CN110702881B - Prediction method of rock-soil material parameter variability result and application thereof - Google Patents

Abstract

The invention discloses a prediction method of parameter variability results of a rock-soil material and application thereof, and aims to solve the technical problems of large measurement amount, time consumption and labor consumption of the rock-soil material in the prior art in random field probability analysis. The prediction method can be applied to the analysis and the measurement of various geotechnical parameters and engineering structure parameter space variability influence results, realizes the efficient and accurate prediction of countless or maximum measurement results by using a small amount of measurement results with limited times, saves calculation power, is simple, convenient, efficient, time-saving and labor-saving, is accurate and reliable in prediction, and can be applied to various civil engineering and can take safety and effectiveness and economy of engineering construction cost into consideration.

Description

A Prediction Method for Variability Results of Geotechnical Material Parameters and Its Application

technical field

The invention relates to the technical field of geotechnical engineering measurement and analysis, in particular to a method for predicting the variability results of geotechnical materials and its application.

Background technique

Numerical analysis method is an important method that has been widely used in geotechnical engineering measurement, research and analysis and design. Traditional numerical analysis is mostly based on the assumption of isotropy or homogeneity of geotechnical or engineering materials, without considering the characteristics of spatial variability of material parameters. During the long-term tectonic movement of the crust, the parameters of rock and soil mechanics, joints, fault distribution, temperature field, seepage field, etc. have the characteristics of anisotropy, and show strong spatial variability, especially the foundation of human beings. Projects such as pit excavation, tunnels, underground workshops, and slopes are generally located on the surface or within a depth of hundreds or even tens of meters, and the spatial variability of geotechnical material parameters is particularly significant. If the variability is ignored in the calculation and analysis of related projects, it will cause a large measurement error, which will bring security risks to the implementation of subsequent projects.

Therefore, according to the characteristics of spatial variability of geotechnical materials, the uncertainty of the distribution of geotechnical property parameters is the focus of urgent research. In short, the method of probabilistic analysis is used to evaluate whether the engineering structure is unstable, and the answer given is no longer the default 100% stable or unstable in the traditional sense, but is transformed into a probability problem, such as 95% stable, thus The engineering numerical simulation results are more consistent with the actual engineering.

In the numerical simulation analysis and calculation research, in order to consider the spatial variability of material parameters and achieve the purpose of probability analysis according to the numerical simulation measurement results, it is usually considered that the studied property parameters obey a certain distribution function (such as the commonly used lognormal distribution). function), thereby generating hundreds or even thousands of sets of parameter random numbers, and on this basis, perform hundreds or thousands of calculations (one calculation for each set of random numbers), and obtain hundreds or thousands of corresponding random numbers. The measurement results are used for probabilistic analysis of the parameter measurement results.

As we all know, for complex numerical models, especially modern numerical models, the number of units is increasing, and the amount of calculation is huge. It takes a day, a week, a month or even longer for each calculation. At the same time, as mentioned above, probabilistic analysis requires as few as hundreds of times or as many as thousands of calculations until the calculation results converge, then a complete numerical probability analysis calculation requires a lot of time and computing power. In addition, the accuracy of the calculation results obtained by a lot of time-consuming is not satisfactory.

Therefore, reducing the time required for calculation and improving the accuracy of forecasting so as to take into account the safety and economy of project implementation are urgent problems to be solved in current project construction.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a method for influencing the results of the variability of geotechnical material parameters (such as elastic modulus, cohesion, friction angle, strength, joints, fault distribution, temperature field, stress field, seepage field, etc.). A prediction method and its application are provided in order to solve the technical problem of large amount of calculation and time-consuming computing power in the probabilistic analysis of random fields of geotechnical materials in the prior art.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical solutions:

Provide a method for predicting the results of the variability of geotechnical materials, including the following steps:

(1) Establish a corresponding finite element numerical model according to the properties of geotechnical materials and engineering accuracy requirements;

(2) According to the covariance matrix decomposition method, the center point coordinates of each element of the obtained finite element numerical model are substituted into the autocorrelation function to obtain the covariance autocorrelation matrix, and then Cholesky decomposition is performed to obtain the upper triangular and lower triangular matrix multiplication;

(3) Based on the standard normal distribution law, generate a standard normal distribution random field from the lower triangular matrix obtained in the previous step; transform the standard normal distribution random field into a normal random field with a mean value of μ and a variance of σ ² ;

