to the present invention. Hereinafter, with reference to FIG. 1, an outline of a stability evaluation procedure according to the present invention will be described.

  In the first step S1, a finite element method model (FEM model) of the target ground is created. Then, an average value of ground physical properties (material constants) is set as a final value (step S1).

Next, in step S2, dynamic analysis of the finite element method model (FEM model) is performed.
In this case, the dynamic analysis is performed with the FEM model model using the average value of the ground physical properties (one case). In addition, a dynamic analysis is performed using an FEM model using standard deviation values of ground physical properties (one case).

  In this way, the dynamic analysis of the FEM model is performed in a total of two cases. In the normal Monte Carlo method, it is necessary to analyze several hundred to several thousand cases. However, in the ground vibration analysis system of the present invention, the calculation time can be significantly reduced by using two cases.

  And the stress at the time of earthquake of the ground in each case is calculated. This earthquake stress is a function in the time domain that changes from moment to moment, but in the calculation, it is a function in the frequency domain.

Next, in step S3, stability evaluation based on the earthquake stress of the ground is performed.
In this stability evaluation, the acting force (time function) of the assumed slip line is obtained by the Monte Carlo method based on the average value calculated in step S2 and the standard deviation earthquake stress (frequency function).
In addition, the resistance obtained by the coefficient of friction and the direct stress (restraint force) is also based on the Monte Carlo method based on the ground conditions (ground properties) of the target ground and the earthquake stress (frequency function) of the average value and standard deviation calculated in step S2. The resistance force (time function) of the assumed slip line is obtained from the stress as a time function obtained by using. The details of the method for obtaining the acting force and the resistance force using the Monte Carlo method will be described later.
Then, the slip safety factor Fs is calculated from “resistance force / acting force”. This slip safety factor Fs is a function in the time domain that changes from moment to moment, and if it is less than 1.0, the ground may slide during an earthquake.

  Note that the average and standard deviation of the slip safety factor Fs are derived by aggregating the acting force and the resistance force calculated by the Monte Carlo method.

  FIG. 2 is a diagram for explaining an average value of ground physical properties (material constants) and a standard deviation value of ground physical properties. The dispersion of physical property values obtained by ground surveys, etc. is obtained by using a distribution function, for example, a probability density function such as normal distribution, log normal distribution, or binomial distribution, and for each element 1 to element n, an average value and a standard for each element Give the deviation. As a result, a model in which two data sets for calculating the average value of responses and for calculating the standard deviation are set is created. The standard deviation is taken along the distribution route.

[Formulation and method of stochastic finite element method in the present invention]
The equation of motion of the non-damped system of the finite element model is generally displayed in a matrix form as follows.

When Expression (1) is divided into an unknown displacement vector {u _A } and a known displacement vector {u _B },

It becomes. The unknown displacement vector {u _A } is obtained by transforming the upper part of the equation (2) as the following equation.

  When the force {b} due to the boundary condition at the model boundary is incorporated into the equation (3), the following equation is obtained.

  As a conversion to the frequency domain,

It becomes. Here, ω is an angular frequency. When considering the damping, the complex stiffness matrices [K _AA ^* ] and [K _AB ^* ] are used in Equation (5).

  Here, the i-th node response Ui in U is Taylor-expanded around the mean value of the random variable Xk, and the second and subsequent terms are ignored and linear approximation is performed. That is,

It becomes.
Here, x _k is a random variable, and the number thereof is m. From equation (6), the expected value and variance of the displacement u _i are given as follows:

_Here, the average value of _{u xk} is _{x k, Cov} [x _{k, x} l] is the covariance of _{x k} and x _l. The covariance between the displacements u _i and u _j is given by the following equation.

The expected value E [σ _i ], variance Var [σ _i ] and covariance Cov [σ _i , σ _j ] with respect to the stress of each element are obtained as follows. That is, as in the displacement calculation, the stress σ _i is Taylor-expanded around the fracture point of the random variable x _k and the second and subsequent terms are ignored and linear approximation is performed. That is,

Expectation value of the stress sigma _i from equation (10), the covariance of the dispersion and the stress sigma _i and sigma _j is given as follows.

[Description of Method in the Present Invention]
A method of calculating the acting force of the assumed slip line from the mean value and the stress (frequency) of the standard deviation shown in the above-mentioned “formulation and method of the stochastic finite element method” will be described.

