Cover Depth Ratio Research Articles

Stability analysis of tunnel heading in clay with nonstationary random fields of undrained shear strength

The stability problem of a tunnel heading in clay remains a significant challenge in geotechnical engineering. Specifically, when considering the spatial variability of the soil, the stability factor may be influenced by geographically random fields. This study investigates the effect of random fields on a probabilistic analysis of a tunnel heading in undrained clay. The study assumes that the undrained shear strength of the clay increases linearly with depth due to a strength gradient factor. The random adaptive finite element limit analysis is employed to calculate the stability numbers for tunnel headings. Nonstationary random fields with varying vertical correlation lengths are simulated using Monte Carlo simulation technique. The stability analysis takes into account geometry parameters (i.e., cover depth ratio) and nonstationary random field of undrained shear strength parameters. (i.e., strength gradient, coefficient of variation, and vertical correlation length). The results of tunnel face stability using random adaptive finite element limit analysis have also been utilised to assess the probability of design failure over a practical range of deterministic factors of safety. In the context of probabilistic failure analysis, the failure mechanism resulting from varying vertical correlation lengths could influence the probability of design failure. The findings of this study can be of significant interest to tunnel engineering practitioners during the design phase of tunnel heading projects.

Machine learning approaches for stability prediction of rectangular tunnels in natural clays based on MLP and RBF neural networks

In underground space technology, the issue of tunnel stability is a fundamental concern that significantly causes catastrophe. Owing to sedimentation and deposition processes, the strengths of clays are anisotropic, where the magnitudes of undrained shear strengths in the vertical and horizontal directions are different. The anisotropic undrained shear (AUS) model is effective at considering the anisotropy of clayey soils when analyzing geotechnical stability issues. This study aims to assess the stability of rectangular tunnels by adjusting the dimensionless overburden factor, cover-depth ratio, and width-depth ratio in clay with various anisotropic strength ratios. The stability analysis of these tunnels involves employing finite element limit analysis and the AUS model to identify the planes of soil collapse in response to the aforementioned variations. In addition, this study presents the development of soft-computing models utilizing artificial neural networks (ANNs) to forecast the stability of rectangular tunnels across various combinations of input parameters. The findings of this study are presented in the form of design charts, tables, and soft-computing models to facilitate practical applications.

Underground storage tank blowout analysis: Stability prediction using an artificial neural network

Most geotechnical stability research is linked to “active” failures, in which soil instability occurs due to soil self-weight and external surcharge applications. In contrast, research on passive failure is not common, as it is predominately caused by external loads that act against the soil self-weight. An earlier active trapdoor stability investigation using the Terzaghi's three stability factor approach was shown to be a feasible method for evaluating cohesive-frictional soil stability. Therefore, this technical note aims to expand “active” trapdoor research to assess drained circular trapdoor passive stability (blowout condition) in cohesive-frictional soil under axisymmetric conditions. Using numerical finite element limit analysis (FELA) simulations, soil cohesion, surcharge, and soil unit weight effects are considered using three stability factors (Fc, Fs, and Fγ), which are all associated with the cover-depth ratio and soil internal friction angle. Both upper-bound (UB) and lower-bound (LB) results are presented in design charts and tables, and the large dataset is further studied using an artificial neural network (ANN) as a predictive model to produce accurate design equations. The proposed passive trapdoor problem under axisymmetric conditions is significant when considering soil blowout stability owing to faulty underground storage tanks or pipelines with high internal pressures.

Prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum

This study focuses on the analytical prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum considering the volumetric deformation modes of the soil above the tunnel crown. A series of numerical analyses is performed to examine the effects of cover depth ratio (C/D), tunnel volume loss rate (ηt) and volumetric block proportion (VBP) on the characteristics of subsurface settlement trough and soil volume loss. Considering the ground loss variation with depth, three modes are deduced from the volumetric deformation responses of the soil above the tunnel crown. Then, analytical solutions to predict subsurface settlement for each mode are presented using stochastic medium theory. The influences of C/D, ηt and VBP on the key parameters (i.e. B and N) in the analytical expressions are discussed to determine the fitting formulae of B and N. Finally, the proposed analytical solutions are validated by the comparisons with the results of model test and numerical simulation. Results show that the fitting formulae provide a convenient and reliable way to evaluate the key parameters. Besides, the analytical solutions are reasonable and available in predicting the subsurface settlement induced by shield tunnelling in sandy cobble stratum.