The parameters in the normal random field obtained by the transformation and the parameters characterizing the properties of the geotechnical materials are mapped to each element in the finite element numerical model, and the conversion from the random field model to the numerical analysis model is realized;

(4) According to the Monte Carlo strategy, repeat step (3) M times to obtain M groups of random number calculation results;

(5) Divide the random number measurement results of M groups into known quantity group A and to-be-predicted group B ; when grouping, the reasonable prediction results can be obtained, such as equal or even grouping;

(6) Extract a set of random numbers g from the group B to be predicted, and calculate the standard deviation S corresponding to the random number g ; take the initial value of the standard deviation error i % = k % = 0, and calculate the value range U of the standard deviation =[ S (1- i %)～ S (1+ i %)];

(7) Screen out n groups of random numbers whose standard deviation is within the range U from the known quantity group A to form a new large group C ;

(8) Let C′ be the random field matrix of the large group C , B′ be the random field matrix of the group B to be predicted, and calculate D=C′ - B′ , the random number g extracted from the group B to be predicted and The N groups of random numbers in the large group C respectively calculate the F norm ‖ D ‖ _F of the matrix D , and take the calculation result of the random number corresponding to the smallest ‖ D ‖ _F among the n calculation results as the corresponding prediction result;

(9) Repeat steps (5) to (8) to obtain the prediction result of the random number in the group B to be predicted and compare the actual calculation result, and calculate the average error SS ;

(10) Set the increase value of the standard deviation error i % in step (6) to j % each time, then the standard deviation error range of the Nth calculation is i % = k % + M × j %; repeat Steps (6) to (9) N times, N average errors are obtained; the standard deviation error range corresponding to the minimum value of the N average errors is taken as i %, that is, the best standard deviation error range is obtained. value ii %;

(11) Take the random number to be measured from the random field in step (3), use the best standard deviation error range to take the value ii %, repeat steps (6) to (8) until the calculation result converges and stabilizes, obtaining: The predicted result corresponding to the number of repetitions.

Preferably, in the step (2), the selected autocorrelation function is:

——式（i）；

- formula (i);

In formula (i), x , y , z are the coordinate directions of the model; δ _x , δ _y , δ _z are the correlation distances in the x , y , and z directions, respectively; τ _x , τ _y , τ _z are any two Coordinate difference between cells in x , y , z direction.

In the above step (2), the covariance autocorrelation matrix can be expressed as:

C = LU = LL ^T - formula (ii);

In formula (ii), L and U are lower triangular and upper triangular matrices, respectively, and L ^T is the transpose of matrix L.

In the step (10), j %=0.05%～0.1%.

The above-mentioned property parameters of the geotechnical material are parameters that characterize any property of the geotechnical material, such as strength, joints, fault distribution, temperature field, stress field, seepage field, and the like.

The above-mentioned property parameters of geotechnical materials are any one of elastic modulus, cohesion, friction angle, and the like.

The above prediction method can be widely used in the analysis and calculation of geotechnical engineering supporting force, displacement and settlement, joints, fault distribution, temperature field, seepage field, etc.

Compared with the prior art, the main beneficial technical effects of the present invention include:

The prediction method of the invention can be applied to the analysis and calculation of various geotechnical parameters and the results of the spatial variability of engineering structure parameters, and realizes the use of a small number of measurement results of a limited number of times to efficiently and accurately predict countless or extremely large number of measurement results. The method is simple and efficient, saves time and labor, and the prediction results are accurate and reliable. It can be used in various civil engineering projects to take into account the safety of the project and the economy of construction costs.

Description of drawings

Figure 1 is a schematic diagram of the random number calculation process.

Figure 2 is a schematic diagram of a cube elastic constitutive model;

Fig. 3 is the finite element numerical model diagram of the cube;

Fig. 4 is the numerical model diagram of the elastic modulus random field of the cube;

Fig. 5 is the contrast diagram of the random number complete calculation result of a in Fig. 4 and the predicted result;

Fig. 6 is the contrast diagram of the random number complete calculation result of b in Fig. 4 and the predicted result;

FIG. 7 is a comparison diagram of the complete calculation result of the random number of c in FIG. 4 and the predicted result.

FIG. 8 is a schematic diagram of a flow chart for determining the optimal standard deviation error range in the present invention.

FIG. 9 is a schematic flow chart of the improved random number measurement and calculation process of the present invention.

