The Influence of Metro Tunnel Construction Parameters on the Settlement of Surrounding Buildings

Abstract

The construction of tunnels in conditions of dense urban development affects buildings, structures, and engineering communications located at the surface. In this work, through dispersion analysis, factors influencing the settlement of the earth’s surface and buildings during tunneling were selected. Subsequently, a model based on statistically significant parameters that can predict deformations at the pre-design stage was created. This research was conducted using data from geotechnical monitoring obtained during the construction of underground structures, with information about the technological parameters of shield tunneling in the construction of the single-track lines of the Moscow Metro using TBM with face-support pressure and engineering–geological conditions. In the obtained model, there is a clear dependency between the additional displacement of the monitoring object located above the projected tunnel and the average face-support pressure causing the mentioned deformations. The response is also affected by the soil deformation model at the tunnel face, the depth of the tunnel, and the soil excavation for the installation of one ring.

1. Introduction

Today in tunnel construction, the tunnel boring machine (TBM) is used, equipped with a device for maintaining the ground at the face under various soil conditions to ensure the safety of the construction process, known as face-support pressure. At the same time, even with the use of advanced methods, the construction of tunnels can affect previously built buildings and infrastructure facilities [1,2]; however, the efficiency and reliability of the metro system greatly influence the transportation, economic, environmental, and social aspects of cities [3]. Therefore, determining additional displacements resulting from the construction of the facility is an important task. Determining the extent of surface subsidence is intrinsically a relevant issue; for example, land movement can cause damage to property and resources due to groundwater [4].

Currently, at the design stage, engineers are addressing two parallel tasks: (1) assessing the impact of the new construction on the surrounding buildings, assuming that face stability is ensured and there is no emergency situation, and (2) determining the face-support pressure required to maintain face stability and minimize ground surface settlement. The first task is the assessment of additional displacements and is carried out in software packages based on the finite element methods with an optimized soil coefficient parameter [5]. The second task of determining the face-support pressure is carried out at the design stage, taking into account the engineering and geological conditions and the depth along the entire tunnel route. The modern method for determining face-support pressure is considered a preliminary forecast due to the high degree of uncertainty in engineering and geological conditions and requires adjustment of the pressure value during the tunnel construction. Furthermore, during the tunnel construction, surveyors and the tunneling crew again solve different tasks in parallel: surveyors monitor the deformations of the surrounding buildings, and the construction team monitors the technological indicators of the tunneling process. Thus, tools are required to coordinate these two tunnel construction processes.

The most renowned empirical study in the field of determining surface settlement during tunneling operations was conducted by the scientist Peck [6], who adapted the Gaussian normal distribution curve to describe the settling of the Earth’s surface using data obtained during the construction of the London Underground. Atkinson and Potts [7] analytically described surface settlement in clay and sandy soils. Later, Verruijt and Booker [8] considered surface settlement taking into account tunnel ovalization, which is caused by the compression of the soil mass in which construction is carried out. Face-support pressure also influences additional movements of buildings located in the area affected by tunnel construction [9]. Therefore, time is dedicated separately to inventing methodologies capable of selecting the necessary face-support pressure to maintain face stability. There is an analytical solution [10] that considers multi-layer soil, the support pressure gradient, and the water table level, distinguishing this work from many others. Settlements in the longitudinal section of the planned tunnel are also studied, and it has been established that, in some cases, upward vertical movements (blow-out) have been recorded [2].

Numerical methods for determining the impact of tunnel construction on the surrounding structures are also currently popular, where the influence exerted on settlement by factors such as the relative depth of tunnel placement [11], soil models [12,13], dimensions of the structure, and the load that the structure exerts on the foundation [13] are studied. Other authors have also used numerical analysis and monitoring data to determine the patterns that influence surface deformations [14]. The authors noted that the maximum surface settlement is located above the axis of the tunnel, and when the support pressure exceeds 300 kPa, a surface uplift is observed. It should also be noted that in the work of Peck [6], as in many others [1,7,8,11,15,16], the influence of distance (r) on settlement is observed. In other words, the maximum settlement occurs above the axis of the tunnel.

In the studies [17,18], the authors use methods of artificial intelligence, which are based on applied statistics, to investigate the tunnelling rate, which is an indicator of construction efficiency.

In scientific research, various regression models are used to identify the relationship between variables and determine the variables that have the greatest impact on the parameter.

