Assessment of Settlement Profile Caused by Underground Box Structure Installation with an Artificial Neural Network Model

Abstract

Various empirical equations have been proposed to predict the ground settlement profile caused by the excavation of conventional circular tunnels. However, ground movement for the underground box structure has not been fully studied. In this study, ground settlement induced by underground box installations is investigated using two-dimensional finite element analyses. A new formulation to assess the settlement profile applicable to underground box structure is proposed based on parametric analyses of the changes in ground condition, geometric condition of structure, and construction conditions. This paper also presents a method to predict the maximum surface settlement around an underground box structure with artificial neural networks (ANNs), taking into account nine input variables that have direct physical significance. A MATLAB-based multi-layer back propagation neural network model is developed, trained, and tested with parameters obtained from numerical analyses. The maximum settlement from the ANN model, in conjunction with a new formulation to construct the settlement profile, turns out to be promising, by predicting a settlement profile compatible with field measurement data.

In recent years, the rapid growth of urban areas has led to an increase in the number of underground structures that underpass existing infrastructures or facilities (roads, railways, subways, waterworks, etc.) at shallow depths. For safe construction in complex urban environments, trenchless technology is actively undertaken to avoid interference with existing structures, avoiding re-routing of traffic and any sudden and substantial surface displacement of the overlying roadway or railroad. However, the construction of underground box structures using trenchless excavation will inevitably induce varying degrees of ground movement toward the excavation, resulting in ground surface settlement. Thus, an essential element to minimize possible detrimental effects of ground settlement on existing structures depends greatly on the reliability of the ground settlement profile prediction.

To address this important issue, several researchers have attempted to predict maximum surface settlement induced by shallow tunneling for conventional circular tunnels. Because of the complexity and unknown relationships and interactions between the many parameters affecting surface settlement, deriving a closed-form mathematical solution based on analytical methods is very difficult ( 1 , 2 ). Many researchers have tried to employ other approaches, including empirical methods ( 3 – 9 ), numerical methods ( 10 , 11 ), and laboratory studies (including centrifuge tests) based on small model tests ( 12 ). Although the analytical, empirical, numerical, and laboratory test methods have several advantages in addressing the issue, there are major constraints in application. For instance, in analytical methods there are many simplifications such as a plain strain assumption, elastic behavior, and/or soil isotropy. In laboratory experiments, the effect of some parameters can be well evaluated, though the effect of the problem of scale is somewhat unknown.

Various empirical/analytical equations have been proposed to predict the ground settlement profile caused by excavation of conventional circular tunnels. However, ground movement for the underground box structure has not been fully studied.

Mamaqani developed a surface settlement prediction model using an artificial neural network (ANN) along with finite element analysis for a box jacking method, which is in good agreement with data collected from case studies ( 13 ). The study also highlighted that the empirical method, suggested by Milligan and Marshal ( 14 ) and originally developed for tunneling and pipe jacking, tends to overestimate the maximum surface settlement and underestimate the width of the settlement trough channel. A series of large-scale tests conducted by Um et al. showed that maximum heaving and settlement was measured from the center point along with both longitudinal and lateral planes of underground structures ( 15 ). In addition, when the ratio of cover depth to the diameter of the jacking pipe is larger than 1.5, deformation of the surrounding soil seems to decrease significantly.

ANN is a complex mathematical model, or computational model, inspired by the structural aspects of biological neural networks, and is widely used in the modeling of nonlinear systems and system identification. Many scientists and researchers use and apply this particular biological concept to conduct their studies. Park ( 16 ) conducted an extensive review on the application of ANN in geotechnical engineering. According to this author, the ANN model has been extensively employed since the early 1990s, for example in constitutive modeling, geo-material characterization, assessment of bearing capacity of pile, slope stability, and evaluation of liquefaction, shallow foundations, and tunnels and underground openings.

In this study, an effort was made to develop an empirical equation to predict settlement profile following installation of underground structures, based on several finite element analysis runs. While previous research conducted by Milligan and Marshall ( 14 ), Bennett ( 17 ), Rogers and O’Reilly ( 18 ), and Liu and Lu ( 19 ) mainly focused on surface and subsurface ground movements caused by pipe jacking or tunneling, the focus of this paper is ground movement and the underground box structure.

