Introduction

Seismic damages to infrastructure projects are unavoidable due to natural, environmental, and field-specific operational influence factors. Due to the gradual nature of the damage, it is vital to evaluate infrastructures regularly to avoid any structural perversion. Unfortunately, tunnels and associated infrastructure damages due to the 1995 Kobe earthquake and 2016 Kumamoto earthquake in Japan, the 1999 Chi-Chi earthquake in Taiwan, and the 2008 Wenchuan earthquake in China discarded the belief in the structural safety of underground structures during seismic events (Zhang et al. 2018; Tsindis et al. 2020; Wang et al. 2021).

Jammu and Kashmir is located in the northwestern Himalayas, which is one of the world’s most active seismic regions, with major earthquakes provoked in 1555, 1828, 1885, 1905, and 2005. The 2005 Kashmir earthquake (Mw=7.6) was one of the worst, with over one lakh people killed and infrastructure projects including bridges, retaining walls, and dams destroyed (Durrani et al. 2005). This area has witnessed mega infrastructural projects including bridge abutment, tunnelling, and expansion of railway tracks and national highways, which are going to help the overall economic development of the region (Ansari et al. 2022a, b). The Udhampur Srinagar Baramulla Rail Link (USBRL) project is a 345 km long mega rail project in the Himalayan terrain that is bordered by active seismic sources such as the Main Boundary Thrust (MBT) and Main Central Thrust (MCT). The major tectonic source and alignment of the USBRL project are shown in Fig. 1. The construction work of major tunnel projects started after the 2005 Kashmir earthquake. The growing infrastructural projects, together with the previous historical record of earthquakes and seismotectonic settings push to examine the seismic damage of tunnels for post-seismic phases.

Fig. 1
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Map of Jammu and Kashmir in NW Himalayas showing active seismic sources and alignment of Udhampur Srinagar Baramulla Rail Link (USBRL) project

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Mathematical modelling is the process of describing a real-world problem in mathematical terms, usually in the form of equations, and then using these equations to both understand the original problem and discover new features about it (Foucquier et al. 2013; Xia et al. 2022). The mathematical models can be used to analyze structural behaviour in response to earthquakes (Harichandran and Vanmarcke 1986; Özdamar and Pedamallu 2011; Valaskova et al. 2018). Problem-driven mathematical models of natural and social phenomena in which the selection of relevant mathematics is part of the problem-solving process (Zhang et al. 2022). To solve the earthquake shelter location-allocation problem, a multi-objective, hierarchical mathematical model was developed, along with an interleaved modified particle swarm optimization algorithm and genetic algorithm (Ihueze and Onwurah 2018; Zhao et al. 2019). Modelling underpins much of our understanding of the world and enables tunnel engineers to design earthquake-resistant underground structures. In the current study, six variables from the data set of the Himalayan region are used as input layers, including peak ground acceleration (PGA), source to site distance (SSD), overburden depth (OD), lining thickness (t), tunnel diameter (Ф), and geological strength index (GSI), and a Feedforward Neural Network (FNN) is trained using a deep learning approach. The training and adaptation learning functions were represented by TRAINLM and LEARNGDM, respectively. The cumulative weightage factor for the output layer was provided by FNN. After the neurons have been trained, target data are used to verify the network’s robustness. Through conceivable hits and trials, the weightage elements are resolved, and a mathematical equation in terms of damage index is developed. The Seismic Tunnel Damage Prediction (STDP) Model proposed in the present study is compared with the tunnel damage data sets from the 1999 Chi-Chi earthquake, the 2004 Mid-Niigata earthquake, and the 2008 Wenchuan earthquake.

For the 2004 Mid-Niigata earthquake, the R-value for the suggested STDP model and the NETD model is nearly comparable. The MAE for the CETD Model differs from others since the data set for the Chi-Chi earthquake was found to be unevenly distributed. When compared to the WETD model, the DL neural network computes a larger value of R. The “STD multiple graphs” is presented which have a four-sector graph based on the logical order of the input variables. Seismic design guidelines for tunnelling projects are also proposed in earthquake-prone areas. This diagram provides information on damage indexing, damage pattern, and crack predictive specification. It also analyzes the risks involved and the implications for transportation network serviceability. Mitigation measures must also be implemented for all expected damage states. The proposed seismic tunnel damage prediction (STDP) model, STD multiple graphs, and design guidance can be applied to any earthquake-prone tunnelling project worldwide.

