Inversion Analysis Method for Tunnel and Underground Space Engineering: A Short Review

Round 1

Reviewer 1 Report

Review of the manuscript “Inversion analysis method for tunnel and underground space engineering in China: a short review”

by Song et al. Submitted to APPSCI-2324647

GENERAL COMMENTS

This paper presents a short review on the inversion analysis method for tunnel and underground space engineering, and it includes some research progresses and presents some challenging and complex tunneling problems in the context of informatization digitalization. Moreover, some shortcomings of this method are illustrated, and further developments and future trends are also presented. According to the high-quality standards of the Applied Sciences, the paper can be considered for publication after some revisions. Some major and minor comments are summarized as follows.

MAJOR/MINOR COMMENTS

u  The TITLE is not quite appropriate, because I wonder why the authors mention ”in China” in this title. It does not correspond to the following introductions and discussions.

u  The INTRODUCTION is essentially a disordered list of concise (sometimes vague and imprecise) statements about what other authors did in the past in the field. The mere sum of these statements is far from a coherent analysis of the current state of the art and certainly does not suffice to support the paper’s motivations. The authors must relate the referenced works to each other by highlighting the advancements and significant theoretical/applied results of each piece of research. The motivation of the manuscript should be illustrated more clearly and concisely. Moreover, the authors can not only just illustrate other studies. The advantages and disadvantages of the previous studies should be illustrated more clearly, and the authors should illustrate more clearly why they write this short review.

u  The overall logic of the manuscript looks a bit confusing, so some revisions should be done.

u  Some equations have been included and illustrated. More illustrations should be added here, and some references should be cited.

u  Future developments and problems should be presented in detail.

u  There are many other different methods in solving these problems, so why the authors choose this method.

u  Too many references in Chinese are cited, so more relative references should be included.

u  The English should be improved significantly.

Author Response

Dear editor,

Manuscript ID: applsci-2324647

Title: Inversion analysis method for tunnel and underground space engineering: a short review

We would like to thank applied science for giving us an opportunity to revise our manuscript. We thank the reviewers for their read and thoughtful comments on previous draft. We have carefully taken their comments into consideration in preparing our revisions, which have helped us to complete a clearer and more convincing manuscript. The following summarizes how we responded to reviewer comments.

Thanks for considering our manuscript.  

Best wishes,

1.The Title is not quite appropriate, because I wonder why the authors mention ”in China” in this title. It does not correspond to the following introductions and discussions.

Response: Thank you very much for your valuable comments. The title of this manuscript is changed to "Inversion analysis method for tunnel and underground space engineering: a short review".

2.The Introduction is essentially a disordered list of concise (sometimes vague and imprecise) statements about what other authors did in the past in the field. The mere sum of these statements is far from a coherent analysis of the current state of the art and certainly does not suffice to support the paper’s motivations. The authors must relate the referenced works to each other by highlighting the advancements and significant theoretical/applied results of each piece of research. The motivation of the manuscript should be illustrated more clearly and concisely. Moreover, the authors can not only just illustrate other studies. The advantages and disadvantages of the previous studies should be illustrated more clearly, and the authors should illustrate more clearly why they write this short review.

Response: Thank you very much for your valuable comments. The author gives a more detailed description of the lack of writing motivation in the introduction and the advantages and disadvantages of previous studies. As for the exposition of the research progress and important theories, the author also adds the corresponding content in the introduction, but it is limited by the detailed description of the research results of the development of inversion theory in the first section "The development and main research contents of inversion theory", so the length of this part in the introduction is weakened.

In addition, three new references have been added for supplementary explanation, The reference numbers are 4, 5, 6 respectively.

4.Waterhouse W C. Gauss's first argument for least squares[J]. Archive for history of exact sciences, 1990: 41-52.

5.Fujino Y, Siringoringo D M, Ikeda Y, et al. Research and implementations of structural monitoring for bridges and buildings in Japan[J]. Engineering, 2019, 5(6): 1093-1119.

6.Greenhalgh S A, Bing Z, Green A. Solutions, algorithms and inter-relations for local minimization search geophysical inversion[J]. Journal of Geophysics and engineering, 2006, 3(2): 101-113.