Many box-type structures are being constructed under roadways and railroads at a relatively shallow cover depth in South Korea, as illustrated in Figure 1; therefore, it is necessary to estimate subsurface settlement realistically to mitigate any disasters. In this study, an ANN model is employed to predict the subsurface settlement profile based on finite element analysis results, to compare with a proposed empirical equation and limited field measurements.

Settlement Trough for Underground Box Structures

Most of the empirical methods are based on measurements in full-scale circular-type tunnels during boring, or after the completion of construction in the long term. Such results are considered as the most reliable, but they cannot be generalized because of the differences in physical and geometrical properties from one given site to another. These empirical methods need to be verified for application to the construction of underground box structures.

Review of Empirical Methods

There are many research examples clarifying the characteristics of ground motion when a tunnel is excavated. The maximum settlement amount (S_max) and the position of the inflection point (i) are depicted by a normal distribution curve on the form of subsidence on the cross-section of the tunnel, as shown in Figure 2.

Peck ( 3 ) presented the settlement curves of a single-wire tunnel using field measurements, assuming the absence of volume change via

S (x) = S_{\max} \exp (- \frac{x^{2}}{2 i^{2}})

where

$S$ = the surface settlement;

$x$ = the transverse distance from tunnel centerline;

$S_{\max}$ = the maximum settlement; and

$i$ = the position of inflection point.

The inflection point (i) is a parameter determined by the ground condition. From the model test and various field measurement data, several studies have proposed it, as summarized in Table 1.

Table 1.

Different Empirical Equations for the Estimation of Settlement Trough Width, i

References	Width of settlement trough, $i$	Basis for empirical solution
Peck ( 3 )	$i / R = {(Z_{0} / 2 R)}^{n}$ ; $n = 0.8 - 1.0$	Field observations
Attewell and Farmer ( 4 )	$i / R = a {(Z_{0} / 2 R)}^{n}$ ; $a = 1.0, n = 1.0$	Field observations of UK tunnels
Atkinson and Potts ( 5 )	$i = 0.25 (Z_{0} + R)$ ; loose sand $i = 0.25 (1.5 Z_{0} + 0.5 R)$ ; dense sand/OC clay	Field observations and model tests
Mair et al. ( 6 )	$i = 0.5 Z_{0}$	Field observations and centrifuge tests
Clough and Schmidt ( 7 )	$i / R = a {(Z_{0} / 2 R)}^{n}$ ; $(a = 1.0, n = 0.8)$	Field observations of UK tunnels
O’Reilly and New ( 8 )	$i = 0.43 Z_{0} + 1.1$ ; cohesive soil, 3 ≤ Z0 ≤ $35 m$ $i = 0.28 Z_{0} - 0.1$ ; granular soil, 6 ≤ Z0 ≤ $10 m$	Field observations of UK tunnels
Rankin ( 9 )	$i = k Z_{0}$ ; $k = 0.5$ for clay	Field observations

Note: $Z_{0}$ = the depth of tunnel below ground (at tunnel spring line), $R$ = tunnel radius.

In addition, Aversin ( 20 ) and Arato ( 21 ) proposed a formula through half of the settlement width (L) rather than the inflection point (i):

S (x) = S_{\max} {(1 - x / L)}^{4.54} \exp (4.54 x / L)

S (x) = S_{\max} (\frac{0.75}{\exp {(2 x / L)}^{2}} + \frac{0.25}{\exp {(2 x / L)}^{4}})

Evaluation of Surface Settlement by Numerical Analysis Method

Numerical analyses were performed using PLAXIS 2D 8.6 finite element analysis program to estimate the surface settlement profile of underground box structures. To consider the shallow cover depth (C) of underground box structures in the urban environment, three cases (2 m, 3.5 m, and 7.5 m depth) were considered for the numerical analyses. In the case of a cross-sectional shape, it is set as square cross-section (7.5 m × 7.5 m) for box structures for the comparison with the circular cross-section (diameter = 7.5 m).

The Mohr–Coulomb plasticity theory was applied for the plain strain 15-nodes element, and the ground condition was assumed to be weathered soil, properties that account for the majority of the shallow stratum in South Korea, as summarized in Table 2. For the box structure, a linear elastic model was assumed with different properties for box structure and circular tunnel, respectively. For the consideration of real construction conditions in the field, the effects of groundwater and overcut were also included in the numerical analyses. Overcut excavation is required to reduce friction forces and facilitate steering during construction ( 13 ). In this study, the overcut size was set at 50 and 100 mm.

