Machine learning approaches for predicting the construction time of drill-and-blast tunnels

Dataset preparation

Data sits at the heart of every ML project; without a rich, well-organized dataset, even the most sophisticated models stumble and fail. That’s why the first step in any new system is to pinpoint the key variables that steer the outcome, and only then proceed to collect evidence that shows how each one behaves. For the present study, twenty features were compiled through discussions with tunnel engineers, a review of older papers on tunnel performance, and initial tests that assessed the strength of each factor’s association with the available data. The final list includes only items that the team could measure on-site, that appeared in records from several tunnel jobs, and that had already demonstrated their significance for both drilling speed and machine staffing. Editors deliberately spread the picks across four areas: (i) ground conditions, (ii) tunnel shape and size, (iii) design of supports and reinforcements, and (iv) the day-to-day running of the project. To ensure the dataset accurately reflects the challenges teams face underground, we compiled records from eight bored-and-blasted road tunnels constructed in various Iranian regions between 2012 and 2023. We reviewed field logs, design notes, geotechnical studies, and post-build as-built reports, resulting in a comprehensive dataset comprising 500 individual data points. The information covers both what was planned and what happened on-site, with each entry double-checked by site engineers. By way of illustration, lining thickness is recorded as the size the crew achieved once the work finished, not the figure given on the blueprints; shotcrete thickness, meanwhile, is broken into two clear pieces: the average layer on the tunnel walls (ShL), and the first protective cover on the face (SF), ensuring they do not get confused with each other. Keeping these measures apart lets us see better how early support from face shotcrete and later wall shotcrete together shape the speed at which the tunnel is driven forward. Additionally, the primary measure we are concerned with (construction time) is captured as the total man-hours spent for every meter of advance, averaged over a sliding window of tunnel length, so one day’s hiccups do not skew the picture. Researchers also examined how the measures interact with each other in the physical world. Take overbreak volume (GOB) and shotcrete thickness (ShL); when more rock is removed than planned, extra concrete is needed, so these two are linked. That connection stayed intact during preprocessing and was rechecked in the correlation review. General summary statistics for the dataset are listed in Tables 1 and 2, with Table 1 showing the continuous values and Table 2 covering the categorical data.

Figure 1 uses violin plots to illustrate the distribution of all input and output variables, allowing readers to quickly identify each variable’s range, density, and number of peaks. Such a display helps identify skew, multiple clusters, and concentrated zones that could influence how well an ML model learns. The database behind these graphics was compiled from several real tunnel projects, and each entry was painstakingly checked to remove identical records, where every value matched across different tunnels. The variables shown in the plot combine both categorical and numerical data, and their shapes indicate the dataset’s variety and overall coverage. Wide and even spreads of numerical values usually help ML methods, because they mean no single condition dominates training. Take the RMR; its scores range from approximately 6 to 83, indicating that the records encompass tunnels dug through very soft to extremely tough rock. This broad range gives the models a solid chance to learn how shifts in RMR affect construction time under all the ground conditions represented by the data. Similarly, the thickness of each ShL and the amount of GOB follow skewed, non-normal distributions that mirror the everyday ups and downs found on site. These spreads matter because they help expose the nonlinear links analysts care about. In contrast, categorical items such as GW and NDS sit in clean, distinct buckets, allowing the models to tell one work situation from another without second-guessing. When viewed together, the plots do more than show whether any single variable dominates; they make it easy to see how balanced and varied the input is, and they reassure us that the data can withstand the broader test of generalization.

Exhaustive analysis of the dataset

In the preceding section, we identified 20 parameters as influential on tunnel construction time. In this section, our objective is to diminish the dimensionality of the data matrix using statistical data analysis, thereby eliminating redundant parameters. Initially, we scrutinize the correlation between input parameters. If the correlation between two parameters is greater than or equal to 0.9, or less than or equal to -0.9, only one parameter is retained while the other is discarded. This is due to the fact that one parameter’s values can be accurately estimated from the other, rendering their effects on the output nearly identical.

