Underground structures, like other geotechnical engineering, have a lot of uncertainties in the whole design process. The traditional design method uses a general safety factor to consider the influence of many uncertain factors. All parameters and variables are assumed to be uncertain values. This is a conventional fixed value design method. Although the average value or a quantile value of some parameters (such as the strength of materials) was found by mathematical statistics, the influence of the discreteness of each parameter on the safety degree was not considered. Therefore, the safety factor method cannot truly reflect the safety reserve of the structure.
At the end of 1960s, the successful application of mathematical statistics and probability methods in structural design encouraged and inspired tunnel workers to seek to study various uncertainties in underground engineering and estimate their impacts through probability methods. In 1970s, the reliability analysis method was extended to more design fields. However, this method is still opposed and questioned by some geotechnical engineers. Firstly, the mechanism of geotechnical engineering itself is complex, and some problems have not been fully understood; The probability method of geotechnical engineering is still in the development stage, many concepts are unclear and the calculation method is not simple enough. Some people are not familiar with probability theory and methods. These difficulties have also prompted some geotechnical workers to devote themselves to research. They absorbed the results of probability analysis of ground structure and carried out special research according to the characteristics of geotechnical engineering and underground engineering. Although they have not completely solved the technical key, they have achieved gratifying results. The research shows that the more serious the uncertainty, the more vitality the probability and reliability analysis methods can show.
1992, the state bureau of technical supervision issued the unified standard for reliability design of engineering structures as a guide for other types of engineering structures. Railway, highway, water conservancy, port and other industries have successively carried out the compilation of unified standards for structural design. As an important part of the above-mentioned projects, tunnel and underground engineering are also put on the agenda by adopting probabilistic limit state design. Some technical problems need to be solved, as well as practical problems. At present, the application of reliability analysis in underground engineering is going through a process from rough to fine, from simple to complex, and back to simple and practical.
2. Study on the probability characteristics of geotechnical parameters.
When determining the physical and mechanical parameters and original stress state of surrounding rock, the precondition of analyzing the mechanical behavior of underground structure is analyzed. For important large structures (such as underground powerhouse of hydropower station, etc. ), it is usually necessary to drill holes in the surrounding strata and conduct a series of tests to obtain relevant parameters. The longitudinal length of traffic tunnel is much longer than the transverse length, and the surrounding rock passing through it is also changing, which is usually calculated according to the comprehensive mechanical parameters of various surrounding rocks. After introducing reliability, the probability characteristics of these physical parameters must be considered. The research results in this field are of great significance to the reliability analysis of underground structures.
2. 1 Study on reliability of surrounding rock classification standard
Generally, when designing a tunnel, it is necessary to determine the surrounding rock category of the tunnel on site. All kinds of surrounding rock classification have their own set of standards. However, due to the fuzziness or uncertainty of the standard itself, or different people's understanding and treatment of the standard are different, the evaluation results of different people on the same surrounding rock will tend to be consistent in general, but not exactly the same. The randomness of surrounding rock classification deserves our further study.
China has made a lot of achievements in the classification and grading of surrounding rocks, but unfortunately, all departments are still not unified. Professor Lin of Northeastern University put forward the dynamic classification method of surrounding rock stability, and Professor Li Qiang put forward the fuzzy cluster analysis method. In the dynamic analysis method, the distribution of classification standards is preliminarily analyzed, and the classification standards are studied by mathematical statistics. On the function of defining the reliability of grading standards, the distribution law is tested by Kolmolov method. The grading standards and evaluation standards of grading methods are put forward.
2.2 Probability processing of geological data
Detailed geological exploration should be carried out for large underground projects and key long tunnels. However, there must be uncertainty and contingency to obtain the geological conditions and surrounding rock parameters around full-length tunnels or large-scale underground projects from limited exploration data. Probability method can reduce the probability of misjudgment. For example, Bao, a researcher at the Yangtze River Academy of Sciences, used the probability method to deal with the stratigraphic boundary between drilling holes in dam foundation, and obtained more reasonable results.
There are often some abnormal geological points in the stratum, such as weak interlayer and cavity. They have great influence on the construction and operation of underground engineering. To this end, we must first make clear their possibility, approximate location and nature, and then analyze their influence through reliability analysis. Bercher( 1979) and Tang (1987) estimated the probability and statistical characteristics of geological anomalies in a certain area under the conditions of given borehole layout and geological history inference. They first give a prior probability of no abnormality, and then derive a modified probability of no abnormality and joint distribution according to Bayes formula based on a series of borehole data.