Fig. 10 is the contrast diagram of the random number complete calculation result of a in Fig. 4 and the improved prediction result of the present invention;

Fig. 11 is the contrast diagram of the random number complete calculation result of b in Fig. 4 and the improved prediction result of the present invention;

FIG. 12 is a comparison diagram of the complete calculation result of the random number of c in FIG. 4 and the improved prediction result of the present invention.

Figure 13 is a photo of the interior scene of the front end of the shield machine during the construction of a tunnel project;

Figure 14 is a photo of the interior scene after the construction of a tunnel project is completed.

Figure 15 is a schematic diagram of the geological section structure at the location of a tunnel project.

Figure 16 is the finite element numerical model diagram of a tunnel project.

Figure 17 is the curve diagram of the support stress and the center displacement of the face of a tunnel project.

Fig. 18 is a numerical model diagram of a tunnel's cohesion random field;

Figure 19 is a comparison diagram of the complete calculation results of random numbers of a tunnel cohesion random field numerical model and the prediction results before and after improvement.

Figure 20 is a numerical model diagram of a random field of friction angle in a tunnel;

Figure 21 is a comparison diagram of the complete calculation results of random numbers of a random field numerical model of a tunnel friction angle and the prediction results before and after improvement.

Detailed ways

The specific embodiments of the present invention will be described below with reference to the accompanying drawings and examples, but the following examples are only used to describe the present invention in detail, and do not limit the scope of the present invention in any way.

The analysis software involved in the following examples are conventional application software unless otherwise specified; the involved steps and methods are conventional methods unless otherwise specified.

The following embodiments and test examples, unless otherwise specified, are described by taking 600 groups of random numbers as an example. Test Example 3 uses 500 groups of random numbers as an example to illustrate.

Example 1: Establishment of a random field model for the spatial variability of soil parameters

Based on the FLAC ^3D numerical analysis software, the random field is combined with numerical analysis in a random generation method to generate a random field. Specific steps are as follows:

(1) According to the object to be measured (such as geotechnical structure, engineering structure, etc.) and related engineering accuracy requirements, use the finite difference software FLAC ^3D to establish a finite element numerical model, and set the established numerical model to contain n elements in total, then , using the software built-in fish language to output the coordinate information of the center point of each unit in the model (the x , y coordinates of the center point of the output unit of the two-dimensional model, the x , y , and z coordinates of the center point of the output unit of the three-dimensional model), and store in a text file, thus completing the first step of random field generation.

(2) Using the coordinate information of the center point of the numerical model unit output in step (1), combined with the autocorrelation function, according to the covariance decomposition theory, the second step of random field generation is completed.

The autocorrelation function is used as shown in formula (i):

——式（i）；

- formula (i);

In formula (i), δ _x , δ _y , δ _z are the correlation distances in the x , y , and z directions, respectively; τ _x , τ _y , τ _z are the coordinates between any two units in the x , y , and z directions, respectively Difference, for the two-dimensional numerical model of the xoy plane, it can be considered that τ _z is always equal to zero.

The unit center point coordinate information output in step (1) is brought into formula (i), and the autocorrelation coefficient of each unit center point coordinate relative to other unit center point coordinates (including itself) is calculated by formula (i). An n × 1 matrix can be obtained from the calculation result of the autocorrelation coefficient of a single unit, and an n × n covariance autocorrelation matrix C _{n × n} can be obtained by analogy with n units. Using Cholesky decomposition, C _{n × n} is expressed as the multiplication of upper and lower triangular matrices, as shown in equation (ii):

C = LU = LL ^T - formula (ii);

In formula (ii), L and U are lower triangular and upper triangular matrices, respectively, and L ^T is the transpose of matrix L.

(3) Using the lower triangular matrix L calculated in step (2), based on the standard normal distribution function, generate a standard normal distribution random field;

Set Y to be n column vectors that are independent of each other and obey the standard normal distribution. Combined with the lower triangular matrix L obtained by the calculation in step (2), the calculation formula of the standard normal distribution random field Z can be obtained, such as formula (iii) shown:

Z = LY - formula (iii);

That is, using the random column vector Y , a random field Z of different standard normal distributions is obtained.

(4) Using the standard normal distribution random field Z calculated by formula (iii), the calculation formula of the target normal random field ZS with mean value μ and variance σ ² is generated, as shown in formula (iv):

ZS = σZ + μ - formula (iv).