  FIG. 3 is a diagram for explaining a method of calculating the acting force on the assumed slip line. Hereinafter, the calculation procedure will be described with reference to FIG.

  First, the stress on the assumed slip line by the finite element method model of the average value and the standard deviation is obtained in the frequency domain (step S11). Note that the calculation data “FIG. 3 (a) Fourier spectrum at the average value of stress” and “FIG. 3 (b) Fourier spectrum at the standard deviation of stress” in step S11 add the stress of each element on the assumed slip line. It is the value. For the calculation of “Fourier spectrum in FIG. 3 (b) standard deviation (σ) of stress”, either the + σ side or the −σ side is used, but both may be obtained as necessary.

  Next, using the mean value in the frequency domain and the stress of the standard deviation obtained in step S11, each frequency is varied by the Monte Carlo method (step S12). Thus, a plurality of models, for example, hundreds to thousands of models are prepared. At this time, it is preferable that the distribution of amplitudes at each frequency when dispersed using the Monte Carlo method is varied so as to substantially match the average value and standard deviation at that frequency. In the following, it is assumed that N is the number of models that are dispersed using the Monte Carlo method.

  Then, by obtaining a Fourier spectrum of the stress dispersed by the Monte Carlo method, a Fourier spectrum shown in FIG. 3C is obtained (step S13).

Further, stress in the time domain (FIG. 3 (d)) is calculated from the Fourier spectrum of the stress dispersed by the Monte Carlo method by FFT (fast Fourier transform) (step S14). Thereby, the stress in each time domain in the N models dispersed by the Monte Carlo method is obtained.

The acting force on the assumed slip line can be obtained from the shearing force of the obtained stress and the length of the slip line. Thereby, the acting forces in the N models in the time domain are obtained.

  Further, the resistance force is obtained by a friction coefficient and a direct stress. An example of an equation for determining the resistance force is shown in Equation (1).

    Resistance R = (c + σtanΦ) × L (1)

here,
c: Adhesive strength Φ: Internal friction angle σ: Direct stress (restraint pressure)
L: The length of the slip line. In the formula (1), the adhesive force c and the internal friction coefficient Φ are treated as the friction coefficient.

  When obtaining the resistance force R, the friction coefficient is varied by the Monte Carlo method, and N models of friction coefficients are prepared. From the friction coefficients of the N models and the direct stress in the N models, The resistances of the N models in the time domain are obtained respectively.

  Next, the slip safety factor Fs “resistance force / action in the N models in the time domain is determined by the acting forces of the N models in the time domain on the assumed slip line and the resistance forces of the corresponding N models in the time domain. Sought “force” respectively. From the time history distribution of the N slip safety factors Fs in this time domain, the time history of the average value of the slip safety factor Fs and the time history of the standard deviation of the slip safety factor Fs are obtained.

[Numeric calculation example]
Next, the method used in the ground vibration analysis system of the present invention is compared with the calculation result of the conventional Monte Carlo method. That is, a comparison between the calculation method using the first-order approximation method according to the present invention and the analysis result of a typical Monte Carlo method using the conventional stochastic finite element method is performed to verify the validity of the analysis method according to the present invention.

As an analysis model condition, an analysis model (two-dimensional FEM model) is shown in FIG. FIG. 5 shows the ground physical property classification of the analysis model. The object of analysis is embankment, and FIG. 6 shows the ground physical properties of the analysis model. The ground physical properties shown in FIG. 6 are used as the ground physical properties, and are used when creating models of the two cases shown in step S2 of FIG. Further, although not shown in FIG. 4, the friction coefficient is found given to each ground segment as further ground properties. The area indicated by the physical property number in FIG. 5 corresponds to the ground characteristic specifications of the physical property number in FIG. The analysis example shown here is a linear analysis.

FIG. 7 is a diagram showing an example of input seismic motion, FIG. 7 (a) shows an acceleration time history, and FIG. 7 (b) shows an acceleration response spectrum (h = 0.05). The unit of the vertical axis is “Gal: cm / s ^2, which is a unit when the strength of shaking caused by an earthquake is expressed by the acceleration of ground motion”. FIG. 8 shows an example of an assumed slip line to be analyzed.