Seismic tunnel damages

The roadway and railway are the two most convenient modes of transportation. The availability of space is a major mishap for the establishment of such networks. To overcome this, underground spacing is an outstanding alternative and this leads to an increase in the demand for tunnel construction. The earthquake-resistant design of such infrastructure projects is extremely challenging. The 1995 Kobe earthquake in Japan caused major damage to tunnels and underground infrastructure, disrupting the entire transportation network (Hashash et al. 2001). One of the devastating incidents in 1999 was the Chi-Chi earthquake in Taiwan, which damaged 49 of the 57 tunnels. The tunnel portals have been severely damaged, with minor to moderate level cracking as well as spalling in the tunnel lining (Wang et al. 2021). During 2004 Mid Niigata earthquake in Japan injured over 4790 people, demolished or collapsed more than 0.1 million dwellings, and damaged 49 tunnels (Jiang et al. 2010).

The 2005 Kashmir earthquake triggered the whole state of Jammu and Kashmir resulting in infrastructure and socioeconomic loss (Ansari et al. 2022a). During this event, the unlined northern portal of the Muzaffarabad tunnel collapsed (Durrani et al. 2005; Aydan et al. 2010). Following the 2005 Kashmir earthquake, the 2008 Wenchuan earthquake in China (Mw=8) destroyed billions of dollars in property and infrastructure losses, particularly in hilly tunnels along the Wenchuan highway (Roy and Sarkar 2017). This earthquake was one of the most tremendous earthquakes in the Asian continent affecting around 0.2 million people in China. This earthquake primarily damaged the 52 highway tunnels in mountainous areas (Lai et al. 2017).

Shrestha et al. (2020) highlighted the damages to the Melamchi tunnel in Nepal, which were caused by the 2015 Gorkha earthquake (Fig. 2). The 2016 Kumamoto earthquake is the most recent example of a large magnitude (Mw=7.3) earthquake inflicting damage to underground infrastructure, notably the Tawarayama tunnel, which is located 22.4 km from the main event’s epicenter (Zhang et al. 2018). In Europe, similar to the damage to the Bolu tunnel in Turkey in 1999, the San Bendetto tunnel in Italy was destroyed by the Norcia earthquake in 2016 (Callisto and Ricci 2019). Table 1 shows the specifics of tunnels that have been damaged by significant earthquakes.

Table 1 List of tunnels damaged during major earthquake events
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Lining spalling and portal collapses were the most visible seismic damage in multiple mountain tunnels during the 1999 Chi-Chi earthquake and the 2008 Wenchuan earthquake During these two earthquakes, most of the tunnels exhibit extensive lining deformation. The two principal portal failure types are stratum deformation and spandrel cracking (Ansari et al. 2022a, b). The most typical types of pavement damage seen in tunnels affected by large magnitude earthquakes are uplift, cracking, and groundwater leakage in construction joints and concrete lining (Yu et al. 2016). The majority of the tunnels damaged in the 2004 Niigata earthquake had wall deformation, with heaving mechanisms at the bottom slab and distorted sidewalls (Wang et al. 2021). A few typical examples of seismic tunnel damage are presented in Fig. 2.