In nature, geotechnical parameters (such as elastic modulus, cohesion, friction angle, strength, joints, fault distribution, temperature field, stress field, seepage field, etc.) mostly obey lognormal distribution. The mean is μ _1n and the variance is σ ^{2 1n} , which is transformed into a standard normal distribution with a mean of μ and a variance of σ ² by formula (v) and formula (vi).

——式（v）；

- formula (v);

——式（vi）；

- formula (vi);

The parameter coefficient of variation COV is expressed by formula (vii):

——式（vii）。

- Formula (vii).

(5) Using the built-in language of FLAC3D, the parameters in the random field ZS generated in step (4) are assigned to the units in the model in one-to-one correspondence, and the calculation is performed, so as to realize the realization of parameter variability in the numerical model.

(6) According to the Monte Carlo strategy (Monte Carlo method), repeat steps (3) to (5) M times to obtain M calculation results for probability analysis.

Example 2: Calculation of random numbers in random fields with spatial variability of soil parameters

In order to solve the technical problems of large amount of calculation and time-consuming and labor-intensive in the random field probability analysis in the prior art, the present invention adopts the prediction method of predicting the calculation results of an infinite number of random fields with the calculation results of a finite number of random fields, that is, setting two random field calculation results. Airport matrices A and B , and calculate D=A - B , by calculating the F-norm of matrix D , as shown in formula (viii):

——式（viii）；

- formula (viii);

When the value of ‖ D ‖ _F tends to zero, A and B should get the same calculation result.

1. Establish a corresponding numerical analysis model based on the method described in Embodiment 1, generate 600 groups of random numbers, and use the calculation results of 50 groups to predict the remaining 550 calculation results.

The prediction process is shown in Figure 1, which is as follows:

(1) A group of random numbers A is randomly selected from the 550 groups of random numbers to be predicted that are not repeated.

(2) Calculate ‖ D ‖ _F by using formula (viii) to calculate the random number A drawn in the first step and 50 groups of random numbers with known calculation results respectively, and take the random number corresponding to the smallest ‖ D ‖ _F among the 50 calculation results . Calculate the result as the corresponding prediction result.

(3) Repeat steps (1) and (2) 550 times to obtain the prediction results of 550 groups of random numbers.

2. Use the settlement value of the center point of the three-dimensional cube elastic body to verify the above prediction method, and compare the prediction results with the actual simulation calculation results to verify the accuracy of the prediction method.

As shown in Figure 2, a cube-shaped element model with a side length of 10 meters is established. The boundary conditions of the model are that except the top surface is a free surface, normal constraints are imposed on the rest of the boundaries. The model with a side length of 10 meters in Figure 2 is divided into 2744, 10648, 21952 units (as shown in a, b, and c in Figure 3).

For the convenience of principle explanation, elastic constitutive is adopted in all models, Poisson's ratio is taken as 0.23, and density is taken as 1800Kg/m ³ . The elastic modulus is set to obey the log-normal distribution, the mean value is 24MPa, the coefficient of variation COV is 0.3, and the correlation distance δ _x = δ _y = δ _z = 2 m . The method of Example 1 is used to generate 600 groups of elastic modulus random numbers for model units a, b, and c in Fig. 3, respectively. In Fig. 4, a, b, and c respectively represent a group of random numbers that form a typical elastic modulus. Spatial distribution map, different cell colors/grayscales represent different elastic modulus values.

Further, a vertical downward stress of 2MPa is applied to the top surface of the model in a, b, and c in Fig. 4, and the vertical displacement value of the center point of the top surface is monitored.

According to the numerical calculation results, the vertical displacement values of the 600 top surface center points of a, b, and c in Fig. 4 can be obtained respectively. Using the above random number prediction method (as shown in Figure 1), the calculation results of the first 50 groups of random numbers are also used to predict the calculation results of the remaining 550 groups of random numbers for a, b, and c in Figure 4 respectively. Take the number of random arrays as the abscissa, and the average vertical displacement value as the ordinate, and compare the predicted results with the actual complete calculation results.

For models a, b, and c in Figure 4, the final comparison results are shown in Figures 5 to 7, respectively.

It can be seen from Figures 5 to 7 that although the predicted curve obtained by the above-mentioned random number prediction method and the actual complete calculation curve are generally consistent in trend, except for a few (Figure 6), the two are generally consistent. The degree of prediction is poor, and the prediction effect is still unsatisfactory. Therefore, further improvement is necessary to obtain more accurate and reliable prediction results.

