# Inversion Analysis Method for Tunnel and Underground Space Engineering: A Short Review
## 2 The Development and Main Research Contents of Inversion Theory  
### Development of Inversion Theory  
In the 19 th century, researchers relied mainly on empirical methods or engineering analogies to solve engineering problems due to the limitations of science and technology. With the introduction of calculus and solid mechanics theory into tunnel and underground engineering, the combination of theory and experience was realized. The previous empirical method was upgraded to a \"semi-empirical and semi-theoretical\" analysis method. However, the research objects of tunnels and underground engineering are nonlinear, non-homogeneous, and have complex and variable boundary conditions. Therefore, the theoretical analysis method can only solve simple linear problems, and its engineering applicability is poor.  
In the middle of the 20 th century, efficient simulation methods such as the finite element method, discrete element method, and boundary element method became the main means of model analysis with the development of computer technology. The application of theoretical methods in engineering was also extended. However, the simulation method does not solve the problem of low accuracy of theoretical analysis, and there is a large gap between theoretical analysis results and actual results. There are three main reasons for this gap. First, there is uncertainty in the selection of the characteristic parameters of the surrounding rock. The rock parameters obtained from a few boreholes in the field and indoor and outdoor tests have large deviations from the actual ones. Second, there are more assumptions in constructing the model. In the research process, there is often a tendency to treat the surrounding rock mass as a homogeneous isotropic continuous medium and adopt the load-structure model for numerical calculation with large errors. Third, it is impossible to consider the dynamic construction process. Although the strength reduction method is used in the simulation analysis, which can approximate the excavation process, it cannot be adjusted according to the problems occurring in the field and has poor timeliness.  
The complex physical and mechanical properties of engineering research objects lead to more or fewer problems in both field in situ tests and laboratory tests. The analytical method and numerical analysis method also have their inevitable defects, making it necessary for researchers to rely on displacement, stress, and other information from field measurements to determine the characteristic parameters of the surrounding rock. This method of determining the model and parameters based on field monitoring and control information is called inversion analysis.  
The inversion analysis method is not only based on relevant theoretical research but also based on actual measurement, which is both theoretical and practical. It can connect the two for solving more complex engineering problems. Since the early 1970s, the research of engineering parameters through on-site monitoring data of tunnels and underground projects has gradually developed. After more than 40 years of effort, the inversion theory has well developed, and a complete theoretical system has formed. Its development process can be broadly divided into four stages.  
Figure 1: Research frame of inversion analysis method in tunnel and underground space engineering.