The main purpose of regression analysis is to find a model that most accurately explains the relationship between one or more predictors (independent variables) and a response (dependent variable).

The fundamental factor for choosing a model in this study was the assumed nature of the relationship between the response and the predictors. It is assumed that forecasting precipitation and its relationship with predictors is described by a linear dependence and is not exponential or exponential. Multiple linear regression is presented in Equation (1) and is the most common type of regression [19]. The model is an equation of a straight line that best fits the data:

y = b₀ + b₁∙x₁ + b₂∙x₂ + b₃∙x₃ + … + b_n∙x_n + ε,

(1)

here y is the the dependent variable; b₀, b₁, b₂, b₃, and b_n are the regression coefficients; x₁, x₂, x₃, and x_n are the independent variables; and ε is the random variable (the unexplained part of the response value).

To evaluate the quality of the regression model, there are several methods that need to be used together to check the adequacy of the model. One of the methods commonly used to assess the adequacy of the model is the coefficient of determination (R²), which indicates the proportion of the variance in the dependent variable that is explained by the independent variables [20]. This coefficient ranges from 0 to 1. The higher the value, the better the quality of the model. However, a high coefficient of determination does not always correspond to a strong relationship between the variables. A value close to 1 may be due to a pronounced trend that is not causally related [21].

The linear relationship between the independent parameters of the multiple regression model is called multicollinearity and is characterized by high correlation dependence [22]. Some consequences of this relationship between explanatory parameters can complicate the analysis of results, as it is not always possible to unambiguously determine the contribution of each independent parameter, leading to incorrect determination of the coefficient of regression, etc. [22].

Thus, when analyzing the adequacy of the model, it is necessary to consider the possible influence of this phenomenon on the results and try to prevent it through known methods, such as excluding the correlated parameter from the model or increasing the sample size [22].

The significance of the entire equation can be assessed using the Fisher’s F-test, which examines whether the hypothesis is different from zero by comparing the actual F-value to the critical F-value [23]. Additionally, the significance of each parameter individually can be determined using the p-value criterion, which is assessed similarly to the F-criterion [24].

Another tool for assessing the influence of regression model parameters on the independent variable can be an analysis of the coefficients b₁, b₂, b₃, …, b_n obtained from the results of the analysis of variance. Regression coefficients are numerical values that can be negative or positive, and they are used as weighting coefficients [25]. They indicate the direction and degree of influence of each parameter on the final outcome. Weighting coefficients also help determine which model parameter has the greatest impact on the predicted value.

Previously, the authors of this study had already used statistical methods to determine the impact of excavation on the vertical and horizontal movements of tunnels [26]. Additionally, the authors had previously obtained results from regression analysis in their prior work [27], which established that statistically significant parameters for the settlement of an object over one monitoring cycle include the face pressure (P_avg), the relative parameter (P_avg/H) where H is the depth of the tunnel, the number of floors of the structure (L) under which construction is performed, and the distance from the tunnel to the monitoring object (r). However, the last parameter contributes the least to the amount of settlement out of all the listed parameters. Additionally, it has been determined that, within the available data set, there is no observed dependency of the settlement over one cycle of geotechnical monitoring on the volume of injected grouting solution into the space between lining and soil mass (v) and the volume of soil removal for the installation of one ring (V). It should also be noted that the derived models were compiled without the characteristics of the soil mass.

Among similar works on the construction of underground mined tunnels, a study can be highlighted which presents a proven, effective equation for determining settlement, which takes into account the horizontal-to-vertical-stress ratio, cohesion, and deformation modulus of the soil [28].

In a similar study for TBM, the tunnel burial depth was about 12.0 m∼26.5 m and the influence of parameters on surface settlement was also examined. It was found that, in the first test section, the most significant impact on the dependent variable is exerted by total thrust, torque, cutter-head rotation speed, advance speed, and grouting pressure, while in the second section, the key influencing parameters are total thrust, cutter-head torque, advance speed, earth pressure, and grouting pressure. The construction of the tunnel was carried out predominantly in clayey soils, residual soil, and andesite [29].