Example 3: Improvement of Random Number Calculation in Random Field of Spatial Variability of Soil Parameters

The inventor found in the long-term engineering practice and experimental research that to determine whether the calculation results of two groups of random numbers are the same, in addition to the _similarity of ‖D‖F , it should also be related to the standard deviation, because the standard deviation can reflect a set of parameters and data. Degree of dispersion. On the premise of ensuring that the standard deviation of the two sets of data is within a certain error range, finding the random number calculation result corresponding to the smallest ‖ D ‖ _F as the prediction result can greatly improve the prediction accuracy. However, the value of the error range of the standard deviation cannot be too large, otherwise the constraint effect of the standard deviation cannot be reflected; the value of the error range of the standard deviation cannot be too small, otherwise the ideal prediction result cannot be obtained. Therefore, there is a problem of the optimal error range value.

Therefore, the improvement of the present invention is divided into two steps:

The first step is to use the calculation results of random numbers with a certain sample size (50 groups in this example) to obtain the best standard deviation error range; among them, the larger the sample size, the more accurate the random number calculation results of the random field. high;

In the second step, the prediction results are obtained by using the optimal error range and the two constraints of ‖ D ‖ _F.

1. The value of the optimal standard deviation error range

The best standard deviation error range is obtained by using the calculation results of 50 groups of known random numbers. The process of determining the value of the best error range is shown in Figure 8. The specific steps are as follows:

(1) Divide 50 groups of random numbers with known calculation results into two groups A and B , each of which contains 25 groups of random numbers;

(2) One of the two groups A and B is designated as the known quantity, and the other is designated as the group to be predicted. Here, it is assumed that the large group A is a known quantity, and the large group B is the group to be predicted;

(3) Extract a group of random numbers g from the large group B , and calculate the standard deviation S corresponding to the random number g ;

(4) Give a small initial value of standard deviation error i % = k % (assume k = 0.1), so as to calculate the value range of standard deviation U = [ S (1- i %) ~ S (1 + i %)];

(5) Screen out group random numbers whose standard deviation is within the range U from the large group A to form a new large group C ;

(6) Calculate ‖ D ‖ _F from the random number g extracted from the large group B and the N groups of random numbers in the large group C using formula (viii), and take the smallest ‖ D ‖ _F among the N calculation results . The random number calculation result is used as the corresponding prediction result;

(7) Repeat steps (3) to (6) 25 times to obtain the prediction results of 25 groups of random numbers in the large group B ;

(8) Compare the prediction results of 25 groups of random numbers in the large group B obtained in step (7) with the corresponding actual calculation results, and calculate the average error SS ;

(9) Set the standard deviation error range i % in step (4) and the increase value of each calculation is j % (assuming j=0.1 ), then the standard deviation error range of the M -th calculation is i % = k % + M × j %; repeat steps (3) to (8) M times to obtain M average errors;

(10) Take the standard deviation error range corresponding to the minimum value of the M average errors as i %, as the best standard deviation error range and take the value ii % (in this case, ii = i ).

2. Random number prediction process

Using the obtained best standard deviation error range ii % and 50 groups of known random number calculation results, the calculation results of the remaining groups (such as 550 groups) of random numbers are predicted. The prediction process is shown in Figure 9. The specific steps are:

(1) Extract a group of random numbers g from the 550 groups of random numbers to be predicted, and calculate the standard deviation S corresponding to the random number g ;

(2) According to the best standard deviation error range ii %, the value range of standard deviation U = [ S (1- ii %) ~ S (1+ ii %)];

(3) Screen out N groups of random numbers whose standard deviation is within the range U from 50 groups of random numbers with known calculation results to form a new large group C ;

(4) Calculate ‖ D ‖ _F from the random number g extracted from the 550 groups of random numbers to be predicted and N groups of random numbers in the large group C using formula (viii), and take the smallest ‖ D ‖ among the N calculation results The random number calculation result corresponding to _F is used as the corresponding prediction result;

(5) Repeat steps (1) to (4) 550 times to get the prediction results of 550 groups of random numbers.

Test Example 1: Validation of Improved Prediction Method

Continue to use the cube-shaped unit model with a side length of 10 meters established in Example 2, that is, the calculation results of the random field models a, b, and c in Figure 4, and use the calculation results of the first 50 groups of random numbers to predict the remaining 550 groups of random numbers. For the calculation results, the predicted results obtained by the method described in the third embodiment and the method described in the second embodiment are compared with the actual complete calculation results.

The results are shown in Figures 10 to 12, from which it is not difficult to see that the improved prediction method of the present invention is more consistent with the complete calculation results, which shows that the method of the present invention greatly improves the accuracy of prediction.