The revised content is as follows:

In the field of tunnel and underground engineering, the main research objects are the characteristics of excavated rock mass and the surrounding geological environment. During the extremely long process of rock mass formation, a large number of cracks and pores will form in the structure. Coupled with the influence of groundwater, the rock mass will become a discontinuous body composed of various media. This results in extremely complex physical and mechanical properties of the rock mass [1, 2]. Therefore, it is important to invert the initial ground stress and related parameters from on-site monitoring and measurement of displacement, stress, strain, and other multivariate information. By doing so, a tunnel excavation and support plan can be formulated. With the development of construction technology and measurement means, many researchers have begun using measurement data to invert the initial ground stress, structural load, and material characteristic parameters. This replaces previous test methods and facilitates application in follow-up projects.

The inverse analysis method involves analyzing physical information data (such as displacement, deformation, stress, strain, or load) measured in the field to establish an effective mapping relationship from the data sample space to the model identification space. It includes two parts, one is the model identification problem of identifying the model structure style closest to the actual deformation law [3] (such as the constitutive model of geotechnical medium) from the change law of monitoring data. The other part is by discussing the inversion model under linear elastic and nonlinear conditions (stress-strain relationship, time and settlement deformation relationship). Various or individual mechanical parameters (such as initial ground stress, structural load, and physical parameters) in the inversion system are identified.

Nowadays, many problems are accompanied by inverse problems, such as the most commonly used least square method, which was first proposed by the famous German mathematician Gauss in 1795 to calculate the trajectories of planets and comets [4]. In the bridge structure monitoring, the researchers use the back analysis method to analyze the building structure under the condition of environmental vibration and strong wind. The performance is evaluated, and the results are close to the measured value [5]. In solid geophysical problems, researchers process geophysical data and extract geological data and physical models that are closest to the actual situation [6]. Combined with the data collected by local seismic stations, the prediction of earthquakes in other areas can be realized, and this process is the inversion of geophysical information. Thus it can be seen that in practical engineering problems, the study of inverse problems has higher practical value, but compared with forward analysis, the inverse analysis still has the characteristics and difficulties of strong nonlinearity, ill-posedness, and a large amount of calculation.

With the fourth Industrial Revolution, there is a growing focus on scientific and technological innovation and technological renewal in various engineering fields. Scholars are increasingly using intelligent inversion analysis methods based on optimization algorithms, computer vision, and data mining to solve difficulties existing in the inversion analysis method itself.At the same time, the problems faced by rock mechanics, such as "limited discretization of data", "complexity of failure mechanism" and "uncertainty of influencing factors" have further promoted the discussion of artificial intelligence (Artificial Intelligence,AI) in geotechnical engineering. Through the in-depth study of AI, a relatively intelligent mechanical analysis and calculation model is obtained, and a computer integrated intelligent system with the ability of self-perception, reasoning learning and active decision-making is developed to solve the rock mass mechanics problems that need to be dealt with by human experts, so as to solve all kinds of tunnel and underground engineering problems in complex geological environment.

However, current research on the application of inversion theory and its analysis method in tunnel and underground engineering is limited to a specific direction, and there are few summary articles on the application of inversion analysis method in this field. This paper analyzes the reasons for the formation of inversion theory in tunnel and underground engineering, summarizes the development process of inversion theory in four stages, and discusses the main research direction of inversion theory in tunnel engineering. The research progress of domestic and foreign scholars applying traditional and intelligent back analysis methods to inverse analysis of initial ground stress, supporting structure load, and tunnel characteristic parameters is summarized. The paper concludes with a call for realizing the diversification of inversion models and the intellectualization of inversion analysis methods in tunnel and underground engineering in the information and intelligent era. The structure flow chart of the article is shown in Figure 1.

3.The overall logic of the manuscript looks a bit confusing, so some revisions should be done.

Response: Thank you very much for your valuable comments. With regard to the logical confusion of the relevant articles mentioned by the reviewers, the author first briefly explains the formation and development of the inversion analysis theory, and believes that the inversion theory has been relatively perfect at present, and its practical application has experienced three stages of generation, evolution and innovation. It has entered the intelligent stage, and the main contents of the inversion theory in tunnel and underground engineering are analyzed. The reason why the initial ground stress, supporting structure load and surrounding rock characteristic parameters are selected as the research objects in the following three sections is that by reading a lot of literature, we find that these three types of target unknowns are the research focus of tunnel and underground engineering, and any project needs to consider the above three types of unknowns. Firstly, the reason for analyzing the initial in-situ stress is that when any tunnel or underground project is constructed, the change of in-situ stress caused by excavation is the first to occur. Accurately calculating the initial in-situ stress and understanding its development process are critical for subsequent construction. When the excavation reaches a certain depth, it is necessary to use steel arch, bolt and other structures for support, and use advanced geological prediction for monitoring. Therefore, the analysis of support structure load can better guarantee the reliability and safety of the construction process. Finally, the reason for the inversion analysis of the surrounding rock characteristic parameters is that the definition range of the parameters is relatively wide. After removing the first two target unknowns, such as elastic modulus, creep parameters, Poisson 's ratio, etc., all belong to the surrounding rock characteristic parameters. In the final discussion, it is helpful to supplement the inversion theory in tunnel and underground engineering. In each section, the application of traditional inversion analysis method and intelligent inversion analysis method in this kind of unknown quantity will be further explained, so that the full text content is complete and the logical framework is perfect.