Stability evaluation of elliptical tunnels in natural clays by integrating FELA and ANN

The stability of tunnels in clayey soil is a major concern for underground space technology. Clay has anisotropy in shear strength induced by depositional and sedimentation processes. For the numerical analysis of geotechnical stability problems, the anisotropic undrained shear (AUS) model can account for this anisotropy of clayey soils. In this study, the stability of the elliptical tunnel (stability factor: σs-σt/suc) with varying elliptical shape (width-depth ratio: B/D) placed at different embedment depths (cover-depth ratio: C/D) in clay with different anisotropy (anisotropic strength ratio: re) and varying dimensionless overburden factor (overburden factor: γD/suc) is evaluated using finite element limit analysis and the AUS model. The failure planes are also evaluated for the above variations. Based on the numerical outcome, the artificial neural network (ANN) is utilized to establish the equation for predicting the stability of the elliptical shape tunnel with different shapes (i.e., width-depth ratio), and varying overburden, cover-depth ratio, varying anisotropic strength ratio of clay. The present study results are presented as design charts, tables, and equations so that they can be used in practice.

Terzaghi's three stability factors for pipeline burst-related ground stability

A recent study on active trapdoor stability has been completed by the authors using Terzaghi's three stability factors approach. It was concluded that the superposition approach is an effective way to evaluate the stability of cohesive-frictional soils. This technical note aims to extend the previous active trapdoor study to perform a stability assessment of a passive planar trapdoor (i.e., a blowout condition) in cohesive-frictional soil. Note that this passive trapdoor problem represents the blowout stability of soils due to defective pipelines under high water main pressures, in spite of the frequent media news about the water main bursts which enlightens the relevance of the problem. Numerical solutions of upper and lower bound finite element limit analyses are presented in form of the three stability factors (Fc, Fs, and Fγ), which consider the effect of cohesion, surcharge, and soil unit weight respectively. In the event of passive trapdoor stability, this technique can be used to determine a critical blowout pressure due to a water mains leak. The study continues with a series of sensitivity analyses with a widely selected range of parameters including the cover-depth ratio (H/B) and the drained frictional angle (ϕ). The influence of these parameters on the three stability factors is discussed, and a practical example of adapting these approaches is also introduced. All numerical results are provided in the forms of design charts and tables that can be efficiently used with confidence in design practice.

Upper bound solution of passive instability on the face of longitudinal inclined shallow buried shield tunnel based on rotation–translation mechanism

To better evaluate the passive failure mode of shallow shield tunnel faces in sandy soil strata, tunnel faces passive failure mode was investigated considering the longitudinal inclination in this study. A three-dimensional rotation–translation mechanism that simultaneously considers the longitudinal inclination of the tunnel and partial failure of the tunnel face based on the upper bound limit analysis method was presented. The mechanism comprised two rigid translation blocks and one rigid rotation block. Subsequently, the reliability of the proposed mechanism was verified using the horizontal rigid translation mechanism and numerical simulation considering the longitudinal inclination. Finally, the effects of tunnel longitudinal inclination (δ), cover depth ratio (C/D), soil internal friction angle (ϕ), and the possible presence of uniform surface surcharge (σS) on the limit support pressure of the tunnel face and the partial failure range was assessed. The results indicated that the partial failure range of the tunnel face gradually increased with δ When C/D<1. Conversely, global failure of the tunnel face occurred at different longitudinal inclinations when C/D≥1. The rotation angle (θ) of the rotational failure zone was sensitive to the longitudinal inclination (δ) and decreased with δ at the same coverage depth ratio.