Test Example 2: Application in Tunnel Shield Engineering

(1) Project overview

A proposed station and interval tunnel in Zhengzhou City are located in the Huanghuai alluvial-proluvial plain area. The terrain is slightly undulating. The surrounding area is newly built or existing municipal roads and green belts. There are many surrounding buildings and urban municipal pipelines, and the engineering construction environment is relatively complex. .

The mileage of the starting point of the underground section of the railway project is CK79+195.230, the mileage of the boundary between the U-shaped groove section and the buried section is CK79+457.235, the mileage of the boundary between the buried section and the shield well is right CK79+624.818, and the starting mileage of the shield section is CK79+ 640.882, the end mileage of the shield section is CK80+469.385; the length of the U-shaped groove is 262.005m; the length of the buried section is 167.583m; the shield section is 809.162m (short chain 19.341m).

(2) Shield excavation method

According to the preliminary survey data, the minimum buried depth of the line in this project is about 7.39m, and the maximum buried depth is about 10.0m (without considering artificial fill). According to the successful experience of applying earth pressure balance shield in Zhengzhou rail transit project, the design institute recommends earth pressure balance shield, and the diameter of shield machine cutter head is 6.3 meters.

The front-end scene of the shield machine during the construction of the project is shown in Figure 13; the internal scene after the construction is completed is shown in Figure 14.

The starting mileage of the shield tunnel on the left line of the project is CK79+640.882, and the burial depth is 7.39m at this time. When the mileage increases to the left CK79+800.775, the tunnel burial depth is 10.0 meters (without considering artificial filling), after that, the underground engineering is basically Buried at a depth of about 10.0 meters.

(3) Variability analysis of geotechnical parameters

By drilling holes and conducting laboratory test analysis of the collected rock mass materials, the geological section structure can be obtained as shown in Figure 15, and the mechanical parameters (average values) of different soil layers are shown in Table 1. It is applied to the model as a load in the calculation.

Table 1 Recommended values of mechanical parameters of each soil layer (average value)

。

.

(4) Tunnel random field construction

The shield method is used to excavate the tunnel, and the stability of the front face is very important to the smooth progress of the project. Therefore, a normal stress is often applied to the face as a supporting force in engineering. The smaller the support force is, the greater the displacement value of the center of the face. Therefore, there is a critical minimum support force to ensure the stability of the face. Once the support force is less than this critical value, the face will become unstable. Unstable displacement occurs, affecting the safety of construction.

The Mohr-Coulomb criterion is a commonly used yield criterion in engineering. The only parameters required are the friction angle and cohesion, which can be obtained through laboratory experiments. Therefore, the Mohr-Coulomb criterion is still selected as the yield criterion for numerical analysis.

For the example of this project, in order to study the size of the minimum supporting force, the method described in Example 1 is used to establish the finite element numerical model of the tunnel (as shown in Figure 16). The diameter of the shallow circular tunnel is 6.3 meters and the depth is 10 meters (consistent with the actual project); the lengths in the x , y , and z directions are 26.3m, 35m, and 30m, respectively. Except for the free surface at the top of the z direction, the rest of the boundaries of the entire model are normal constraints. Divided into 22152 units.

The values of the basic parameters are shown in Table 1. The analysis values of the spatial variability of cohesion and friction angle are the same as the results of the laboratory test. For the cohesion, the coefficient of variation of silty clay is 0.3, and the correlation distance is 2m. ; The coefficient of variation of silt is 0.25, and the correlation distance is 2.3m; for the friction angle: the coefficient of variation of silty clay is 0.2, and the correlation distance is 1.6m; the coefficient of variation of silt is 0.18, and the correlation distance is 1.3m.

(5) Determination of minimum support force of shield tunnel

As shown in Figure 16, a circular tunnel is excavated, and a support normal stress P is applied to the excavation plane (ie, the face of the tunnel), and the horizontal displacement of the center point of the face of the tunnel is monitored. During the calculation process, it gradually decreases Supporting the normal stress P , and recording the displacement value DY of the center point of the face along the Y direction, a series of stress P and the corresponding displacement DY can be obtained, taking the stress value P as the abscissa and the displacement value DY as the ordinate , the stress-displacement curve is obtained as shown in Figure 17.

It can be seen from Figure 17 that after passing point B, the horizontal displacement increases sharply with the decrease of support stress P , and it can be considered that the support stress corresponding to point B is the minimum support stress.