2.3 Study on random field of soil parameters
According to the research, the coefficient of variation of soil parameters can reach 0.29, which is far greater than the uncertainty of the calculation model. The probability characteristics of soil parameters have gone through two stages. Early research was based on random variables. Later research focused on the application of random field theory.
It is not difficult to understand that the characteristics of geotechnical engineering are controlled by the average characteristics of geotechnical engineering in a certain spatial range. Statistical features obtained from a single sample are called point features. There is a certain relationship between point characteristics and spatial characteristics. The variance of spatial average elements should be less than that of point elements. It is the spatial mean variance of soil parameters that controls the reliability of geotechnical engineering, not the point variance. Therefore, the probability analysis of soil parameters is a random field problem. For the strata with spatial distribution, there are differences and certain correlations between different points due to the relationship between deposition and burial conditions. This correlation will weaken with the increase of the distance between two points. Correlation distance is an important parameter in the study of random field of geotechnical reliability. Relevant scholars put forward the physical meaning, collective meaning and practical calculation method of correlation distance, and put forward the annual experience value of correlation distance in different strata. The influence of parameters of different statistical methods on reliability analysis is studied.
2.4 The research on statistical characteristics of rock mass characteristics needs to be strengthened.
In recent years, due to the practical needs of reliability analysis of soil slope stability, pile foundation bearing capacity and foundation bearing capacity, the study of soil probability characteristics has been promoted. The research results of soil probability characteristics promote the practical reliability analysis of the above typical projects. Because the constitutive relation of rock mass is more complex, joints, cracks and bedding have greater influence on rock mass characteristics, and the uncertainty of rock underground engineering calculation model is more prominent. For many uncertain rock engineering, reliability analysis is more necessary. Domestic survey and design departments have also accumulated a lot of rock data, but few people have participated in sorting it out by probability method. Japan's work in this area deserves attention. They analyzed and sorted out the distribution characteristics, mean value, variability and relationship of main indexes (such as uniaxial compressive strength, compression deformation coefficient, shear strength, dry density, etc.). Various surrounding rocks (such as granite, diorite, conglomerate, sandstone, mudstone, etc.). ), for reference.
3. The results of stochastic analysis method of action effect.
Action effect is an important comprehensive random variable in reliability analysis, which requires a lot of calculation work. At present, the fixed value analysis method of underground structure action effect, whether it is "load-structure" mode or "stratum-structure" mode, mostly adopts finite element analysis, and also adopts three-dimensional finite element when considering spatial action. There are two main methods for rock formations with developed cracks and joints:
A. The theory of continuum mechanics is still adopted, but the constitutive relation reflecting the characteristics of discontinuous rock mass should be sought or the mechanical properties of joints and cracks should be considered as additional conditions, and then the solution should be obtained;
B. apply block theory to find key blocks. It is also a common method to invert the mechanical indexes of strata by using the measured displacement information. Problems that must be solved in stochastic analysis based on the above methods after introducing reliability.
3. 1 progress of stochastic finite element method
The application of finite element method in random media began in the early 1970s. It was mainly used for geotechnical theory and stress analysis at that time. The basic idea is to adopt Monte Carlo simulation method. This method is based on a large number of deterministic calculations, and the cost is high. The stochastic finite element method for structural static calculation was first put forward by K.Handa of Sweden in the mid-1970s, and Hisada and Nagagri of Japan made a systematic study of the stochastic finite element method in the late 1980s. Since then, stochastic finite element theory has developed in two directions. One is finite element statistical analysis based on perturbation expansion; The other is the local average of random fields. The specific methods are: Newman stochastic finite element method; Stochastic finite element maximum entropy method; Finite element first-order and second-order moment method; Stochastic finite element response surface method: perturbation stochastic finite element method, etc. The above methods have their own characteristics, some of which are rigorous in theory, but have a large amount of calculation; Some of them are approximate and easy to calculate. Response surface method, perturbation method and Monte Carlo method are all used in tunnel reliability analysis in China.