  FIG. 9 is a diagram showing a comparative example of the calculation result of the average time history in the slip safety factor, and a comparative example of the average time history in the slip safety factor Fs (Fs = resistance force / acting force) of the assumed slip line. Is shown. FIG. 9A shows a calculation result by the conventional Monte Carlo method, and FIG. 9B shows a calculation result by the analysis method of the present invention. Thus, the similarity between the two results is recognized, and it can be seen that the result of the analysis method of the present invention accurately represents the analysis result of the Monte Carlo method.

  FIG. 10 is a diagram showing a comparative example of the calculation result of the standard deviation time history in the slip safety factor, and the standard deviation time history of the slip safety factor Fs (Fs = resistance force / acting force) of the assumed slip line. A comparison is shown. FIG. 10A shows the calculation result by the conventional Monte Carlo method, and FIG. 10B shows the calculation result by the analysis method of the present invention. Thus, the similarity between the two results is recognized, and it can be seen that the result of the analysis method of the present invention accurately represents the analysis result of the Monte Carlo method.

  As described above, the ground vibration analysis system of the present invention is compared with the results of the conventional Monte Carlo method, and the obtained knowledge is summarized below.

  First, focusing on the analysis method of the present invention and the analysis result of the Monte Carlo method, which is representative of the stochastic finite element method, there is not much difference between the two results, so the validity of the analysis method of the present invention is recognized. It is done.

  Secondly, comparing the analysis method according to the present invention and the number of cases when the Monte Carlo method was used, the analysis method according to the present invention was 2 cases and the Monte Carlo method was 100 cases. Moreover, in the calculation days in a specific computing system, the analysis method according to the present invention was 1 day, and the Monte Carlo method was 10 days. Therefore, the economic effect of the analysis method according to the present invention is recognized.

  Moreover, FIG. 11 is a figure which shows the structural example of the ground vibration analysis system by this invention, and has shown about the part directly related to this invention.

  The ground motion analysis system 101 includes a control unit 102 that controls the entire server, a communication interface 103 that connects the communication network 100 and the ground motion analysis system 101, a processing program unit 110, and a database 130 that records data necessary for ground analysis. have.

  The processing program unit 110 includes the following processing units.

  An average value finite element method model generation processing unit (average value finite element method model generation means) 111 calculates an average value of ground physical properties and generates a finite element method model using the average value of ground physical properties.

  A standard deviation value finite element method model generation processing unit (standard deviation value finite element method model generation means) 112 obtains a standard deviation value of ground physical properties and generates a finite element method model using the standard deviation values of ground physical properties. .

  An assumed slip line setting processing unit (assumed slip line setting means) 113 sets an assumed slip line of the ground to be analyzed.

  The input seismic motion setting processing unit (input seismic motion setting means) 114 sets an input seismic motion that gives an external force applied to the ground.

  The average value earthquake stress calculation processing unit (mean value earthquake stress calculation means) 115 uses the finite element method model using the average value of the ground physical properties and the input earthquake motion as an external force to calculate the stress at the time of the earthquake on the assumed slip line. calculate.

  The standard deviation value earthquake stress calculation processing unit (standard deviation value earthquake stress calculation means) 116 uses a finite element method model using the standard deviation value of ground physical properties, and the input seismic motion is an external force and an earthquake on the assumed slip line. The stress is calculated.

  The action force calculation processing unit (action force calculation means) 117 calculates the action force on the assumed slip line by the Monte Carlo method based on the earthquake stress by the average value and the earthquake stress by the standard deviation value.

  The ground resistance calculation processing unit (ground resistance calculation means) 118 is subjected to the stress in the time domain obtained by the Monte Carlo method based on the earthquake stress by the average value and the earthquake stress by the standard deviation value, and the analysis target. Find the resistance at the slip line based on the physical properties of the ground.

  The safety factor calculation processing unit (safety factor calculation means) 119 calculates the action force on the assumed slip line calculated by the action force calculation processing unit 117 and the resistance force on the assumed slip line calculated by the ground resistance force calculation processing unit 118. Based on this, the slip safety factor Fs (resistance force / action force) is obtained.

  The database 130 includes physical property data of the ground, generated finite element method model data, calculation result data, and the like.