Fig. 2
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Illustration of seismic tunnel damages a collapse of the unlined portal during 2005 Muzaffarabad earthquake (Durrani et al. 2005); b sheared-off liner during 1999 Chi-Chi earthquake (Wang et al. 2021); c lining collapse during 2008 Wenchuan earthquake (Yu et al. 2016); d spalling and shotcrete falling during 2015 Gorkha earthquake (Shrestha et al. 2020); e inclined cracks during 2016 Kumamoto earthquake (Zhang et al. 2018) and f transverse ring cracks during 2016 Norcia earthquake (Callisto and Ricci 2019)

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Deep learning and its applications for earthquake problems

Conceptualization of deep learning and neural networking

Soft computing assists users in solving real-world problems by giving approximate solutions that traditional and analytical models cannot offer. Artificial intelligence (AI) has grown in popularity and acceptance among researchers in fields such as engineering, technology, medicine, cognitive science, mathematics, and so on. AI is like biology or mathematical science that examines how to construct intelligent systems that can solve problems creatively by replicating human capabilities (Hinton and Salakhutdinov 2012; Zhang et al. 2021). In terms of machine learning (ML), it is a subset of AI that allows systems to automatically learn and improve from experience without being explicitly designed (Jordan and Mitchell 2015). Deep neural learning, or DL, is a type of ML that gains enormous strength and flexibility by learning to represent the world as a layered hierarchy of concepts without explicitly extracting characteristics (Fig. 3). Under the assumption of no noise, the accuracy of DL predictions will gradually improve as the dataset grows (Talkhablou et al. 2019; Meraj et al. 2021). It essentially gives effective tools for dealing with the data and extracting useful information for accurate decision-making. Feedforward, recurrent, convolutional, and generative adversarial are the four DL models useful for various engineering applications.

Fig. 3
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Conceptual relationship between the existing soft computing techniques

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Artificial Neural Network (ANN) adheres to the biological learning process that exists in the human brain, intending to create a highly intelligent system that corresponds to neurons (Fukushima and Miyake 1982; Barrow 1996). Feedforward Neural Network (FNN) consists of three layering systems including input, output, and hidden (Phoon 2020). This is mostly used to solve complex judicial-specific modelling and mathematical formulations. A recurrent Neural Network (RNN) has the unique ability to detect past data based on real-time judgmental ideas (Pascanu et al. 2013). LSTM is a more advanced variant of RNN that has three gate controllers known as the input, forget, and output gates (Yuan et al. 2019; Chen et al. 2020). Every piece of information that passes through this unit must be chosen whether it should be remembered or forgotten, and then assigned to the appropriate gate. For image identifications, pictorial representation, and decorative modelling, Convolutional Neural Network (CNN) is popular which works based on the stability of kernels. In the field of infrastructure and transportation engineering, the CNN model is applicable for traffic signal design. For the case of Generative Adversarial Network (GAN), parallel training of generator and discriminator is performed for fake samples.

Applications of deep learning algorithms

The earthquake-related problems are bristling with uncertainty and involve numerous elements that cannot be directly determined by seismologists and geophysicists. The researchers use soft computing technologies to handle numerous seismic effects-based challenges and assessment issues. DL technique is useful to handle big data with perfection and defined grouping for engineering problems. AI can handle randomized searches and approximate reasoning. Transfer learning techniques can be used for prediction modelling by employing ML algorithms (Abdulnaby et al. 2016; Alhassan et al. 2018; Biswas et al. 2018). Unsupervised clustering methods are required for damage prediction in ML-based transportation network assessment projects. Table 2 enlists the various applications of deep learning algorithms in the field of earthquake engineering, disaster risk, geophysical modelling, and mathematical predictions.

Table 2 Practicable applications of soft computing in the earthquake domain
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Architecture of algorithm for the proposed prediction model