The aim of this work is also to use statistical methods to investigate the impact of tunnel construction on the movements of the surrounding buildings and the Earth’s surface using data from geotechnical monitoring, actual technological parameters obtained during tunneling, and information on the plan and elevation placement of the tunnel, as well as engineering–geological conditions. In this study, the authors intend to conduct an analysis not for a single cycle of geotechnical monitoring, as is commonly performed in other studies [27,28,29] on this topic, but to examine the influence of various factors on the accumulated settlement. By doing so, we minimize the impact of the geodetic instrument’s measurement error on the research results, as the error is within ±5 mm, which often does not exceed the deformation error for a single monitoring cycle.

Therefore, the authors suggest that the impact of constructing metro tunnels using a closed method with a TBM can be minimized by controlling the tunneling process parameters. However, it is necessary to investigate which parameters most significantly influence settlement.

2. Materials and Methods

All the initial data, the processing results of which are presented below, were provided by LLC “Institute ‘Mosinzhproekt’” (Moscow, Russian Federation). The reliability of the data is ensured by the use of high-precision geodetic surveying and calibrated equipment for determining soil properties.

In this study, a multiple regression model is employed in which the dependent variable is the total settlement of the object accumulated over a distance of 10 m along the planned route up to the point where geotechnical monitoring is conducted. The information on the plan and elevation placement of the tunnel, technological parameters with average values over 10 m, and characteristics of the soil mass act as independent variables.

Samples for building regression models were obtained during the construction of the left interstation tunnel of the Rublyovo–Arkhangelskaya metro line (RAL) using a TBM with a cutting diameter of 6.6 m, as well as during the construction of the right and left interstation tunnels of the Troitskaya metro line (TL) using a TBM with a cutting diameter of 6.28 m. The outer diameter of the left RAL tunnel is 6.3 m, and the diameter of the right and left TL tunnels is 6.0 m.

Settlement of the monitoring object is taken as the dependent variable in this study to determine the parameters that have the greatest impact on the response. Separate models were analyzed with and without the parameter of the volume of grout injected into the space between the lining and soil mass, as the actual values are present in the dataset only for the construction of the RAL tunnel.

Before constructing the main regression model, criteria were selected among the following parameters, which can be conditionally divided into five groups:

• Geotechnical monitoring data:
  • Absolute (cumulative) settlement of the monitoring object for all cycles when the TBM is at the deformation control benchmark (S), mm (1);
• Geometric parameters:
  • Distance from the center of the tunnel to the deformation control benchmark (r), m (2);
  • Depth of the tunnel from the surface to the tunnel crown (H), m (3);
• Weighted average characteristics of the soil mass:
  • Cohesion of the soil at the tunnel face (c₁), kPa (4);
  • Internal friction angle of the soil at the tunnel face (φ₁), degrees (5);
  • Deformation modulus of the soil at the tunnel face (E₁), kPa (6);
  • Cohesion of the soil above the tunnel (c₂), kPa (7);
  • Internal friction angle of the soil above the tunnel (φ₂), degrees (8);
  • Deformation modulus of the soil above the tunnel (E₂), kPa (9);
• Technological parameters obtained during tunneling:
  • Average face-support pressure unloading vertically and along a distance of 10 m along the design route until reaching the deformation control benchmark in the plan (P_avg.10), bar (10);
  • Average ground output for installing one ring over a distance of 10 m along the design route until reaching the TBM deformation control benchmark in the plan (V₁₀), t (11);
  • Average volume of grout injection into the space between the lining and soil mass over a distance of 10 m along the design route until reaching the TBM deformation control benchmark in the plan (v₁₀), m³ (12);
• Characteristics of the surrounding buildings:
  • Number of stories of the building located in the tunnel construction influence zone (L), fl. (13). When processing surface monitoring data, the number of floors is considered as 0.

The face-support pressure was determined at the design stage based on the following condition:

P ≥ P_w + P_g,

(2)

here P_w is the magnitude of the groundwater pressure at the level where the weight load pressure is determined; and P_g is the magnitude of the horizontal soil pressure at the level where the weight load pressure is determined.

The division of soil mass characteristics into two conditional parts, “at the tunnel face” and “above the tunnel” was carried out in order to detail the forecasting model and localize the area of influence of the parameters on the dependent variable.

Table 1. The range of values of the selection parameters.