The Pearson correlation coefficient is employed to quantify the correlation between input parameters. This coefficient, ranging from − 1 to + 1, measures the degree of relationship between two variables. A coefficient of + 1 indicates a perfect positive correlation, meaning that an increase or decrease in one variable corresponds proportionally with an increase or decrease in the other. Conversely, a coefficient of -1 signifies a perfect negative correlation, where a rise in one variable corresponds with a reduction in the other. A coefficient of zero denotes no relationship between the variables.

Figure 2 presents the correlation matrix derived via Pearson’s method among numerical parameters. It reveals that the correlation coefficient between the DC parameter and each of the RMR and GSI parameters is 0.93. Consequently, the DC parameter is eliminated. Furthermore, the correlation coefficient between the RMR and GSI parameters is 0.99, indicating that one parameter can be accurately inferred from the other. Hence, we remove the GSI parameter and retain the RMR parameter. The correlation coefficients between all other parameters are below 0.9 (and above − 0.9), necessitating the inclusion of these parameters. As a result, out of the initial 16 numerical input parameters, two parameters (GSI and DC) are excluded, leaving 14 parameters for further analysis.

We now aim to evaluate the impact of each numerical input parameter on the tunnel construction time, eliminating those that do not significantly influence the output. This is achieved through parameter sensitivity analysis, a crucial method for discerning the most impactful inputs and discarding those with negligible effects. Incorporating superfluous variables adds unnecessary complexity to the model and can degrade its accuracy and execution efficiency. Moreover, reducing the dimensionality of input data simplifies the model, particularly for future applications involving new tunnels, by minimizing the number of required input parameters.

In this study, we employ the P-value method to identify redundant input variables. The P-value is a statistical measure used in feature selection to assess the significance of each variable within a model. It is commonly applied in statistical hypothesis testing, especially in the context of null hypothesis testing, where it is assumed that no relationship exists between the variables. The P-value helps determine the statistical importance of a feature relative to other variables. Suppose the P-value is below a specified significance threshold (typically 0.05). In that case, it indicates that the observed results are highly unlikely under the null hypothesis, allowing us to reject the null hypothesis and affirm that the feature has statistical significance. The P-values are typically calculated using a univariate linear regression model for each input variable with respect to the target variable. This classical statistical approach assesses the individual correlation and significance of each feature within a linear framework, serving as a preliminary screening method to identify features that have statistically meaningful relationships with the output.

It is essential to note that the P-value is calculated using different methods, depending on the type of parameters. Since our objective at this stage is to ascertain the correlation between numerical input parameters and construction time, and given that all parameters under consideration are numerical, the t-test method is employed to calculate the P-value.

The P-values reflecting the relationship between each numerical input parameter and the tunnel construction time are presented in Table 3. All numerical parameters, except the MD parameter, exhibit P-values less than 0.05. This indicates a significant relationship between these parameters and the construction time parameter, with a confidence level exceeding 95%. Therefore, except for the MD parameter, other parameters are considered influential on the construction time of tunnels.

We now aim to examine the correlation among the non-numerical input parameters (GW, IPE, NML, and NDS) and the tunnel construction time parameter. For this purpose, we determine the correlation using the P-value. In this step, the Chi-square method is used to calculate the P-value. The resultant P-values for this scenario are presented in Table 4. The P-values for all these parameters in relation to the construction time parameter are below the threshold of 0.05. Consequently, these parameters are also recognized as significant non-numerical factors influencing the tunnel construction time.

The statistical analysis of the data revealed that, with the exception of the DC, GSI, and MD parameters, the remaining input parameters initially selected should be regarded as influential on tunnel construction time. Consequently, the dataset utilized in this research encompasses seventeen input parameters (GW, IPE, NML, DNS, CA, RMR, IPES, MN, ShL, SF, LT, BN, BL, BD, SC, Fo, and GOB) along with one output parameter (tunnel construction time). Figure 3 shown a visual flowchart summarizing the parameter selection process:

Encoding the nominal parameters

It is crucial to note that numerical and nominal parameters cannot be used concurrently within the same dataset for training ML models. To address this issue, it is essential to transform the nominal parameters into numerical codes. In this research, we employ the One-Hot encoding method. One-Hot encoding is a widely used technique, known for its effectiveness except when the categorical variable has an excessive number of values. Typically, this method is unsuitable for variables with more than 15 distinct values. One-Hot encoding generates new binary columns, each representing one of the variable’s possible values. To elucidate this process, we demonstrate the encoding of the GW parameter, which includes four states: Dry, Wet, Drop, and Flow. Suppose the GW parameter has five samples with the states Dry, Dry, Flow, Drop, and Wet, respectively, as shown in Fig. 4 (left side). Using One-Hot encoding, the values of this variable are transformed into four separate columns titled Dry, Flow, drop, and Wet, as illustrated in Fig. 4 (right side). Thus, instead of a single GW parameter, we have four distinct parameters named Dry, Flow, Drop, and Wet. For instance, in Fig. 4 (right side), the first sample is encoded with a 1 in the “Dry” column and 0 in the “Flow,” “Drop,” and “Wet” columns. This encoding is similarly applied to the second sample, which is also “Dry.” For the third sample, a 1 is entered in the “Flow” column and 0 in the remaining columns. This pattern is repeated for the other samples accordingly.

Sensitivity analysis based on MI test

At an earlier stage of this study we used P-value tests to sift through the input data and see which factors really mattered for tunnel construction time. That round let us cut out noise and keep only variables that had a clear statistical link with the outcome. Yet P-values, useful as they are, fall short of showing how much each surviving factor pushes the time up or down, let alone putting them in a clear order of importance. To fill that gap, we now run a second round of checks, this time leaning on MI test, which looks at how much information each input actually shares with the output. Although we call both reviews sensitivity analysis, they serve different ends:

• The P-value work in Sect. 3.2 zeroed in on whether a factor mattered at all;

• The MI test here digs deeper, letting us score each factor by how strongly it moves construction time and stack them from most to least influential.

MI is a flexible statistical tool that measures how much knowing one variable reduces uncertainty about another, in this case between each input feature and construction duration. Because it captures both straight-line and twisting patterns, a higher MI score clearly shows stronger dependence between the two, no matter how complex the link. Using MI this way reveals whether geological conditions, structural choices, or work flows truly push the schedule longer or shorter.

The MI value is derived from Eq. 1, where \(\:x\) and \(\:y\) represent input and output parameters, respectively.

When holding the input parameter (\(\:x\)) constant, the MI value becomes zero, indicating no discernible connection between parameter \(\:x\) and the output (\(\:y\)). The maximum MI value varies depending on the data type. If the input and output parameters possess identical or completely opposite values (i.e., an R² value of 1 or -1), the MI value reaches its peak, signifying a linear relationship between the two parameters. Hence, the higher the MI value between two parameters, the more intertwined their relationship, facilitating the identification of one parameter’s state from the other.

Initially, to calculate the maximum expected value of MI between an input parameter and the tunnel construction time, we set \(\:x=y\) in Eq. 1. This means the tunnel construction time parameter is considered both as an input and an output. Under these conditions, the maximum expected MI value was determined to be 4.67. The closer the MI value between an input parameter and the tunnel construction time is to this maximum value, the more linear the relationship, and conversely, the further away, the less linear.

This study uses MI analysis for two main reasons. First, it gives a broad and sturdy measure of dependence that picks up both straight-line and twisty links between the input factors and construction time, capturing patterns traditional correlations or plain p-values might miss. That broad view matters when ML models like GPR and ANN are being trained, because those tools aim to learn the sort of complex, bent behaviour MI is built to find. Second, the MI scores let us rank the features by how much each adds to explaining the target outcome. That ranking not only makes the models easier to read, it can guide future work in thinning the dataset or picking the strongest predictors, especially when records are scarce. Although nothing was dropped solely because of a low MI score here, the exercise backed up earlier tests and shed light on how much each input really drives the models performance.

Table 5 presents the MI values between the input parameters and the tunnel construction time. According to this data, tunnel construction time exhibits the highest sensitivity to parameters related to the excavation method and geological conditions, such as GOB, CA, RMR, and IPES. Conversely, parameters associated with rockbolts, mesh, and IPE display the least sensitivity in predicting tunnel construction time. The lower sensitivity of these parameters can be attributed to their narrower range of variation within the dataset compared to other parameters.