Selection of input variables

Tunnelling involves various difficult situations such as squeezing, creeping, water infiltration, shear zone creation, faulting, and so on. Aside from this, a few uncertain circumstances, such as impact and blast loading, may occur. In such instances, predictive modelling comes into play and provides an estimate of the future damage states. For important problems like intersecting tunnels, anisotropic conditions, and geological variability overlain by seismic, impact, or blast loading, mathematical formulation-based predictive modelling serves as a ready-to-use toolbox. The practical application of DL is expanding, particularly in the realm of mathematical modelling (Kochhar et al. 2022; Biswas and Sinha 2021; Nanda et al. 2021; Raaj et al. 2022). In this study, an algorithm based on the Feedforward Neural Network (FNN) is utilized to create a prediction model of future damages caused by seismic loading. Peak ground acceleration (PGA), source to site distance (SSD), overburden depth (OD), lining thickness (t), tunnel diameter (Ф), and geological strength index (GSI) are passed down to create the input layers of the neural network. These input parameters were taken from the previously conducted site-specific seismic studies for the Jammu and Kashmir (Ansari et al. 2022a) as well as technical reports of the Udhampur Srinagar Baramulla Rail Link (USBRL) project (Rajesh 2013; Ram 2015; Yusoff and Adhikari 2017; Sharma and Manchanda 2018; Singh and Sherpuri 2018; Riella et al. 2019). The Udhampur Srinagar Baramulla Rail Link (USBRL) project, a 345 km long railway line connecting the Baramulla with the Indian Railways network offers Jammu and Kashmir an easy way of transportation option (Tomar 2013; Sharma and Panwar 2017; Wani and Alamgir 2017; Kumar 2018; Rohilla and Surinder 2018; Ahmad and Dhang 2019; Wingler 2020). The sectional length of Udhampur-Katra, Katra- Quazigund, and Quazigund -Baramulla are commissioned for traffic and works are in various stages of progress with mean sea level (MSL) varying from 660 to 1723 m. The alignment and structural details for each subsection are mentioned in Table 3.

Table 3 Comprehensive detailing of the subsections of the USBRL project
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Table 4 provides the details for the input parameters used in the present study. For each layer, five distinct classes are suggested. All these classes and their frequency distribution are presented in Fig. 4.

Table 4 Parametric contributions of inputs employed for modelling
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Fig. 4
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Input parameters for operating the neural network

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Model formulation

In this work, 70% of the training input–output datasets were used to train FNN, while 30% of the testing datasets were used to validate the competence of FNN using MATLAB chronic trait. The correlation between input layers and output layers was generated in FNN by establishing a chain of interconnected neurons (Fig. 5). The input and output variables are defined by x = (PGA, SSD, OD, t, Ф, GSI) and y = (Damage Index), respectively. When using the training dataset to analyze the intricate yet orderly network, the neurons are joined into numerous layers and weight is assigned to each neuron repeatedly. Following a series of trial and error simulations, it was contrived that a normal three hidden layers (H1, H2, H3) of a neural network with 108 neurons yielded the best results. TRAINLM and LEARNGDM were used to represent the training and adaptation learning functions, respectively. LOG-SIG is a nonlinear activation function adopted for neurons in hidden layers. PURELIN is used as the transfer function for output layers. Table 5 provides the statistical context for the input parameters.

Fig. 5
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Feedforward Neural Network (FNN) used in the present study

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Table 5 Parametric contributions of inputs employed for STDP Model
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Methodology

The damage pattern of tunnels during previous earthquakes in Taiwan, Japan, and China show that underground structures are likewise vulnerable to extreme ground motion. Looking at previous devastation scenarios of tunnels and accompanying transportation networks tightens the belt of safe seismic design for associated designers and tunnel experts. The tunnel damage states are authenticated based on the value ranges of the Damage Index (\(DI\)). \(DI\) is traditionally determined by dividing the actual bending moment (\(M\))by the capacity bending moment (\({M}_{\text{RD}}\)). From dynamic time history, the actual bending moment (\(M\)) is quantified based on the analytical approaches. The capacity bending moment (\({M}_{\text{RD}}\)) is a material-dependent parameter, that can be estimated based on the material and geometrical properties of tunnels. In the present study, site-specific data are used to build a prediction model based on simplified factors. Special emphasis is placed on the ease of availability and significant contribution of variables from the input basket. Tunnel construction, installation, monitoring, and maintenance are difficult aspects of the infrastructure industry in the Jammu and Kashmir region. The frequency of earthquakes in the Himalayan region necessitates the development of a risk prediction technology capable of predicting damage patterns before the occurrence of actual seismic events.