4.Some equations have been included and illustrated. More illustrations should be added here, and some references should be cited.

Response: Thank you very much for your valuable comments. There are five formulas in this manuscript, according to the opinions of the experts in reviewing the manuscripts, the attached drawings are added to the first formula, as shown in the following figure, and the parameters in the formula are further explained in detail; by quoting the relevant literature (Smyth G K. Nonlinear regression[J]. Encyclopedia of environmetrics, 2002, 3: 1405-1411), the second formula is further supplemented and verified. The last three formulas have been explained by literature citations, and no relevant illustrations have been added in the literature, so they have not been changed in the original text.

Fig. 1 selection of computational domain coordinates

5.Future developments and problems should be presented in detail.

Response: Thank you very much for your valuable comments. The author re-expounds the existing problems and future development of back analysis method in tunnel and underground engineering. This paper gives a more detailed explanation of the three existing problems, and extends the research prospect to the application of deep learning algorithm, The revised content is as follows:

Problems and prospects of inversion analysis method

The inverse analysis method has been used to solve relevant parameter inversion problems since the 1970s. It has been half a century since its inception, and during this period, many scholars have applied this method to various engineering fields. They continue to innovate and improve. With the rapid development of computer technology and observation methods, numerical analysis methods such as the finite element method and boundary element method, as well as monitoring methods such as ground penetrating radar and advanced geological prediction TSP system, have made the research of back analysis in tunnel engineering problems flourish.

Despite this progress, there are still some problems in the current research of tunnel and underground engineering. The main findings are as follows:

1. The reliability of initial geostress inversion in complex geological environments is low. Currently, the stress function used in the back analysis method of initial ground stress is relatively simple. Additionally, the existing theory of rock mechanics based on static research cannot fully reflect the stress field under complex geological conditions, such as high ground stress, high temperature, and long buried depth.
2. Lack of objective indicators to evaluate the accuracy of back analysis. The accuracy of the back analysis results mainly depends on whether the network model can establish an effective nonlinear mapping relationship. However, the types of network models are various, the level of obtaining data information is uneven, and the actual engineering types are also different. Therefore, determining an index to objectively evaluate the accuracy of all kinds of back analysis methods has not been solved yet.

• The process of data processing is difficult to share in real-time. Currently, a large-scale information platform for tunnel monitoring data and geological hazard information sharing has not been established. Furthermore, data mining has a high cost. As a result, some small and medium-sized tunnel projects cannot realize the dynamic optimization of the construction process according to the existing monitoring data. This increases the difficulty of this kind of tunnel construction. However, the quality of on-site data acquisition is also limited by excavation conditions and monitoring equipment. Coupled with the spatio-temporal variability of geological conditions, it is difficult to achieve the relationship between the network model and numerical analysis results in data analysis.

1. Intelligent back analysis methods are costly. The current artificial intelligence technology is not mature, and its way of dealing with problems involves rigorous analysis, calculation, and logical reasoning. This cannot be solved completely without human intervention. To a large extent, it needs to rely on the expert system to make the final decision, and a lot of human and financial resources will be spent on data mining, collection, and storage in this process.

With the increasing trend of cross-disciplinary fields, the intelligent back analysis method has proven to be highly effective in solving tunnel engineering problems. However, this method does not solely depend on neural networks or optimization algorithms; instead, neural networks serve as a foundational component. Based on this theory, we can consider the following four aspects to realize diverse intelligent back analysis methods, improve the premature convergence of optimization algorithms, and enhance the reliability of inversion results. The main results are as follows:

1. Once the autonomous learning process is established, the inversion computing model can actively understand data and make decisions in complex environments. By combining advanced geological prediction, remote sensing, and the use of electromagnetic or waveform signals, monitoring methods can be improved and optimized to make data analysis more accurate and speed up inversion analysis.
2. To better consider tunnel and underground engineering characteristics and find solutions to problems encountered in engineering practice, we should not be limited to relying on various complex optimization algorithms to obtain accurate inversion results. Optimization algorithms are only one of many excellent tools that need to cooperate with engineering practice to realize their practical value. No matter how accurate a tool is, if it does not match its work, it will not be able to maximize its benefits.