Three-dimensional undrained face stability of circular tunnels in non-homogeneous and anisotropic clays

The advanced 3D finite element limit analysis is employed to examine three-dimensional (3D) face stability of circular tunnels in undrained clays with the impact of strength non-homogeneity and anisotropy. The soil behaviour for all analyses is governed by the anisotropic undrained shear (AUS) strength model, which requires three anisotropic undrained shear strengths that are simply evaluated from conventional laboratory tests. The upper and lower bound solutions of 3D face stability of circular tunnels are accurately analyzed by considering four dimensionless parameters, including the cover-to-depth ratio, the overburden stress factor, the strength gradient ratio, and the anisotropic strength ratio. The significance of four dimensionless parameters on the stability load factor of the 3D face stability of circular tunnels, and the predicted failure mechanisms due to the influence of cover depth ratios, are also illustrated. A nonlinear regression analysis is employed to the computed data, which enables a new design equation of the factor of safety incorporating the conventional stability number. Thus, the new tunnel stability factors are proposed for the first time in the literature. A comprehensive application of the proposed safety factor equation is also presented and compared. The 3D effects of the tunnel face configuration between 3D geometry and 2D plane strain heading on the tunnel stability factors are also discussed. The new proposed design equation of the factor of safety provides an accurate and practical tool in assessing face stability of circular tunnels in non-homogeneous and anisotropic clays.

Undrained Stability of Opening in Underground Walls in Anisotropic Clays

A two-dimensional (2D) finite-element limit analysis (FELA) was performed under plane strain conditions to investigate the undrained stability of tunnel launch with a rigid wall in anisotropic clays. The anisotropic undrained shear (AUS) failure criteria were applied to identify anisotropic soil behaviors. The average bound solutions were employed to compute the stability load factor. Different sensitivity analyses were carried out to determine the effect of cover–depth ratio (C/D), overburden factor (γD/suTC), and anisotropic strength ratio (re) on the load factor (N) of the opening in tunnel launching with a rigid wall. The failure patterns that were predicted by certain parameters were explored and investigated. To adopt a practical approach, some new design charts for the undrained stability of tunnel launching with a rigid wall in anisotropic clays were devised.

A meso-scale numerical modelling method for the stability analysis of tunnels in sandy cobble stratum

This paper presents a meso-scale numerical modelling method to investigate the stability of tunnels in sandy cobble stratum. Using Monte Carlo simulation, Python routine is implemented to randomly generate and filter the location information of blocks including center coordinates, sizes and orientation angles, then extract and import them into CAD modelling software in batches to mesh. The problem of overlapping detection for elliptical and ellipsoidal blocks is solved based on affine transformation, achieving higher efficiency and applicability than the existing methods. Then, using the proposed numerical modelling method, convergence-confinement analysis of circular tunnels with different cover depths is performed in plane strain condition. Meanwhile, face stability analysis of shield tunnels is carried out in three-dimensional condition. Results show that sandy cobble stratum may not be in accordance with the scale-independent soil-rock mixture. Blocks with small sizes are geotechnically significant and contribute much to the overall strength. When the cover depth ratio reaches a certain level, limit support pressure remains basically unchanged due to the strong arching effect above tunnel crown, while permissible support pressure increases approximately linearly to control deformation. Compared with the multi-scale model, hardening soil model considering the overall strength is suitable for the stability analysis of tunnels in sandy cobble stratum at the macro-scale with high precision, while the macro homogeneous model ignoring the presence of blocks provides a conservative (i.e. uneconomical) prediction for the design of tunnel stability.

Design Equations for Predicting Stability of Unlined Horseshoe Tunnels in Rock Masses

This paper aims to propose new stability equations for the design of shallow, unlined horseshoe tunnels in rock masses. The computational framework of the upper- and lower-bound finite-element limit analysis is used to numerically derive the stability solutions of this problems using the Hoek–Brown failure criterion. Five dimensionless parameters including the width ratio and the cover-depth ratio of the tunnels, as well as the normalized uniaxial compressive strength, the geological strength index, and the yield parameters of the Hoek–Brown rock masses, are considered in the study. Selected failure mechanisms of the horseshoe tunnels in rock masses are presented to portray the effect of all dimensionless parameters. New design equations for stability analyses of horseshoe tunnels are developed using the technique of nonlinear regression analysis and the average bound solutions. The proposed stability equations are highly accurate and can be used with great confidence by practitioners.