Deep learning (DL) has advanced rapidly in recent years, with the potential to significantly alter and enhance the role of data science in a wide range of problems dealing the infrastructure resilience. Hoang and Tran (2019) demonstrated the validity of using metaheuristics to solve optimization problems in project and construction management, where metaheuristics are high-level procedures that find, generate or select heuristics for optimization. DL algorithms have been implemented in a variety of site safety problems subjected to disaster orientation (Kalakonas and Silva 2022; Mosavi et al. 2018; Falcone et al. 2020; Bernardi et al. 2021; Latif et al. 2021; Tehrani et al. 2022). Rafiei and Adeli (2017) propose a novel earthquake early warning model based on neural dynamic classification and optimization. In the present study, FNN provided the cumulative weightage factor for the output layer. At the initial stage, the weightage factor of all input–output data sets is combined to make the relationship between the specified input variable through training the neurons. After the neurons have been trained, target data are utilized to test the robustness of the network line.

The tag scattering for the training and testing data sets is depicted in Fig. 6. For class RED, tagging percentages of around 8 and 6 were recorded for data picked for training and testing, respectively. The influence of these data sets is evaluated for three neuron apportionment scenarios. As illustrated in Fig. 7, neural network Model 2 produced an average level of Mean Square Error (MSE) and is used as the desired network for further predictive modelling.

Fig. 6
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Tag distribution of various classes for training and testing data sets

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Fig. 7
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Filtration of error and selection of best neural network model in the present study

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Table 6 displays the results of both the training and testing data sets. Both data sets have demonstrated great performance in terms of specified criteria.

Table 6 Attributes of STDP model during training and testing phase
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The weightage factors are finalized through conceivable hits and trials, and a mathematical equation in terms of damage index is established. This provides the possible damage states for post-seismic scenarios. Neural networks aided in the identification of damage by robotizing the procedure and obtaining sustainable perfection pitch. The generalized form of the mathematical equation presenting the prediction model is presented in Eq. 1.

$$\text{ln}\left(DI\right)= A+B$$
(1)

where, \(A= \left[\frac{\left(SSD \times {OD}^{0.002}\right)+{\left(\frac{PGA}{t}\right)}^{4.2}}{GSI+ {\varPhi }^{4.2}}\right]\) and \(B= 1.15\). The factor “\(A\)” is the damage governing factor. The range values of \(A\) for different damage states are urged in Table 7.

Table 7 Proposed ranges of Damage Index (DI) for various damage states\(\left(DS\right)\)
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The final form of the Seismic Tunnel Damage Prediction (STDP) Model is given in Eq. 2.

$$\text{ln}\left(DI\right)= \left[\frac{\left(SSD \times {OD}^{0.002}\right)+{\left(\frac{PGA}{t}\right)}^{4.2}}{GSI+ {\varPhi }^{4.2}}\right]+1.15$$
(2)

Seismic hazard analysis can be utilized to get the seismic input variables (PGA and SSD) used in Eq. 2. Aside from these two, the rest of the criteria can be found in the planning and execution reports of any infrastructure project. Equation 2 can be solved for any damage state if the required variables are available. The seismic demand and capacity can be estimated backward based on the proposed damage states. This computation will be useful for any design revisions in seismically-prone tunnelling projects.

Results

Performance assessment of proposed prediction model

The proposed mathematical equation-based prediction model can be used to evaluate the damage scenarios for underground structures located in seismic-prone areas. In the discipline of predictive modelling, performance evaluation is a critical step after developing a model or equation. The R Score is used to assess the proposed model presented in Eq. 2. R values vary from 0 to 1 and can be calculated using Eq. 3.

$$R= \frac{TP}{TP+FN}-\frac{FP}{TN+FP}$$
(3)

In this study, G125-25-25 was identified as one of the best data sets, with R value of 0.2157. Table 8 displays performance indicators for all defined data sets. RG25-25-25 is the best arbitrary data set that was identified through random sequencing. Table 9 highlights a list of arbitrary data sets and their performances.