• By combining numerical analysis software with better flexibility, compatibility, and visualization, as well as simulation technology and intelligent technology with BIM technology, machine learning, computer vision, and other means, the inversion process can expand in the interactive direction, gradually moving from bottom to top applications.

1. Using deep learning to enhance the recognition ability of traditional algorithms for object features under complex structures can investigate the root cause. Intelligence aims to achieve a better imitation of the way of thinking and expression of the human brain, and inversion analysis aims to get the predicted results more easily. Real intelligence can get the final result without relying on a large amount of data, but it still has to be supported by a large amount of data, making the optimization algorithm of intelligent inversion must be established in a new round.
2. The deep learning network structure should strengthen the expandability of use. Most of the network structures, including fully connected neural networks, convolutional neural networks, and cyclic neural networks, are mainly for supervised learning, which is often limited by artificially labeled sample feature information in the process of use and unable to mine deeper feature information. On the other hand, the unsupervised learning network structure, such as generative countermeasure neural networks, has the ability to extract key information from a large amount of unmarked data and has great potential for development. The use of this kind of network structure can be increased when using intelligent back analysis methods to solve tunnel and underground engineering problems in the future.
3. To achieve a breakthrough in tunnel construction and underground traffic design and construction technology with super-long buried depth under complex conditions, it is necessary to further strengthen countermeasures for large deformation and strong erosion and optimize construction equipment in harsh geological environments. In the process of urban rail transit construction, it is necessary to refine the construction management system, improve the efficiency of network operation and maintenance, and form new construction mode ideas to complete the innovation of tunnel engineering technology and inversion theory.

 

6.There are many other different methods in solving these problems, so why the authors choose this method.

Response: Thank you very much for your valuable comments. In the 19th century, limited by the development of science and technology, tunnel engineering usually uses traditional empirical method and engineering analogy method to solve engineering problems, so it is difficult to achieve the rationality of the design scheme and the safety of the construction process. In the middle of the 20th century, with the rapid development of computer technology, a series of numerical simulation methods based on finite element, discrete element and boundary element have replaced the traditional analytical method and become the main means to solve underground engineering problems. however, some experts and scholars believe that the models used in numerical analysis methods usually have many assumptions and can not effectively consider the dynamic construction process. Therefore, it does not effectively solve the problem of low accuracy of engineering analysis. At the same time, it also seriously affects the development of numerical analysis methods.

With the proposal and application of the New Austrian method, the tunnel construction technology has been greatly developed, and the tunnel construction scale is getting larger and larger, resulting in a large number of on-site monitoring data, which provides another idea for researchers to determine rock mass parameters. that is the back analysis method. As one of the three key elements of the New Austrian method, monitoring and measurement plays a vital role in the whole process of tunnel construction, and timely grasp the first-hand data of on-site monitoring. and collect the stress, strain and displacement changes between the surrounding rock and the supporting structure in the process of tunnel excavation, which is of great significance for subsequent construction control. The back analysis based on the feedback of on-site displacement monitoring information is not only attached to the relevant theoretical research, but also based on the actual measurement, which is both theoretical and practical, and the displacement monitoring data are easier to obtain than the stress-strain data. it effectively solves the problem that it is difficult to simulate the real situation of rock mass by in-situ experiment.

With the arrival of the fourth Industrial Revolution, the on-site monitoring technology has been further innovated, and the measurement scheme has been continuously refined, creating a new platform for the transmission and sharing of all kinds of engineering information. The parameters obtained by the inversion are simulated as the input parameters of the numerical model, and according to the calculation results, a reasonable design basis is provided for the dynamic excavation and support optimization of the subsequent tunnel, which can better ensure the construction safety and reduce the construction risk.

Therefore, we choose this method to solve the problem.

 

7.Too many references in Chinese are cited, so more relative references should be included.

Response: Thank you very much for your valuable comments. Based on the statistics of the Chinese references in the references, a total of 36 articles were found. After further detailed search, 16 of them were replaced by English references, while the remaining 20 Chinese references were retained, because some of these references were published for a long time. No corresponding English literature has the same research content. In addition, these documents are representative and published in very outstanding journals in China, and their influence is very far-reaching. The number of 16 papers replaced by English papers was 24, 29, 33, 39, 43, 44, 51, 54, 55, 57, 64, 65, 91, 92, 95, 97. The number of the remaining 20 Chinese papers was 10, 21, 22, 25, 26, 27, 28, 32, 34, 46, 47, 50, 52, 53, 58, 59, 60, 74, 81, 86. For the replaced literature, the original content has been revised accordingly to ensure that the content of the article is consistent with that of the literature.