Table 2.

Material Properties for the Finite Element Method Analysis

Ground conditions		Underground structure properties
Material model	Mohr–Coulomb	Material model	Linear elastic
Unit weight (kN/m³)	18	EA(kN/m)	2.44E+7^* / 6.10E+6^**
Elastic Modulus (kN/m²)	200,000	EI (kN/m²/m)	2.03E+6^* / 1.27E+5^**
Poisson Ratio (υ)	0.3	Thickness (D)	1^* / 0.5^**
Cohesion (kN/m²)	30	W (kN/m/m)	25
Friction angle (deg.)	33	Poisson Ratio (υ)	0.15

Note: *property for box structure and **for circular tunnel.

Maximum Surface Settlement

The maximum surface settlement of the underground box structure was larger than that of the circular tunnel. As the overcut size was increased in the underground box structure, the amount of maximum settlement also increased because of soil collapse into the overcut space, as shown in Figure 3.

The effect of overcut in the circular tunnel became insignificant compared with the underground box structure condition. In addition, the maximum settlement tends to increase with the decrease of the cover depth, particularly in the case in which the groundwater level is assumed to be on the surface.

Settlement Trough

Normalized maximum settlement (S/S_max) was introduced to compare the empirical methods summarized in the previous section for different shapes of structures. In the case of the circular tunnel not accounting for the groundwater level, the numerical analysis results and the conventional empirical methods generally matched well, as shown in Figure 4a except for O’Reilly’s method, which might be attributed to the “i” value computed. However, in the case of underground box structures, large deviations have been observed after the 1D range from the structure as shown in Figure 4b. This is because the stress distribution around the structure in the middle of excavation varies depending on the shape of the structure, and the arching effect of the ground cannot be sufficiently mobilized for the shallow depth of underground structures. Overall, the underground box structure yields a larger maximum settlement than the circular tunnel based on numerical analysis, since the curves, in terms of normalized maximum settlement (S/S_max), become smoother with respect to distance from the structure, indicating larger settlement-induced zone.

Figure 5 shows the results obtained when the groundwater level is assumed to be located on the ground surface, along with free drainage condition into the tunnel. It can be seen that there are large deviations between the existing empirical methods and numerical analyses regardless of the sectional shape. This is because the existing empirical methods mainly derive from measurement data for cases where there is no volume change in the undrained condition, in most cases. It is shown that the effect of underground excavation tends to be significant under the conditions in which drainage occurs within granite-weathered soil below groundwater.

New Suggestion of Settlement Trough for Underground Box Structures

The modified Gaussian curve of the following form is found to be a better fit to the predicted soil settlement profiles from the PLAXIS analyses for underground box structures described earlier:

S (x) = S_{\max} \frac{n}{(n - 1) + \exp [α {(\frac{x}{i})}^{2}]}, n = e^{α} \frac{2 α - 1}{2 α + 1} + 1

where

$n$ = the shape function parameter controlling the width of the profile; and

$α$ = the correction factor to ensure that $i$ remains at the inflection point.

For the drainage condition, the influence of the tunnel excavation effect was accommodated by changing the inflection point of the settlement shape curve, as shown in Figure 6b. It is suggested to use $i = 0.5 Z_{0}$ , $α = 0.25$ (for no ground water condition), and $i = Z_{0}$ , and $α = 0.005$ (for ground water at the surface condition) for an underground box structure through the Microsoft Excel Solver analysis. However, these values need to be defined based on further evaluations.

Development of the ANN Model

ANN is a complex mathematical model inspired by biological neurons; it is the emulation of biological neural networks and is widely used in modeling of nonlinear systems and system identification. Generally, its powerful information processing function depends on four factors: input–output properties (activation characteristics) of network units (neurons), network topologies (connection modes of neurons), connection weights (synaptic strength), and neuron thresholds (special connection weights). An ANN generally consists of an input layer, hidden layers, and an output layer. Every layer includes many neurons, and the numbers of layers and neurons in each layer are determined by the user with respect to the scale of the problem. All neurons in the structure have interconnections between each other, similar to the biological nervous system. The ANN transfers latent knowledge or laws in related inputs to the network’s site by processing the inputs, and it includes general laws based on the calculations performed on the numerical inputs or examples. The underground excavation problems based on ANN are generally classified as two types: one is the nonlinear relationship of parameters, which is established by the data provided by finite element analyses data and/or field measurement data; the other is the prediction system for the latter period based on the experience gained and the in-situ measurement data gathered from past projects.