No	Parameter	Range of Values	Unit of Measurement
1	Distance from the center of the tunnel to the deformation control benchmark (r)	0–59.1	m
2	Depth of the tunnel from the surface to the tunnel crown (H)	14.27–35.63	m
3	Average face-support pressure at a distance of 10 m (Pcp.10)	1.33–3.15	bar
4	Average ground output at a distance of 10 m (V10)	65.40–84.54	t
5	Number of stories of the building (L)	0–12	fl.
6	Cohesion of the soil at the tunnel face (c1)	4–33.99	kPa
7	Internal friction angle of the soil at the tunnel face (φ1)	24.69–37.00	deg.
8	Deformation modulus of the soil at the tunnel face (E1)	23,000–31,283	kPa
9	Cohesion of the soil above the tunnel (c2)	22.92–37.53	kPa
10	Internal friction angle of the soil above the tunnel (φ2)	19.47–27.92	deg.
11	Deformation modulus of the soil above the tunnel (E2)	29,025–34,098	kPa
12	Average volume of grout injection a distance of 10 m (v10) *	3.68–4.76	m3

* Injection volume data are provided only for the RAL; Note: The range of values of soil characteristics is represented by weighted averages.

shows the parameters on which the model was compiled and the ranges of values that advise them.

The analyzed sample does not include above-normative displacements of monitoring objects and technical parameters obtained during emergency situations. Consequently, the statistical model for predicting absolute settlement considers continuous operation of the tunnel boring machine, excluding cases of stoppage for routine maintenance and scheduled works (cleaning of the primary grouting system, splicing and extension of the conveyor belt, high-voltage cable, planned gyroscopic orientation in the tunnel, etc.).

The regression model was created using the “Data Analysis” option in Excel. The final form of the model was compiled through an iterative process, and the algorithm for its formation is provided below.

3. Results

In this section, the parameters from Section 2 are analyzed using statistical methods. It is important to note that the selection of significant parameters for the final model is accomplished in several steps following the scheme shown in Figure 1.

To briefly explain the model creation algorithm, one should perform an analysis of variance, ensuring that the model retains only those parameters with p-values below 0.05 and without multicollinearity. The final equation is then assembled using the last regression coefficients of the significant parameters. Of course, this flowchart applies to equations with F-significance >0.05 and an optimal R² value.

3.1. Stage 1: Primary Regression Model

The first analysis of variance was conducted on a sample of 201 observations. The parameters presented in Section 2. were considered for the first iteration, except for parameter v. The assessment of the results of the analysis of variance allows for the conclusion that the equation is statistically significant, as the F-significance in this sample is 8.66285 × 10⁻³⁴ << 0.05 = α. The coefficient of determination R² = 0.62, which, according to Chaddock’s scale [30], cannot be considered as a high value. The standard error of the model was 2.37 mm. Nevertheless, when analyzed in conjunction with other metrics, within the scope of this study, this value may be sufficient for determining significant parameters.

It should be noted that, out of the eleven parameters claimed in this model, the following parameters were found to be significant:

• Depth from surface to vault (H), m,
  p-value = 4.37412 × 10⁻⁶ << 0.05 = α;
• Average ground pressure for 10 m (P_avg.10), bar,
  p-value = 1.13748 × 10⁻²⁷ << 0.05 = α;
• Average ground output for installing one ring (V₁₀), t,
  p-value = 0.001014007 < 0.05 = α;
• Deformation modulus in the tunnel face (E₁), kPa,
  p-value = 0.023281021 < 0.05 = α.

Additionally, a correlation matrix, presented in

Table 2. Summary of the results of regression statistics and analysis of variance.

Parameter	S, mm	r, m	H, m	Pavg.10, bar	V10, t	L, fl.	c1, kPa	φ1, deg.	E1, kPa	c2, kPa	φ2, deg.	E2, kPa
S, m	1.00	-	-	-	-	-	-	-	-	-	-	-
r, m	−0.01	1.00	-	-	-	-	-	-	-	-	-	-
H, m	0.06	0.33	1.00	-	-	-	-	-	-	-	-	-
Pavg.10, bar	0.65 *	−0.01	0.33	1.00	-	-	-	-	-	-	-	-
V10, t	−0.05	0.03	0.21	0.15	1.00	-	-	-	-	-	-	-
L, fl.	0.14	0.32	0.63 *	0.14	0.03	1.00	-	-	-	-	-	-
c1, kPa	0.15	0.10	0.25	0.09	0.17	0.46	1.00	-	-	-	-	-
φ1, deg.	−0.18	−0.12	−0.29	−0.10	−0.18	−0.48	−0.99 *	1.00	-	-	-	-
E1, kPa	0.47	0.13	0.44	0.32	0.17	0.51	0.56	−0.62 *	1.00	-	-	-
c2, kPa	−0.09	−0.06	−0.30	−0.20	0.12	−0.11	0.01	0.04	−0.25	1.00	-	-
φ2, deg.	−0.17	0.03	0.09	0.03	−0.21	−0.08	−0.23	0.20	−0.24	−0.84 *	1.00	-
E2, kPa	−0.31	−0.02	−0.28	−0.24	0.04	−0.21	−0.15	0.22	−0.62 *	0.78 *	−0.40	1.00

* The cells with correlation coefficients indicating the presence of multicollinearity between parameters are highlighted in bold.