Table 8 Performance assessment of selected data set for proposed STDP Model
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Table 9 Performance assessment of arbitrary data set for proposed STDP Model
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Validation of proposed prediction model

The Seismic Tunnel Damage Prediction (STDP) Model proposed in the present study is compared with the tunnel damage data sets from the 1999 Chi-Chi earthquake, the 2004 Mid-Niigata earthquake, and the 2008 Wenchuan earthquake. Table 10 summarizes the damage states of tunnels affected by these three seismic events. The correlation coefficient (R), mean absolute error (MAE), mean absolute percent error (MAPE), and root mean squared error (RMSE) are considered as system governing markers (SGM) to execute the proposed STDP model. These markers are estimated using the following mathematical relationships (Eqs. 4 to 7).

$$R= \frac{\sum ({x}_{i}-\stackrel{-}{x})({y}_{i}-\stackrel{-}{y})}{\sqrt{\sum {({x}_{i}-\stackrel{-}{x})}^{2}\sum {({y}_{i}-\stackrel{-}{y})}^{2}}}$$
(4)
$$MAE= \frac{{\sum }_{i=1}^{N}\left(\left|{x}_{i}-{y}_{i}\right|\right)}{N}$$
(5)
$$MAPE= \frac{{\sum }_{i=1}^{N}\left(\frac{{x}_{i}-{y}_{i}}{{x}_{i}}\right)}{N}$$
(6)
$$RMSE= \sqrt{\frac{\sum {({x}_{i}-{y}_{i})}^{2}}{N}}$$
(7)

\(N\), \({x}_{i}\), \({y}_{i}\), \(\stackrel{-}{x}\) and \(\stackrel{-}{y}\) are the total number of data sets, measured output, estimated output, mean measured value, and mean estimated value, respectively. SGM considers PGA as a major input variable, for the proposed model and actual models of the previous earthquake are enlisted in Table 11. The suggested model can accurately estimate \(DI\)because the data points are typically placed close to the perfect fit, where predictions match observations. For the 2004 Mid-Niigata earthquake, the R-value for the suggested STDP model and the NETD model is nearly comparable. The MAE for the CETD Model differs from others since the data set for the Chi-Chi earthquake was found to be unevenly distributed. However, the proposed model is determined to be the best fit with the NETD and WETD models. The proposed model’s good performance for the Himalayan region with acceptable predictive ability and accurate performance on testing data demonstrates the model’s potential to predict the damage states for earthquakes in diverse ground scenarios covered by structural heterogeneity.

Table 10 Percentage of damaged tunnels during historical earthquake events
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Table 11 PGA based execution of STDP Model with other DL models for historically damaged tunnels
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Considering the percentile effect of all input variables, an analogous study of all prediction models is done. The comparison of the proposed damage index (\(D{I}_{proposed}\)) and actual damage index (\(DI\)) are presented in Fig. 8. The STDP model has a somewhat considerable variance from the other models. The data from the CETD model are closer to the 1:1 line, indicating a stronger connection between the measured and anticipated data values. When comparing the proposed model to the WETD model, the DL neural network computes a higher value of R. As a result, the DL-based prediction model can be used securely to calculate the DI for the seismic design of the tunnels under consideration during post-seismic scenarios.

Fig. 8
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Comparison between the proposed STDP model with other models for historical earthquakes

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It should be clear that the range of the training data limits the validity of the DL-based prediction model. For the best fitting of all models, the ranges of input variables are revised to develop the seismic design guidelines for tunnelling (Table 12).

Table 12 Revised values for input variables
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Discussions