The main objective of this research is to develop an ANN model to estimate maximum surface settlement associated with box structure installation, using the following nine factors: (1) soil cohesion (c), (2) soil unit weight (γ), (3) soil modulus of elasticity (E), (4) soil friction angle (φ), (5) box culvert height (h), (6) box culvert width (w), (7) overcut size (s), (8) depth of box culvert from the surface (H), and (9) groundwater condition, as shown in Figure 7. A total of 216 underground box structure models generated from PLAXIS program runs and corresponding maximum surface settlements were recorded.

As described earlier, a neural network consists of a layer of neurons or cells that are connected to each other, receiving data inputs and transferring them to outputs through the hidden layer. A hidden layer is a layer between input and output layers whose neuron is connected to other neurons. There is no exact rule to select the optimal number of neurons in the hidden layer. However, there are some rules of thumb that are available to find the number of hidden neurons. Mamaqani ( 13 ) recommended that the number of hidden neurons depends on the number of input parameters. He suggested considering 1.5 times the number of parameters in the input layer. Masters ( 23 ) proposed a three-layer network in which the hidden layer would have sqrt(n×m) neurons (where n is input and m is output neurons). In developing an optimal ANN, the data are divided into three subsets, such as training data set, validation data set, and testing data set. The training process is an important step to enhance the ANN model and adjust the weights. The aim of the training process is to reduce errors between the actual output values and target output values by updating the connection weights in the neural network. Weights are adjustable scaler parameters of the neurons, and represent the synapse. A set of input signals x_i (i = 1,2,…,n) is summed up with hidden neurons j and computes its outputs y_j as function of f, where, w_ji-weight connections from neuron j to neuron i, and f is a sigmoidal function:

y_{j} = f (\sum_{i = 1}^{n} w_{j i} x_{i})

Validation data are used to verify and determine the performance of the trained ANN model. The validation set is for tuning the parameters to show how well the network is performing. In addition, the validation data set is used to calculate the accuracy of the algorithm in terms of mean square error (MSE) using

MSE = \frac{1}{n} \sum_{i = 1}^{n} {(\bar{Y_{i}} - Y_{i})}^{2}

where

$n$ = number of data;

$\bar{Y_{i}}$ = vector of n predictions; and

$Y_{i}$ = vector of true values.

Once the final model is determined, a testing data set is developed to assess the actual predictive power of the ANN model. The test data set is not used in the model-building process.

Methodology

In a general ANN system, the activation function, also known as the transfer function, is used to convert the result of the weighted sum of a neuron’s inputs into a wanted output value. This conversion is achieved by calculating the neuron state by introducing a non-linearity in the functioning of the neuron. Among the transfer functions available, the sigmoidal function has been found most efficient through its better performance ( 13 , 22 ).

In this study, feedforward network architectures and the Levenberg–Marquardt training function available in MATLAB, along with a program that fits the purpose of this study, were used to predict the surface vertical displacement based on 216 generated data sets from finite element method analysis. Of the total data set, 70% was used as training data, 15% for validation, and 15% for testing data. The performance of an ANN model can be measured via the MSE of the model, as shown in Figure 8a. The MSE varies along with number of iterations of model (called “epoch” in MATLAB), and lower MSE indicates enhanced performance. In this analysis, MSE reached a minimum 11.18 at seven epochs. The training continued for six more iterations before the training stopped. Another step in validating the network is to create a regression plot, which shows the relationship between the outputs of the network and the targets. The performance of the ANN model was also checked in terms of R² value obtained from linear regression analysis among variables, as shown in Figure 8b. In this analysis, the R² value is generally more than 0.95.

Once the ANN model was determined based on the least MSE, shown in Figure 8, the model was applied to the whole dataset to compute the average error percentage using

Average Percentage of Error (%) = \frac{R_{ANN} - R_{PLAXIS}}{R_{PLAXIS}} \times 100

where

$R_{ANN}$ = the maximum settlement obtained by ANN model; and

$R_{PLAXIS}$ = the maximum settlement obtained by PLAXIS.