, was obtained, from which several conclusions can be drawn. Firstly, the correlation coefficient R = 0.65 indicates a moderate relationship between the investigated variables, absolute subsidence (S), and average ground pressure for 10 m (P_avg.10).

Secondly, of interest within this sample is the positive relationship between the parameters number of floors (L) and depth from the surface to the tunnel vault (H), which is supported by a correlation coefficient of R = 0.63.

One possible explanation for this relationship could be the increase in the depth of compressible stratum depending on the number of building floors and the potential consistent matching of the depth of the compressible stratum with the depth of the tunnel vault.

In other words, digging a tunnel at a depth of 10 m under a two-story building corresponds to digging a tunnel at a depth of 20 m under a five-story building. However, the study of the relationship between the parameters number of floors (L) and depth from the surface to the tunnel vault (H) is not the subject of this study, and the parameter characterizing the surrounding buildings will not be used in the final equation due to multicollinearity with the parameter depth from the surface to the tunnel vault (H) and p-value > 0.05 = α.

The third conclusion that can be drawn regarding the multicollinearity of parameters is the relationship between the parameters of the 3rd group of the sample, which relates to the characteristics of the soil mass. An analysis of Table 2 shows that the highest correlation is observed between the parameters of cohesion and the internal friction angle for the soils both in the tunnel face and above the tunnel. There is also a relationship between the deformation modulus itself and the deformation modulus with the strength characteristic. These patterns are presumably explained by the laws of soil mechanics, but it is necessary to note this in order to justify the use of one parameter from group No. 3 in the final regression model, in combination with the p-values obtained from the analysis of variance, from an econometric perspective. Therefore, to establish the final equation, it is necessary and sufficient to use only one parameter from group No. 3, the soil deformation modulus at the tunnel face (E₁) with a p-value = 0.023281021 < 0.05 = α.

The analysis of the regression coefficients obtained from the analysis of variance allows us to conclude that the parameter with the highest weight coefficient (b₃ = 7.14) and, consequently, the largest contribution to the response variable [25], absolute settlement (S), is the parameter of face-support pressure at 10 m depth (P_avg.10) with a p-value = 1.13748 × 10⁻²⁷. Thus, this parameter is the most significant among all parameters considered in this model.

It is suggested to conduct a more detailed analysis of the parameter (P_avg.10) and examine the numerical characteristics presented for it. Figure 2 shows the histogram of the distribution of the analyzed parameter, from which it can be concluded that the histogram has an asymmetrical shape, being one-tailed [31]. On the vertical axis, the number of measurements is indicated, and on the horizontal axis, the intervals of actual face-support pressure are shown.

The investigated parameter ranges from 1.31 to 3.31; however, the highest number of values (99) falls in the range from 2.51 to 2.71 inclusive (conditional range 2).

The depth of the projected tunnels from the surface to the vault ranges from 14.3 m to 35.6 m. The fewest values are found in the range from 1.31 to 2.31 (range 1) and from 2.91 to 3.31 (range 3). The face-support pressure of range 1 is observed at various sections of the depth of the projected tunnel, predominantly including sections near station complexes, with some values closer to the middle of the segments. Range 3 is encountered when the depth of the tunnel is 20 m or more.

The average face-support pressure on the studied sections was 2.5 bars with an average depth of 26.9 m for the projected tunnel, with the mode (the most frequently occurring value in the sample) being 2.59 bars.

3.2. Stage 2: Optimized Regression Model

The next step is the development of a regression model using only significant parameters identified as a result of the analysis of variance.

A re-analysis of the results of the analysis of variance allows us to conclude that this equation is also statistically significant, just like the previous one, with an F-significance of 1.08371 × 10⁻³⁷ << 0.05 = α and a coefficient of determination R² = 0.60. The standard error of the model was 2.39 mm. The combination of these metrics allows us to state that the equation is statistically significant and explains approximately 60% of the variability in the data.