8.The English should be improved significantly.

Response: Thank you very much for your valuable comments. The revised paper has been proofread professionally in English to avoid serious English words and grammatical errors.

Author Response File: Author Response.pdf

Reviewer 2 Report

This manuscript studied the issue of “Inversion analysis method for tunnel and underground space engineering in China: a short review”.

First of all, I would like to thank the authors of this manuscript for the effort they put into making it. The paper needs to be rewritten and its objectives well redefined. On the other hand, I have added some comments with the main objective of improving the manuscript. In my opinion, the subject of the paper is remarkably interesting. However, the paper needs some major revisions.

i. What is the innovation point or significance of the study for this article? Please make clear the novelty and contribution of the manuscript and its results as compared to the extensive literature available. The manuscript does not provide a clear objective of the study. What does it add to the subject area compared with other published manuscripts?

ii. Results are merely present and there are no scientific findings are discussed. What is the difference between this manuscript and the article, “Structural stability evaluation technology of Jiangjungou tunnel based on displacement back analysis” or “Theoretical research on the back analysis of the internal force of the supporting structure of a multi-center circular arch tunnel” and 10.1109/TGRS.2020.3046454 that was published before?

iii. In figure 5, the axis units are not clear and what is the actual measurement point means?

iv. The figure 9 is not clear. This should be explained in detail.

v. Results are merely present and there are no experiment results for satisfy the conclusions. The introduction on similar work is very limited and does not cover similar experiences on the topic. I strongly recommend authors give a broader overview of similar works on the topic. The introduction should focus on the content related to the topic of the article.

vi. All the parameters used in the text should be defined. I suggest the authors provide a nomenclature.

vii. In conclusions, the useful data is not provided and the words prove general and lack of academic contributions. Please provide more specific details, evidence and arguments in the conclusions. The current conclusion is rather generic. The discussion is rather basic and short.

viii. DOIs are missing in the list of References.

ix. The English language could be improved as well as the format of the manuscript; though overall English is acceptable.

Author Response

Dear editor,

Manuscript ID: applsci-2324647

Title: Inversion analysis method for tunnel and underground space engineering: a short review

We would like to thank applied science for giving us an opportunity to revise our manuscript. We thank the reviewers for their read and thoughtful comments on previous draft. We have carefully taken their comments into consideration in preparing our revisions, which have helped us to complete a clearer and more convincing manuscript. The following summarizes how we responded to reviewer comments.

Thanks for considering our manuscript.  

Best wishes,

1.What is the innovation point or significance of the study for this article? Please make clear the novelty and contribution of the manuscript and its results as compared to the extensive literature available. The manuscript does not provide a clear objective of the study. What does it add to the subject area compared with other published manuscripts?

Response: Thank you very much for your valuable comments. The extensive literature are mostly limited to the traditional research methods when introducing the application of inversion theory in tunnel and underground engineering, and mainly focus on a specific research direction. However, there are few overview articles that specifically introduce the application of inversion analysis methods by comparing and summarizing the traditional and intelligent inversion analysis methods in the field of tunnel and underground engineering. Compared with the previous reference, the novelty of this manuscript is that it not only reviews the application of traditional back analysis methods in tunnel and underground engineering, but also complements the research status of intelligent back analysis in this field, and the two parts are supported by different cases. More specifically, this manuscript summarizes the research progress of domestic and foreign scholars using traditional back analysis methods and intelligent back analysis methods for the back analysis of initial ground stress, supporting structure load, and surrounding rock characteristic parameters. It also looks forward to how to realize the diversification of tunnel and underground engineering inversion models and the intelligence of back analysis methods in the information age and big data era.

2.Results are merely present and there are no scientific findings are discussed. What is the difference between this manuscript and the article, “Structural stability evaluation technology of Jiangjungou tunnel based on displacement back analysis” or “Theoretical research on the back analysis of the internal force of the supporting structure of a multi-center circular arch tunnel” and 10.1109/TGRS.2020.3046454 that was published before?