The seismic vulnerability depicts the probability of a region or any structural constituent of infrastructure projects being damaged during a ground motion with the maximum peak ground acceleration for a defined set of epicentral distance and earthquake magnitude of a specific event. The risk reduction process involves both active and passive steps. Active steps involve avoiding or reducing hazards, while passive steps involve choosing particular mitigation methods (Kim et al. 2020). Seismic design guidelines are required to obtain a clear picture of the expected damages and level of vulnerability to which the structure is subjected. The data set of the Himalayan region, with a focus on the USBRL project and previous devastating earthquakes that triggered underground utilities, such as the 1995 Kobe earthquake, the 1999 Chi-Chi earthquake, the 2004 Mid-Niigata earthquake, and the 2008 Wenchuan earthquake, were considered to back-calculate the damage governing parameters using proposed Seismic Tunnel Damage Prediction (STDP) model. The seismic design guidelines provided considering historical case studies by fitting all data in the proposed model. For this purpose, input variables are accounted within the revised limit as suggested in Table 12. The “STD multiple graphs” shown in Fig. 9, is a four-sector graph based on the logical order of the input variables. The comparison of peak ground acceleration (PGA) and source-to-site distance (SSD) from an earthquake deaggregation data set is shown in Graph I (bottom right quadrant). Based on the deaggregation setup provided in Graph I, Graph II (bottom left quadrant) determines the geological strength index (GSI). Graph III (top left quadrant) calculates structural aptitude (SA) from geological strength index (GSI) and earthquake deaggregation setup. SA can be estimated using the following Eq. 8.

$$SA= \frac{0.3 \times t \times OD}{{\varPhi }^{2}}$$
(8)

The probable damage states are predicted using structural aptitude (SA) and geological strength index (GSI), which are reobserved after deaggregation, as shown in Graph IV (top right quadrant). The seismic tunnel damages can be categorized into five major groups. They are none (\({DS}_{0}\)), minor (\({DS}_{1}\)), moderate (\({DS}_{2}\)), extensive (\({DS}_{3}\)), and collapse (\({DS}_{4}\)). The subgrouping is also given for scenarios where the damage index (DI) is more than 2.5. The damage states produced in Fig. 9 are utilized as a starting point to prepare the seismic design guidelines shown in Table 13. These design guidelines detail damage indexing, damage pattern, and crack predictive specification. It also discusses the risks involved and their consequences on transportation network serviceability. Mitigation steps that must be implemented are also recommended for all projected damage states.

Fig. 9
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Seismic tunnel damages (STD) multi-graph for damage states prediction

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Table 13 Seismic design guidelines for damage states and mitigation recommendations for tunnelling projects
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Conclusion

Soft computing advancements have influenced researchers from various fields to adopt the technology and move forward with artificial intelligence. Based on the purpose and availability of prerequisites, the neural network is trained in the deep learning (DL) technique. A few essential research problems cannot be tackled using traditional methods. In such instances, the concept of the deep learning-based mathematical solution is a boon. Understanding the effects of earthquakes on structures necessitates prior experience with historical data sets. This requires the selection of input variables as well as the prior estimation of predicted outcomes. Using data from the Himalayan region, this study attempted to develop a mathematical formulation-based Seismic Tunnel Damage Prediction (STDP) model. To define the neural network’s input layers, site-specific data baskets with peak ground acceleration (PGA), source to site distance (SSD), overburden depth (OD), lining thickness (t), tunnel diameter (Ф), and geological strength index (GSI) are used. 70% of the data set from the Himalayan region is used to train the Feedforward Neural Network (FNN). The remaining 30% of the data is used to test the model after training. The weightage factors are determined through conceivable hits and trials, and a mathematical equation in terms of damage index is established. This model predicts the potential damage states for tunnels under various post-seismic scenarios.

The validation of the STDP model with other models based on historical earthquakes demonstrated its efficiently processing nature for minor instinctive shrewdness. Seismic demand and capacity can be estimated backward based on the proposed damage states. With an R-value of 0.2157, G125-25-25 was identified as one of the best data sets. The proposed model best fits the NETD (2004 Mid-Niigata Earthquake) and WETD (2008 Wenchuan Earthquake) models. After accounting for damaged tunnel data from the 1995 Kobe earthquake, 1999 Chi-Chi earthquake, 2004 Mid-Niigata earthquake, and 2008 Wenchuan earthquake, input variables are modified to fit all in a way that follows a common trend line. The “STD multiple graphs” are also provided, which aid in identifying potential damage states in future earthquakes. The seismic design guidelines include mitigation methods for all probable damage states. The proposed Seismic Tunnel Damage Prediction (STDP) model, STD multiple graphs, and design guidelines can be used for any earthquake-prone tunnelling project anywhere in the world.