All model parameters are statistically significant, with the p-value of each parameter being less than α = 0.05. Furthermore, according to

Table 3. Correlation matrix of parameters for the model with only significant parameters.

Parameter	S, mm	H, m	Pavg.10, bar	V10, t	E1, kPa
S, mm	1.00	-	-	-	-
H, m	0.06	1.00	-	-	-
Pavg.10, bar	0.65	0.33	1.00	-	-
V10, t	−0.05	0.21	0.15	1.00	-
E1, kPa	0.47	0.45	0.32	0.17	1.00

, there is no multicollinearity between the parameters, while the relationship between the response and the parameter of the average face-support pressure for 10 m intervals (P_avg.10) with the highest weight coefficient b₃ = 6.98 is maintained.

Therefore, the equation for multiple linear regression to determine surface settlement looks as follows:

S = −14.82 − 0.20∙H + 6.98∙P_avg.10 − 0.16∙V₁₀ + 0.00049∙E₁

(3)

By analyzing the signs of the regression coefficients, we can conclude that an increase in the average face-support pressure for a 10 m section (P_avg.10) and the weighted average deformation modulus of the tunnel face (E₁) lead to a decrease in the absolute settlement of the monitoring object. At the same time, an increase in the tunnel depth and the average volume of ground output for a 10 m section (V₁₀) results in an increase in the absolute settlement.

It is also important to note that the low value of the regression coefficient b₄ is associated with higher values of the deformation modulus compared to other parameters. Figure 3 shows the influence of each regression coefficient of the significant parameter at the average values of the independent variables.

In many works on related topics, the authors [28,29,32,33,34,35,36,37] resort to this regression model due to its ease of interpretation of results, ease of implementation, and robustness to new data (this type of model is less prone to overfitting).

3.3. Stage 3: Determining the Significance of the Grouting Pressure Parameter into the Space between the Lining and Soil Mass for Surface Settlement

Data on the volumes of grout injection into the space between the lining and soil mass are only available for the construction of the left tunnel of the RAL, consisting of 92 rows of data. In light of the above, a decision has been made to use the data on grouting volumes in combination with the optimized regression model presented in Section 3.2 to ensure an optimal balance of the number of data rows and regression parameters.

The average volume of injected grout when installing one ring, consisting of precast reinforced concrete blocks with a width of 1.4 m, is 4.02 m³. The mode is 4.04 m³. The maximum volume encountered during the excavation of this branch is 4.76 m³, while the minimum is 3.68 m³.

By analyzing the obtained results and

Table 4. Parameter correlation matrix for the model with the parameter of average volume of grout injection into the space between the lining and soil mass.

Parameter	S, mm	H, m	Pavg.10, bar	V10, t	E1, kPa	v10, m3
S, mm	1.00	-	-	-	-	-
H, m	0.11	1.00	-	-	-	-
Pavg.10, bar	0.68	0.53	1.00	-	-	-
V10, t	−0.07	0.34	0.18	1.00	-	-
E1, kPa	0.23	−0.27	−0.05	0.08	1.00	-
v10, m3	0.22	0.38	0.26	0.36	0.33	1.00

, it can be concluded that despite the absence of multicollinearity between the independent variables, with an average coefficient of determination R² = 0.61, F-significance = 2.17435 × 10⁻¹⁶ << 0.05 = α, and a noticeable regression coefficient value (b₅ = 1.48) of the average grout injection parameter, its statistical significance is not achieved because the p-value of this parameter is 0.212, which exceeds the significance level α = 0.05.

4. Discussion

If calculated according to Equation (2) and then ordered in ascending order and superimposed on the actual values (S), the resulting predicted displacements (S_p) will be the graph shown in Figure 4. The predictive model of displacements (S_p) approximates the data obtained from geotechnical monitoring in some way.

Despite the inaccuracies of the model, it can still be useful as it is based on actual values and is statistically significant.

In the predicted model, negative vertical movements (marked with “−”) occur more frequently, while positive vertical movements (marked with “+”) are less common, which may be due to the relatively small number of such cases in the presented sample. This pattern is consistent with the general pattern of studies on this topic [1,2,9,11,13,14,15,16,29].