Response: Thank you very much for your valuable comments. This manuscript is a reference paper, the conclusion is mainly elaborated in the integration, analysis of a large number of reference, concluded that the method in the current situation of each research object is summarized, and put forward their own opinions. Therefore, this manuscript focuses on the discussion of three kinds of target unknowns, such as initial ground stress, supporting structure load and surrounding rock characteristic parameters, and summarizes the research status and scientific discovery of each target unknown quantity. Taking "supporting structure load" as an example, through a large number of literature studies, it is found that the inverse analysis of this kind of unknown quantity has stronger practical significance than the other two kinds of unknown quantity. The reason is that the concept of ground stress and surrounding rock parameters is artificially defined, and the load can be obtained by measurement, which can directly reflect the reliability of engineering design. The three articles "Displacement-based inverse analysis of structural stability evaluation technology for General Gulch tunnel" or "Theoretical study on inverse analysis of internal forces in support structures of multi-centered circular arch tunnel" and "GPRInvNet: inversion of tunnel lining ground-penetrating radar data based on deep learning" (10.1109/TGRS.2020.3046454) only studied the inverse analysis method of one of the target unknowns , and did not systematically sort out and analyze these three types of target unknowns.

3.In figure 5, the axis units are not clear and what is the actual measurement point means?

Response: The axes units have been added to the Figure 7 (the original Figure 5 is adjusted to Figure 7 after full text modification). The relevant content of the actual measurement point has also been added to the paper. The specific contents are as follows:

The author randomly selected 15, 12, 9, and 6 position points as the ' field measured stress ' points. The abscissa 2, 5, 8, 9, 11, and 14 in the figure are the serial numbers of measuring points under the above four position points.

4.The figure 9 is not clear. This should be explained in detail.

Response: The full text has been modified from Figure 9 to Figure 11. The authors give a further detailed explanation of the contents in Figure 11. The relevant content of the actual measurement point has also been added to the paper. The partially modified content is as follows:

Wang et al [81] introduced the elastic-plastic stress-seepage damage coupling model into the intelligent displacement back analysis, and realized the intelligent inversion of tunnel surrounding rock damage parameters. The analysis process, as shown in Figure 11, is divided into three parts, corresponding to (a)-(c) in which part (a) describes the whole calculation process of the intelligent back analysis program. (b) the part briefly explains the implementation process and principle formula of the differential evolution algorithm used in the program, and the part (c) is the calculation results of the elastic-plastic damage mechanical field of surrounding rock and lining after tunnel excavation with and without considering the action of seepage.

5.Results are merely present and there are no experiment results for satisfy the conclusions. The introduction on similar work is very limited and does not cover similar experiences on the topic. I strongly recommend authors give a broader overview of similar works on the topic. The introduction should focus on the content related to the topic of the article.

Response: Thank you very much for your valuable comments. The authors revised the introduction as follows:

In the field of tunnel and underground engineering, the main research objects are the characteristics of excavated rock mass and the surrounding geological environment. During the extremely long process of rock mass formation, a large number of cracks and pores will form in the structure. Coupled with the influence of groundwater, the rock mass will become a discontinuous body composed of various media. This results in extremely complex physical and mechanical properties of the rock mass [1, 2]. Therefore, it is important to invert the initial ground stress and related parameters from on-site monitoring and measurement of displacement, stress, strain, and other multivariate information. By doing so, a tunnel excavation and support plan can be formulated. With the development of construction technology and measurement means, many researchers have begun using measurement data to invert the initial ground stress, structural load, and material characteristic parameters. This replaces previous test methods and facilitates application in follow-up projects.

The inverse analysis method involves analyzing physical information data (such as displacement, deformation, stress, strain, or load) measured in the field to establish an effective mapping relationship from the data sample space to the model identification space. It includes two parts, one is the model identification problem of identifying the model structure style closest to the actual deformation law [3] (such as the constitutive model of geotechnical medium) from the change law of monitoring data. The other part is by discussing the inversion model under linear elastic and nonlinear conditions (stress-strain relationship, time and settlement deformation relationship). Various or individual mechanical parameters (such as initial ground stress, structural load, and physical parameters) in the inversion system are identified.

Nowadays, many problems are accompanied by inverse problems, such as the most commonly used least square method, which was first proposed by the famous German mathematician Gauss in 1795 to calculate the trajectories of planets and comets [4]. In the bridge structure monitoring, the researchers use the back analysis method to analyze the building structure under the condition of environmental vibration and strong wind. The performance is evaluated, and the results are close to the measured value [5]. In solid geophysical problems, researchers process geophysical data and extract geological data and physical models that are closest to the actual situation [6]. Combined with the data collected by local seismic stations, the prediction of earthquakes in other areas can be realized, and this process is the inversion of geophysical information. Thus it can be seen that in practical engineering problems, the study of inverse problems has higher practical value, but compared with forward analysis, the inverse analysis still has the characteristics and difficulties of strong nonlinearity, ill-posedness, and a large amount of calculation.