With the development of stochastic finite element, some people put forward nonlinear stochastic finite element, but the theory is being tried. At present, the popular stochastic finite element method can only determine some numerical characteristics of load effect, such as mean, variance and correlation moment, and it is difficult to determine the probability distribution and higher-order moment of load effect, which can not meet the requirements of reliability analysis. Monte Carlo method can calculate probability distribution, but it has a large amount of calculation. Professor Zhang Xinpei of Chengdu Dianzi University proposed an improved stochastic finite element method. Based on the finite element method, the characteristic function of the load effect of each element of the structure is determined by using the characteristic function between the load array and the stiffness matrix elements, and then the positive digital characteristics of the load effect distribution density function are obtained according to the relationship between the characteristic function and the distribution density function and digital characteristics. This method is simple in concept, easy to implement and meets the requirements of reliability analysis.
3.2 The proposal and application of random block theory
Block theory is a rock mass engineering analysis method first put forward by China scholar Shi Genhua and American scholar R.Goodman. It opens up a new way for the stability analysis of rock mass caverns and slopes, and has been paid attention to and widely used in the world. In block theory, rock mass is cut into independent blocks by discontinuous spatial plane, and the mechanical parameters c and φ on the cutting surface are taken as constant values. Due to the complex formation factors of structural planes in actual rock mass, the occurrence of the same group of structural planes changes in a certain range, and the spatial blocks with variable shapes cut by continuous spatial planes are random. The mechanical parameters of the cutting surface are also random variables. So it is more suitable for probability distribution. The random block theory put forward by Wang Baotian and Wu Shiwei of Hohai University uses random sampling method to calculate the probability of movable blocks and first-order second-moment method to calculate the probability of key blocks. The combination of the two can better solve the problem that the occurrence probability and mechanical behavior of known structural planes are random values. Zhang Guangjian of Nanjing University of Aeronautics and Astronautics compiled a calculation program based on random block theory, analyzed the reliability of tunnel surrounding rock stability, and obtained the reliability indexes of block stability of various surrounding rocks. The conclusion is basically consistent with the design and construction experience. If the field measured data can be statistically analyzed, the results will better reflect the engineering practice.
3.3 Three-dimensional stochastic boundary element method is proposed
Finite element analysis of underground structures, especially three-dimensional analysis, needs to be divided into many units and a lot of computer workload and memory. Especially for the subject of infinite area, discretization in a certain range will ignore the influence of the vast foreign area and bring errors. Therefore, people's attention has turned to some boundary methods, and the corresponding boundary element method has been developed. Tunnel boundary element analysis has obvious advantages, and it has been paid more and more attention at home and abroad. In view of the obvious uncertainty of parameters in underground structure analysis, the research and application of stochastic boundary element method will play a new role in tunnel reliability analysis.
The three-dimensional stochastic boundary method proposed by Pan of Wuhan Institute of Hydraulic and Electric Power takes the boundary element calculation process as the function transformation process, and then Taylor expands the function process when selecting parameters. The average value of stress and displacement is obtained by boundary calculation; Then calculate the values of the first derivative and the second derivative of the related variables to the parameters when taking the average value. Finally, considering the variability of parameters, the variability of calculation results is analyzed. The formula of this method is concise, and the calculation workload is small, which has important reference value for tunnel analysis.
3.4 Stochastic Back Analysis of Surrounding Rock Parameters
Because the physical and mechanical indexes of surrounding rock are difficult to determine, the spot sampling test or direct test data only get the point characteristics instead of the spatial average characteristics of surrounding rock we require. Therefore, the method of inversion of surrounding rock parameters by using displacement information obtained from construction monitoring can meet the requirements of underground structure analysis under certain conditions. At present, the back analysis of fixed value is relatively mature, and many programs have been developed for application. The information on which the back analysis is based is actually a random variable with certain discreteness, and the reliability analysis also requires that the results of the back analysis can show probability characteristics. Therefore, stochastic back analysis has been paid more and more attention. The special book Inversion Theory has an important discussion on the probability of back analysis. The papers of doctoral students majoring in geotechnical and underground engineering from Tongji University, North Jiaotong University and Southwest Jiaotong University all involve the stochastic back analysis of tunnels. At present, there are traditional Monte Carlo method and random perturbation method.