In any case, the authors plan to expand the sample with the aim of applying Machine Learning (ML). With ML, you can use methods that will train on the sample and yield a larger R². On the other hand, it is necessary to understand that the model obtained with ML will be more sensitive to new data [38].

5. Conclusions

Based on the research results, statistically significant parameters were identified, which formed the basis of the regression equation, allowing the assessment of absolute deformations accumulated over a distance of 10 m along the planned route before reaching the planned mark of geotechnical monitoring. The characteristics listed below have statistical significance and were used to create the final equation.

The most significant impact on the settlement size is made by the parameter the average face-support pressure for a 10 m section (P_avg.10). Among all the parameters studied, this one, at its average value, has the greatest effect, reducing settlement by 36%. The next parameter in terms of weight contribution, the soil deformation modulus at the tunnel face (E₁), can also reduce the settlement size by 28% (see Figure 3). However, the average soil excavation (V₁₀) and the depth of tunnel burial (H) at average values may contribute to an increase in settlement by 25% and 11%, respectively. It should be noted that, in a previous study [27] where the authors investigated the impact of parameters on settlement over one monitoring cycle, the soil excavation parameter (V) was not statistically significant. It is important to highlight that in this model, there is no correlation between the parameters P_avg.10 and H, as was noted earlier [27].

Similar to the authors’ previous study [27], within the available volume of data, there is no observed dependency of settlement on the volume of grouting solution injected into the space between the lining and soil mass (v₁₀). Additionally, it should be noted that the distance parameter (r) is not significant, whereas in the authors’ previous work, this parameter was significant but had a minor impact on settlement size compared to other parameters [27]. Thus, the traditional conception of the settlement surface shape in the cross-section, described by the Gaussian curve, may be disrupted by the technological parameter of tunneling, the face-support pressure. This result can be explained as follows: a relatively small excess of the necessary face-support pressure for maintaining face stability causes a rise in the deformation mark within one cycle of geotechnical monitoring.

This result contradicts other contemporary studies [1,11,15,16] and can be explained by the fact that the maximum settlement of the surface occurs in the cross-section of the tunnel at some distance from the axis of the tunnel and away from the zone of active pressure impact.

The difference between this work by the authors and the previous one [27] is that this time engineering–geological conditions are taken into account. The monitoring data are taken not for one cycle, but for 10 m of TBM advancement. The accumulated settlement during this time and the corresponding technological parameters are analyzed.

For comparison with the presented materials, the study of our colleagues [29] is of interest. Both studies, ours and the study of our colleagues [29], involve the construction of a tunnel with similar design solutions. However, the tunnel burial depths and the engineering–geological conditions of construction differ. The study [29] considers settlement along the tunnel axis during one phase of geotechnical monitoring, whereas in our study we also analyze the accumulated settlement of the surrounding buildings, their distance from the tunnel axis, and the number of floors. One important statistical tool for assessing the adequacy of the model, R², is somewhat lower in our study, which is explained by the use of linear multiple regression. This is due to the small sample size. It may not be advisable to process data using machine learning based on a single project, as there is a high likelihood of the model being highly sensitive to new data. Additionally, a distinctive feature of this study compared to [29] is the following: the authors of this study describe the contribution share of each significant parameter in the final equation affecting the settlement magnitude. Nevertheless, the authors note the effectiveness of the model in [29] due to the consideration of a greater number of technological factors that can influence additional settlement.

Furthermore, in this study, the soil massif where construction takes place is fundamentally divided into two zones (soil at the tunnel face/soil above the tunnel), which allows the localization of the influence zone of parameters on the settlement. The obtained results will also be valuable for tunnel construction in dispersive soils at depths ranging from 14 to 36 m.

The final equation, with proper refinement, can form the basis of an add-on for the operator’s onboard computer, which will help relate the face-support pressure to the surface settlement. The composed equation includes two parameters (P_avg.10, V₁₀) that can be adjusted during construction, thereby minimizing the settlement (S). This method of deformation control can be effective because the parameters that can be controlled during construction collectively can influence settlement by up to 61% on average. Additionally, an advantage of the potential control method is that it coordinates the work of two parallel construction crews: the surveyors, who monitor the displacements of objects, and the tunneling crew.

In conclusion of this study, the authors conclude that the face-support pressure has a direct impact on the settlement of objects. Since this parameter can compensate for some additional displacements, it is necessary to develop methods that will improve existing approaches to calculating the face-support pressure magnitude.