With the fourth Industrial Revolution, there is a growing focus on scientific and technological innovation and technological renewal in various engineering fields. Scholars are increasingly using intelligent inversion analysis methods based on optimization algorithms, computer vision, and data mining to solve difficulties existing in the inversion analysis method itself.At the same time, the problems faced by rock mechanics, such as "limited discretization of data", "complexity of failure mechanism" and "uncertainty of influencing factors" have further promoted the discussion of artificial intelligence (Artificial Intelligence,AI) in geotechnical engineering. Through the in-depth study of AI, a relatively intelligent mechanical analysis and calculation model is obtained, and a computer integrated intelligent system with the ability of self-perception, reasoning learning and active decision-making is developed to solve the rock mass mechanics problems that need to be dealt with by human experts, so as to solve all kinds of tunnel and underground engineering problems in complex geological environment.

However, current research on the application of inversion theory and its analysis method in tunnel and underground engineering is limited to a specific direction, and there are few summary articles on the application of inversion analysis method in this field. This paper analyzes the reasons for the formation of inversion theory in tunnel and underground engineering, summarizes the development process of inversion theory in four stages, and discusses the main research direction of inversion theory in tunnel engineering. The research progress of domestic and foreign scholars applying traditional and intelligent back analysis methods to inverse analysis of initial ground stress, supporting structure load, and tunnel characteristic parameters is summarized. The paper concludes with a call for realizing the diversification of inversion models and the intellectualization of inversion analysis methods in tunnel and underground engineering in the information and intelligent era. The structure flow chart of the article is shown in Figure 1.

6.All the parameters used in the text should be defined. I suggest the authors provide a nomenclature.

Response: Thank you very much for your valuable comments. All the parameters in this paper have been explained in the corresponding formula, and no new parameters have been proposed in this paper, and the parameters have been defined by relevant scholars. Therefore, the parameters are not renamed in this article.

7.In conclusions, the useful data is not provided and the words prove general and lack of academic contributions. Please provide more specific details, evidence and arguments in the conclusions. The current conclusion is rather generic. The discussion is rather basic and short.

Response: Thank you very much for your valuable comments. According to the opinions put forward by the reviewers, the conclusions are explained in further detail, as shown below:

Over time, judging the complex mechanical properties of a discontinuous and non-uniform rock mass becomes increasingly difficult. Laboratory experiments and field measurements alone cannot accurately reflect the actual construction process or the dynamic feedback it generates. In response to the demand for production and construction, and the proposal of the New Austrian method, scholars have begun using the changing trend of monitoring surrounding rock displacement to deduce the properties of rock and soil. As a result, the back analysis method has become an effective means of determining the parameters of calculation models. This paper briefly summarizes the reasons for the formation of back analysis methods and introduces the development process of traditional and intelligent back analysis methods. It then summarizes the traditional and intelligent back analysis of three target unknowns: initial ground stress, load of supporting structures, and characteristic parameters of surrounding rock. The main conclusions are as follows:

1. The back analysis method for initial ground stress is becoming increasingly intelligent and informationized due to the continuous improvement and updating of computer function, as well as the rapid development of neural network and machine learning algorithms. The back analysis method is constantly adjusted and optimized according to the tunnel and underground environment under different geological conditions, and the analysis method suitable for the construction method and construction condition of the project is selected. This ensures a seamless connection between the initial geostress back analysis principle and the actual engineering, and improves the practicability and reliability of numerical analysis methods.
2. The accuracy of back analysis of the load of supporting structures largely depends on the deformation data monitored in the field. Compared to the other two kinds of unknowns, the back analysis of this kind has stronger practical significance and can directly reflect the reliability of engineering design. It also contains fewer uncertain factors and assumptions, which makes the back analysis results more well-posed and reliable.

• The inversion of tunnel surrounding rock characteristic parameters is highly ill-posed. To improve the inversion results, more optimization algorithms are needed to analyze unfavorable factors that affect the solution's uniqueness and identifiability. Research methods for this kind of problem are abundant, and the achievements are significant.Currently, the characteristic parameters are obtained by comparing field data with the theoretical model information. With the continuous innovation of computer technology and intelligent calculation methods, and the improvement of field observation accuracy, the inversion results of surrounding rock parameters can be more in line with engineering practice.

8.DOIs are missing in the list of References

Response: The missing doi has been added to the reference except for conference papers, Chinese papers and books, the doi authors of other references have been added.