4. Looking at the new development of reliability analysis method from the characteristics of geotechnical engineering.
The unified standard for reliability design of engineering structures recommends the first-order second-moment method for calculating structural reliability index in appendix 1. At the same time, it is pointed out that a more accurate method should be used to calculate the limit state equation with large coefficient of variation and high nonlinearity. The variability of physical properties of rock and soil is relatively large, which often presents certain correlation, such as the internal friction angle is negatively correlated with cohesion, and the bulk density is positively correlated with compressive modulus and cohesion. Ignoring these correlations will lead to errors in the calculation results. The first-order second-moment method assumes that the basic variables are independent of each other.
At present, two improved first-order second-order moment correlation methods are proposed. One is to change the relevant variables into irrelevant variables, and the variance matrix of the new variables is composed of the variance matrix of the original variables after standardization. Another method is to expand the standard deviation of the limit state equation to get the sensitivity coefficient of the separated variable as a new variable, and then reflect the influence of another variable related to it in the new sensitivity coefficient. The former method is applicable to several related basic variables, while the latter method is only applicable to two related variables.
For nonlinear limit state equations, sometimes the calculation error is too large by equivalent normal method, and sometimes it is difficult to converge. At this time, Monte Carlo simulation is introduced into reliability analysis, and as long as there are many models, accurate failure probability can be obtained. For a small failure probability, a lot of simulation is needed. In order to save time, the calculation method can be improved. In order to avoid the error caused by approximate fitting, it is worth further exploring to use high-order moment generation.
For the problems that some criteria are easily influenced by human factors, fuzzy mathematics method can also be introduced into reliability analysis and developed into fuzzy reliability analysis method. There are many subjective and objective uncertainties in the methods and standards for judging the stability displacement of tunnels. The fuzzy probability analysis method of tunnel stability regards "tunnel stability" as a fuzzy random event, calculates its fuzzy probability, determines the membership function of surrounding displacement of underground tunnel and tunnel stability by fuzzy statistical analysis and inspection combined with comprehensive evaluation of experts, and derives a general expression for calculating the reliability of tunnel stability.
5. Before and after the revision of Code for Design of Railway Tunnels, tunnel reliability
Railway tunnel occupies a large proportion in underground engineering in China, and the second-level unified standard for reliability design of railway engineering has also been issued. The revision of three-level reliability design of railway design code has been put on the agenda. In view of people's doubts or even negative attitudes towards the application of reliability theory in tunnels, the Ministry of Railways organized a number of experts for the first time to conduct a "Feasibility Study on Revising Railway Tunnel Design Code Based on Reliability Theory", and drew a feasible conclusion. In addition, it put forward ways to realize reliability design and topics to be tackled from the aspects of "load-structure" mode, "stratum-structure" mode and empirical design mode based on engineering analogy. The research has passed the expert review and acceptance organized by the Ministry of Railways, and the artificial conclusion is correct. The proposed tunnel supervision reform has clear objectives and feasible paths, which can be used as a guiding document for future tunnel supervision reform.
In order to make it more difficult to revise the design code of railway tunnel gradually according to the reliability design, the competent department of the Ministry of Railways initiated the basic research on revising the tunnel code according to the reliability theory. The research contents include physical indexes of surrounding rock and statistical characteristics of loose pressure of surrounding rock of deep-buried tunnel. Study on statistical characteristics of overburden load of shallow tunnel: experimental study on statistical characteristics of fill load of open-cut tunnel and shed tunnel: study on calculation method of resistance of lining concrete members and statistical characteristics of eccentric compression strength; Study on geometric characteristics of tunnel lining. Shall be borne by the railway colleges and universities respectively. The topic selection of postgraduate thesis in railway universities has also turned to the field of tunnel reliability design.
At the same time, the relevant universities also put forward methods and some suggestions for the reliability design of civil air defense projects. According to the characteristics of the project, the hydropower department is sorting out the statistical parameters of the function and effect of the tunnel project.
6. Concluding remarks
Although the reliability research in the field of geotechnical engineering in China started late, it developed rapidly. There are many topics involved, and the breadth and scale of research in some aspects may exceed that of foreign countries. As an important part of rock engineering, underground engineering and its reliability research are also carried out under the influence and promotion of each other. However, due to the difficulty and wide coverage, it is still in the development stage as a whole. There is little research on rock tunnel; The reliability analysis method based on geotechnical characteristics needs to be broadened; The close combination of reliability research and geotechnical mechanics mechanism needs to be strengthened. Reliability is an inevitable requirement for the design and development of underground structures, which will inevitably promote the further development of engineering technology.
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