  The processing program unit 110 may be realized by dedicated hardware, and the processing program unit is configured by a general-purpose information processing device such as a memory and a CPU (central processing unit). The function may be realized by loading a program (not shown) for realizing this function into a memory and executing it. In addition, it is assumed that an input device, a display device, and the like (none of them are displayed) are connected to the ground vibration analysis system as peripheral devices. Here, the input device refers to an input device such as a keyboard and a mouse. The display device refers to a CRT (Cathode Ray Tube), a liquid crystal display device, or the like.

  Further, a program for realizing the function of the processing program unit 110 in the ground vibration analysis system 101 is recorded on a computer-readable recording medium, and the program recorded on the recording medium is read into the computer system and executed. Thus, processing necessary for the present invention may be performed. The “computer system” here includes an OS and hardware such as peripheral devices.

The “computer-readable recording medium” refers to a portable medium such as a flexible disk, a magneto-optical disk, a ROM, a DVD-ROM, and a CD-ROM, and a storage device such as a hard disk built in the computer system. .
Furthermore, the “computer-readable recording medium” dynamically holds a program for a short time like a communication line when transmitting a program via a network such as the Internet or a communication line such as a telephone line. In this case, it is intended to include those that hold a program for a certain period of time, such as a volatile memory inside a computer system that becomes a server or a client in that case (transmission medium or transmission wave).
The program may be for realizing a part of the functions described above, and further, a program that can realize the functions described above in combination with a program already recorded in a computer system, a so-called difference file (difference). Program).

  Although the embodiment of the present invention has been described above, the ground vibration analysis system of the present invention is not limited to the above illustrated example, and various modifications can be made without departing from the gist of the present invention. Of course. For example, although the Monte Carlo method is used to vary the value, the method is not limited to this, and any method that varies the value around a given value may be used.

  In the present invention, since the stability evaluation of the ground can be performed with a small amount of calculation, the present invention is useful for a ground vibration analysis system, a ground vibration analysis method, a program, and the like.

It is a flowchart which shows the outline | summary of the stability evaluation procedure in the ground vibration analysis system by this invention. It is a figure for demonstrating the average value of a ground physical property (material constant), and the standard deviation value of a ground physical property. It is a figure for demonstrating the calculation method of the acting force in an assumption slip line. It is a figure which shows an analysis model (two-dimensional FEM model). It is a figure which shows the ground physical property division of an analysis model. It shows the ground physical properties of the analysis model. It is a figure which shows the example of an input earthquake motion. It is a figure which shows the assumed slip line made into analysis. It is a figure which shows the comparative example of the calculation result of the time history of the average value in a slip safety factor. It is a figure which shows the comparative example of the calculation result of the time history of the standard deviation in a slip safety factor. It is a figure which shows the structural example of the ground vibration analysis system by this invention. It is a flowchart which shows the procedure of the stability evaluation by a Monte Carlo method. It is a figure which shows the outline | summary of the stability evaluation by a Monte Carlo method.

Explanation of symbols

10 Finite element model (FEM model)
DESCRIPTION OF SYMBOLS 100 Communication network 101 Ground motion analysis system 102 Control part 103 Communication interface 110 Processing program part 111 Mean value finite element method model generation processing part 112 Standard deviation finite element method model generation processing part 113 Assumed slip line setting processing part 114 Input seismic motion Setting processing unit 115 Average value earthquake stress calculation processing unit 116 Standard deviation value Earthquake stress calculation processing unit 117 Action force calculation processing unit 118 Ground resistance calculation processing unit 119 Safety factor calculation processing unit 130 Database

Claims (5)