9.The English language could be improved as well as the format of the manuscript; though overall English is acceptable.

Response: Thank you very much for your valuable comments. The English language in this manuscript has been proofread and improved by the helping of the English professional, and the full-text format has also been modified.

Author Response File: Author Response.pdf

Reviewer 3 Report

The manuscript entitled "Inversion analysis method for tunnel and underground space engineering in China: a short review" is a very interesting work. The authors have done an excellent job of presenting a concise overview of the current state-of-the-art in inversion analysis methods for tunnel and underground space engineering in China. The article provides a comprehensive discussion of the various techniques used in this field and highlights their strengths and limitations. However, some minor English language corrections and grammar mistakes need to be addressed before final acceptance. The manuscript could benefit from a thorough proofreading to ensure that it meets the standards of academic writing. This will help to improve the readability of the manuscript and ensure that the author's ideas are effectively conveyed to the reader. Overall, I recommend that this manuscript be accepted for publication once the necessary revisions have been made. The topic is highly relevant to the field of tunnel and underground space engineering, and the authors have presented a thorough and insightful review of the subject matter. With the appropriate corrections, this manuscript will make a valuable contribution to the literature in this area.

Author Response

Dear editor,

Manuscript ID: applsci-2324647

Title: Inversion analysis method for tunnel and underground space engineering: a short review

We would like to thank applied science for giving us an opportunity to revise our manuscript. We thank the reviewers for their read and thoughtful comments on previous draft. We have carefully taken their comments into consideration in preparing our revisions, which have helped us to complete a clearer and more convincing manuscript. The following summarizes how we responded to reviewer comments.

Thanks for considering our manuscript.

Best wishes,

1.The manuscript entitled "Inversion analysis method for tunnel and underground space engineering in China: a short review" is a very interesting work. The authors have done an excellent job of presenting a concise overview of the current state-of-the-art in inversion analysis methods for tunnel and underground space engineering in China. The article provides a comprehensive discussion of the various techniques used in this field and highlights their strengths and limitations. However, some minor English language corrections and grammar mistakes need to be addressed before final acceptance. The manuscript could benefit from a thorough proofreading to ensure that it meets the standards of academic writing. This will help to improve the readability of the manuscript and ensure that the author's ideas are effectively conveyed to the reader. Overall, I recommend that this manuscript be accepted for publication once the necessary revisions have been made. The topic is highly relevant to the field of tunnel and underground space engineering, and the authors have presented a thorough and insightful review of the subject matter. With the appropriate corrections, this manuscript will make a valuable contribution to the literature in this area

Response: Thank you very much for your valuable comments. We have invited relevant professionals to revised the English language of the full manuscript.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have satisfyingly answered to almost all the points raised in my initial review. 

My opinion is that the paper has been improved, and according to the high quality of Applied Sciences, the paper can be acceptable after the grammar is double checked.

Author Response

Dear editor,

Manuscript ID: applsci-2324647

Title: Inversion analysis method for tunnel and underground space engineering: a short review

We would like to thank applied science for giving us an opportunity to revise our manuscript. We thank the reviewers for their read and thoughtful comments on previous draft. We have carefully taken their comments into consideration in preparing our revisions, which have helped us to complete a clearer and more convincing manuscript. The following summarizes how we responded to reviewer comments.

Thanks for considering our manuscript.

Best wishes,

1.The authors have satisfyingly answered to almost all the points raised in my initial review. My opinion is that the paper has been improved, and according to the high quality of Applied Sciences, the paper can be acceptable after the grammar is double checked.

Response: Thank you very much for your valuable comments. The author will further check the language of the manuscript to ensure that the full text meets the standards required by the journal.

Author Response File: Author Response.pdf

Reviewer 2 Report

The all modification is done and the manuscript suggest be accept in present form

Author Response

Dear editor,

Manuscript ID: applsci-2324647

Title: Inversion analysis method for tunnel and underground space engineering: a short review

We would like to thank applied science for giving us an opportunity to revise our manuscript. We thank the reviewers for their read and thoughtful comments on previous draft. We have carefully taken their comments into consideration in preparing our revisions, which have helped us to complete a clearer and more convincing manuscript. The following summarizes how we responded to reviewer comments.

Thanks for considering our manuscript.

Best wishes,

1.The all modification is done and the manuscript suggest be accept in present form.

Response: Thank you very much for your approval of this paper. The author will further check the full text to ensure that it meets the standards required by the journal.

Author Response File: Author Response.pdf