Park ( 16 ) reported that an over-fitting problem or poor generalization capability frequently occurs when an ANN experiences over-learning. Then, such a well-trained model may not perform well on unseen data set because of its lack of generalization capability. Lee and Lee ( 24 ) utilized neural networks to predict the ultimate bearing capacity of piles. The prediction of the ANN model showed a maximum error of no more than 20% and average summed square error less than 15%. Consequently, the acceptance criterion in terms of average percentage error was set to 15% in this study, based on previous studies. A positive error percentage indicates that the ANN result was overestimated, and vice versa, as shown in Figure 9a. The ANN model seemed to be functional because the average percentage of error was 13.8%, less than the criterion.

The predicted settlement trough for the example case (C = 2.0 m, Overcut = 50 mm, no groundwater condition) results showed that there are good matches between the results obtained from ANN and PLAXIS, as shown in Figure 9b. In this comparison, Peck’s empirical method was selected. After the estimation of maximum settlement from the ANN method, the remaining part of the settlement trough could be drawn with the newly suggested equation, as described in the previous section for underground box structures.

Application of the ANN Model to a Case Study

The ANN, developed based on the numerical analysis, was used to check its applicability for field measurement data. In this study, the settlement measurement data of the transverse underground box structure located at the 1.88 km branch of the Seoul outer circuit roadway in South Korea were considered ( 15 ).

The box structure was designed with 26.8 m width and 8.71 m height, and the ground condition comprised weathered granitic soil. The cover depth was 1.6 m and the longitudinal length of the box structure was 60 m, as shown in Figure 10, a to d. During the construction stage, the maximum surface settlement of 37 mm was measured at the center of the box location.

From the ANN model, the maximum settlement was estimated to be 41.6 mm. With a suggested value in Equation (4) without ground water condition, it was difficult to match with field measurements, so re-calibration was made to find the inflection point and $α$ value ( $i = 1.8 Z_{0}$ , $α = 0.1$ ) to construct a transverse settlement trough, as shown in Figure 10e. This indicates the feasibility of the suggested equation, which can be adjustable depending on various field conditions. While there is a large difference between the field measurement data and the empirical method suggested by Peck, the difference generated from the suggested equation based on the ANN prediction is relatively insignificant considering the variability of ground condition in the field. This limited validation demonstrated the efficiency of the ANN model in conjunction with the suggested equation in the assessment of the maximum settlement of the underground box structure.

Conclusions

A new formulation to assess the settlement profile applicable to an underground box structure is proposed based on parametric analyses of changes in ground condition, geometric condition of structure, and construction conditions. The ANN model is employed to predict the subsurface settlement profile based on finite element analysis results.

The maximum surface settlement of the underground box structure was generally larger than that of the circular tunnel, based on numerical analysis when identical conditions were given.

While estimated surface settlements from previous empirical equations were generally found to be compatible with predictions of finite element analysis in the case of a circular tunnel without taking into account ground water level, the estimated surface settlements of box structures based on empirical equations seemed to underestimate beyond 1D location.

This study proposed a modified equation to incorporate ground water condition and box structure shape, which is more compatible with finite element analysis results.

To develop an ANN model to predict surface settlement caused by excavation of underground structures, a total of 216 finite element analysis runs were made taking into account various soil conditions, depth of cover, ground water level, and structure shape. The influence of overcut size on the surface settlement becomes alleviating in case of a circular shape structure, considered as attributed to the arching effect. At a relatively shallow depth of cover, the surface settlement tends to increase, especially in box-shaped structure considered.

A field case study was employed to limitedly verify the proposed ANN and Equation (4). The i and α values in Equation (4) can be adjusted depending on field conditions, which is deemed feasible.

This study has introduced artificial intelligence for prediction of ground surface settlement based on accumulated numerical analysis data. However, it should be noted that the capabilities of such codes in making accurate predictions is entirely dependent on the quality and the quantity of data used in training the ANN. If the data are deficient or training is inadequate, the proposed neural network-based prediction should be treated with caution. Therefore, the collection and analysis of monitored data should be carefully carried out for guaranteed predictions.

Footnotes

Acknowledgements

This work is part of a research project financially sponsored by the Korea Agency for Infrastructure Technology Advancement. (Grant No. 16SCIP-B108153-02).

The Standing Committee on Subsurface Soil-Structure Interaction (AFS40) peer-reviewed this paper (18-04174).

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