A ground motion analysis system that generates a finite element method model of the ground to be analyzed and evaluates the stability of the ground,
As the unit volume weight, shear rate, shear elastic modulus, Poisson's ratio, damping constant, and strain dependence curve, which are the physical property values required for the finite element method model, the average value for the dispersion of the physical property values obtained in the ground survey by giving an average value FEM model generating means for generating a finite element method model using the mean value of the ground properties,
A standard deviation value finite element method model generating means for generating a finite element method model using the standard deviation value of the ground physical property by giving a standard deviation value with respect to the dispersion of the physical property value of the ground obtained by the ground survey ;
An assumed slip line setting means for setting an assumed slip line of the ground to be analyzed;
An input ground motion setting means for setting an input ground motion that gives an external force applied to the ground;
Using a finite element method model that uses the average value of the physical properties of the ground, using the input seismic motion as an external force, an average value earthquake stress calculating means for calculating stress during an earthquake,
Using a finite element method model using a standard deviation value of the ground physical properties, using the input seismic motion as an external force, a standard deviation value earthquake stress calculating means for calculating a stress during an earthquake,
A ground motion analysis system comprising: an action force calculating means for calculating an action force on an assumed slip line by a Monte Carlo method based on the earthquake stress by the average value and the earthquake stress by the standard deviation value. Ground resistance calculation means for determining the resistance force on the assumed slip line by the Monte Carlo method based on the ground physical properties of the ground to be analyzed, and the stress at the time of earthquake by the average value and the stress at the time of earthquake by the standard deviation value; ,
A slip safety factor Fs (resistance force / action force) is obtained based on the action force at the assumed slip line calculated by the action force calculation means and the resistance force at the assumed slip line calculated by the ground resistance force calculation means. The ground motion analysis system according to claim 1, further comprising a slip safety factor calculation means. A ground motion analysis method that generates a finite element model of the ground to be analyzed and evaluates the stability of the ground,
As the unit volume weight, shear rate, shear elastic modulus, Poisson's ratio, damping constant, and strain dependence curve, which are the physical property values required for the finite element method model, the average value for the dispersion of the physical property values obtained in the ground survey by giving an average value FEM model generation step of generating a finite element method model using the mean value of the ground properties,
A standard deviation value finite element method model generation procedure for generating a finite element method model using the standard deviation value of the ground physical property by giving a standard deviation value for the variation of the physical property value of the ground obtained in the ground survey ,
An assumed slip line setting procedure for setting an assumed slip line of the ground to be analyzed;
Input seismic motion setting procedure for setting input seismic motion that gives external force applied to the ground,
Using a finite element method model using the average value of the physical properties of the ground, using the input seismic motion as an external force, an average value earthquake stress calculation procedure for calculating stress during an earthquake,
Using the finite element method model using the standard deviation value of the ground physical properties, the standard deviation value earthquake stress calculation procedure for calculating the stress at the time of the earthquake using the input seismic motion as an external force,
A ground motion analysis method comprising: an action force calculation procedure for calculating an action force on an assumed slip line by a Monte Carlo method based on the stress at the time of earthquake by the average value and the stress at the time of earthquake by the standard deviation value. Based on the ground physical properties of the ground to be analyzed and the earthquake stress by the mean value and the earthquake stress by the standard deviation value, the ground resistance force calculation procedure for obtaining the resistance force at the assumed slip line by the Monte Carlo method, and ,
A slip safety factor Fs (resistance force / action force) is obtained based on the action force on the assumed slip line calculated by the action force calculation procedure and the resistance force on the assumed slip line calculated by the ground resistance force calculation procedure. The ground motion analysis method according to claim 3, further comprising: a slip safety factor calculation procedure. Generate a finite element method model of the ground to be analyzed, and computer in the ground vibration analysis system to evaluate the stability of the ground,
As the unit volume weight, shear rate, shear elastic modulus, Poisson's ratio, damping constant, and strain dependence curve, which are the physical property values required for the finite element method model, the average value for the dispersion of the physical property values obtained in the ground survey by giving an average value FEM model generation step of generating a finite element method model using the mean value of the ground properties,
A standard deviation value finite element method model generation procedure for generating a finite element method model using the standard deviation value of the ground physical property by giving a standard deviation value for the variation of the physical property value of the ground obtained in the ground survey ,
An assumed slip line setting procedure for setting an assumed slip line of the ground to be analyzed;
Input seismic motion setting procedure for setting input seismic motion that gives external force applied to the ground,
Using a finite element method model using the average value of the physical properties of the ground, using the input seismic motion as an external force, an average value earthquake stress calculation procedure for calculating stress during an earthquake,
Using the finite element method model using the standard deviation value of the ground physical properties, with the input seismic motion as an external force, a standard deviation value earthquake stress calculation procedure for calculating a stress during an earthquake,
A program for executing an action force calculation procedure for calculating an action force on an assumed slip line by a Monte Carlo method based on the earthquake stress by the average value and the earthquake stress by the standard deviation value.

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