The method of finding the minimum support stress is described with reference to Figure 17. During the calculation process, the support stress starts from 50kPa and gradually decreases. Four coordinate points are selected in the AB section, and the selected four coordinate points are as close as possible to point A, and then use The least square method is used to fit the linear equation y = f ( x ) of the support stress and displacement according to the coordinate values of the selected 4 points, and use it as the linear equation of the stable segment. The support stress is from large to small, and the distance DF from the remaining coordinate points in Figure 17 to the straight line equation y = f ( x ) is calculated in turn. When DF is greater than a certain value (through the analysis of this model, the critical value is 0.029m), That is, the support stress of this coordinate point is considered to be the minimum support stress.

Through comparison, it is found that the minimum support stress calculated by the above method is equal to the minimum support stress obtained by using the curve in Fig. 17, which effectively verifies the reliability of the improved method of the present invention.

The Mohr-Coulomb yield criterion has two basic parameters, namely the friction angle φ and the cohesion c, respectively. The influence of the randomness of the friction angle and the cohesion on the support stress is calculated respectively. Since the calculation result of the minimum support force is related to the reduction step size of the support stress in the calculation process, in order to minimize the influence of the step size, the step size is taken as a very small 40pa.

1) Randomness of cohesion

The cohesion is set to obey the log-normal distribution, the coefficient of variation of silty clay is 0.3, and the correlation distance is 2m; the coefficient of variation of silty soil is 0.25, and the correlation distance is 2.3m. The other basic parameters are shown in Table 1. The method described in Example 1 generates 500 sets of random numbers of cohesion for the model shown in Figure 16, and obtains a set of random numbers to form a typical spatial distribution of cohesion, as shown in Figure 18, its different cell colors/grayscales. Corresponding to different cohesion values.

According to the model shown in Fig. 18, the equilibrium is calculated under the action of self-weight to form the original in-situ stress field. After the tunnel is excavated, calculate the minimum support stress corresponding to each group of random numbers of cohesion, and finally obtain 500 minimum support stresses corresponding to 500 groups of random numbers. Use the calculation results of the first 50 groups of random numbers to predict the calculation results of the remaining 450 groups of random numbers. Taking the number of random arrays as the abscissa, and the average value of the minimum support stress as the ordinate, the predicted results obtained by the methods described in Embodiment 3 and Embodiment 2 are compared with the actual complete calculation results. The comparison results are shown in Figure 19, from which it is not difficult to see that the improved prediction method of the present invention is more consistent with the actual complete calculation results, and the prediction accuracy is greatly improved. Considering the spatial variability of cohesion, the minimum support force converges to about 6.25kPa, that is, for this project, during shield excavation, the support force on the face of the tunnel shall not be less than 6.25kPa.

2) Randomness of friction angle

The friction angle is set to obey the log-normal distribution, the coefficient of variation of silty clay is 0.2, and the correlation distance is 1.6m; the coefficient of variation of silty soil is 0.18, and the correlation distance is 1.3m. The rest of the basic parameters are shown in Table 1. The method described in Example 1 was used to generate 500 sets of random numbers of cohesion for the model shown in Figure 16, and a set of random numbers was obtained to form a typical spatial distribution diagram of friction angle. As shown in Figure 20, different cell colors/gray Degrees correspond to different friction angle values.

According to the model shown in Figure 20, the equilibrium is calculated under the action of self-weight to form the original in-situ stress field. After the tunnel is excavated, the minimum support stress corresponding to each group of random numbers of friction angles is calculated, and finally 500 minimum support stresses corresponding to 500 groups of random numbers can be obtained. Use the calculation results of the first 50 groups of random numbers to predict the calculation results of the remaining 450 groups of random numbers. Taking the number of random arrays as the abscissa, and the average value of the minimum support stress as the ordinate, the prediction results obtained by the methods described in Embodiment 3 and Embodiment 2 are compared with the actual complete calculation results. The comparison results are shown in Figure 21. It is not difficult to see that the improved prediction method is more consistent with the complete calculation results, and the prediction accuracy is greatly improved. Considering the spatial variability of the friction angle, the minimum support force converges to about 6.5kPa, that is, for this project, the support force on the face of the tunnel during shield excavation shall not be less than 6.5kPa.

The present invention has been described in detail above in conjunction with the accompanying drawings and embodiments, but those skilled in the art can understand that, without departing from the purpose of the present invention, each specific parameter in the above-mentioned embodiments can also be changed, Forming a plurality of specific embodiments is the common variation range of the present invention, and will not be described in detail here.

Claims (8)

1. A method for predicting parameter variability results of geotechnical materials is characterized by comprising the following steps:

(1) establishing a corresponding finite element numerical model according to the properties of the geotechnical materials and the engineering precision requirement, and generating n' units;

(2) substituting the coordinates of the central point of each unit in the finite element numerical model into an autocorrelation function to obtain a covariance autocorrelation matrix according to a covariance matrix decomposition method, and expressing the covariance autocorrelation matrix as multiplication of an upper triangular matrix and a lower triangular matrix by using Cholesky decomposition;

(3) based on a standard normal distribution rule, generating a standard normal distribution random field by the lower triangular matrix obtained in the previous step; converting the standard normal distribution random field into a normal random field with the mean value of mu and the variance of sigma 2;

mapping parameters in the normal random field obtained by transformation and characteristic rock-soil material property parameters into each unit of the finite element numerical model in a one-to-one correspondence mode respectively to realize conversion from the random field model to the numerical analysis model;

(4) Repeating the step (3) for M times according to a Monte Carlo strategy, thereby obtaining M groups of random number measurement results;

(5) dividing the M groups of random number measurement and calculation results obtained in the previous step into a known quantity group A and a group B to be predicted;

(6) extracting a group of random numbers g from the group B to be predicted, and calculating a standard deviation S corresponding to the random numbers g; taking an initial value of standard deviation error, i% = k%, setting k =0.1, and calculating a value range U of the standard deviation, wherein the value range U is set to be a value range from S (1-i%) to S (1+ i%);

(7) screening n groups of random numbers with standard difference values within the range U from the known quantity group A to form a new large group C;

(8) c 'is a random field matrix of a large group C, B' is a random field matrix of a group B to be predicted, D = C '-B', the random numbers g extracted from the group B to be predicted and n groups of random numbers in the large group C are respectively used for calculating the F norm | D | F of the matrix D, and the random number calculation result corresponding to the smallest | D | F in the n calculation results is taken as the corresponding prediction result;

(9) repeating the steps (5) to (8) to obtain a prediction result of the random numbers in the group B to be predicted, comparing the prediction result with an actual calculation result, and calculating an average error SS;

(10) Setting the increment value of the standard error i% in the step (6) in each calculation as j%, and setting the standard error range value of the Nth calculation as i% = k% + Nxj%; repeating the steps (6) to (9) for N times to obtain N average errors; taking the standard error range corresponding to the minimum value of the N average errors as i%, and obtaining the optimal standard error range value ii%;

(11) and (4) taking the random number to be measured from the random field in the step (3), adopting the optimal standard error range to take the value ii%, and repeating the steps (6) to (8) until the calculation result is stable in convergence to obtain the prediction result corresponding to the repetition times.

2. The method for predicting the result of variability of geotechnical material parameters according to claim 1, wherein in said step (2), the selected autocorrelation function is:

-formula (i);

in the formula (i), x, y and z are coordinate directions of the finite element numerical model; δ x, δ y and δ z are respectively the relevant distances in the x, y and z directions; τ x, τ y, τ z are the coordinate differences in the x, y, z directions between any two units, respectively.

3. The method for predicting the result of variability of parameters of geotechnical materials according to claim 1, wherein in said step (2), the covariance autocorrelation matrix is expressed by Cholesky decomposition as:

C = LU = LL^T-formula (ii);

in formula (ii), L, U are lower and upper triangular matrices, L, respectively^TIs the transpose of the matrix L.

4. The method for predicting the result of variability of geotechnical material parameters according to claim 1, wherein in said step (10), j% =0.05% -0.1%.

5. The method for predicting the result of variability of parameters of geotechnical materials according to claim 1, wherein said parameters of properties of geotechnical materials are parameters characterizing any one of strength, joint, fault distribution, temperature field, stress field, and seepage field of geotechnical materials.

6. The method for predicting the result of variability of parameters of geotechnical materials according to claim 1, wherein said geotechnical material property parameter is any one of elastic modulus, cohesion and friction angle.

7. Use of the method of prediction of the results of variability of parameters of geotechnical materials according to claim 1 in the analysis of structural stability of geotechnical engineering.

8. The use according to claim 7, characterized in that the minimum supporting force of tunnel engineering or the displacement and settlement of the engineering structure are calculated.

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