Uplift Behavior of Pipelines Buried at Various Depths in Spatially Varying Clayey Seabed

The behavior of buried offshore pipelines subjected to upheaval buckling has attracted much attention in recent years. Numerous researchers have made great efforts to investigate the influence of different soil cover depth ratios, soil strengths and pipe-soil interfaces on failure mechanisms and bearing capacities during pipeline uplift. However, attention to soil spatial variability has been relatively limited. To address this gap, a random small-strain finite element analysis has been conducted and reported in this paper to evaluate the influence of the random distribution of soil strength on pipe uplift response. The validity of the numerical model was verified by comparison with the results presented in the previous literature. The spatial variation of soil strength was simulated by a random field. The effect of soil variability on the failure mechanism was determined by comparing the displacement contours of each random realization. Probabilistic analyses were performed on the random uplift capacity obtained by a series of Monte Carlo simulations, and the relationship between the failure probability and the safety factor was also determined. The findings of the present work might serve as a reference for the safety designs of pipelines.

Stability Evaluations of Unlined Horseshoe Tunnels Based on Extreme Learning Neural Network

This paper presents an Artificial Neural Network (ANN)-based approach for predicting tunnel stability that is both dependable and accurate. Numerical solutions to the instability of unlined horseshoe tunnels in cohesive-frictional soils are established, primarily by employing numerical upper bound (UB) and lower bound (LB) finite element limit analysis (FELA). The training dataset for an ANN model is made up of these numerical solutions. Four dimensionless parameters are required in the parametric analyses, namely the dimensionless overburden factor γD/c′, the cover-depth ratio C/D, the width-depth ratio B/D, and the soil friction angle ϕ. The influence of these dimensionless parameters on the stability factor is explored and illustrated in terms of a design chart. Moreover, the failure mechanisms of a shallow horseshoe tunnel in cohesive-frictional soil that is influenced by the four dimensionless parameters are also provided. Therefore, the current stability solution, based on FELA and ANN models, is presented in this paper, allowing for the efficient and accurate establishment and evaluation of an optimum surcharge loading of shallow horseshoe tunnels in practice.

Effect of tunnelling-induced ground loss on the distribution of earth pressure on a deep underground structure

This paper investigated the stress-transfer mechanisms in soil around a circular tunnel (CT) and a rectangular tunnel (RT) using the finite element method (FEM). Compared with the CT, there was a self-weight stress zone in the local soil above the RT, and the shear stress was concentrated only near the sliding surface, which caused the trajectory of the minor principal stress in this area to take an inverted arch shape. Then, a multi-arch model consisting of the end-bearing arch and the friction arch was proposed for estimating the distribution of the vertical earth pressure on a deep RT in dry sand. Unlike the CT, the friction arch in the RT was based on the assumption that the minor principal stress was a circular arc. The distribution factor of the vertical earth pressure on the RT was obtained. Note that a modified coefficient in the distribution factor was introduced, which was obtained by numerical simulation at different cover depth ratios and internal friction angles. Finally, the theoretical, experimental and numerical results were compared to evaluate the validity of the proposed model. The theoretical results in this paper were in good agreement with the experimental and numerical results.

Prediction of the Stability of Various Tunnel Shapes Based on Hoek–Brown Failure Criterion Using Artificial Neural Network (ANN)

In this paper, artificial neural network (ANN) models are presented in order to enable a prompt assessment of the stability factor of tunnels in rock masses based on the Hoek–Brown (HB) failure criterion. Importantly, the safety assessment is one of the serious concerns for constructing tunnels and requires a reliable and accurate stability analysis. However, it is challenging for engineers to construct finite element limit analysis (FELA) algorithms with the HB failure criterion for tunnel stability solutions in rock masses. For the first time, a machine-learning-aided prediction of tunnel stability based on the HB failure criterion is proposed in this paper. Three different shapes of tunnels, i.e., heading tunnel, dual square tunnels, and dual circular tunnels, are considered. The inputs include four dimensionless parameters for the heading tunnel including the cover-depth ratio, the normalized uniaxial compressive strength, the geological strength index (GSI), and the mi parameter. Moreover, dual square and circular tunnels include one more additional parameter namely the distance ratio. The results present the best ANN models for each tunnel shape, providing very reliable solutions for predicting the tunnel stability based on the HB failure criterion.

Neural Network-Based Prediction Model for the Stability of Unlined Elliptical Tunnels in Cohesive-Frictional Soils

The scheme for accurate and reliable predictions of tunnel stability based on an artificial aeural network (ANN) is presented in this study. Plastic solutions of the stability of unlined elliptical tunnels in sands are first derived by using numerical upper-bound (UB) and lower-bound (LB) finite element limit analysis (FELA). These numerical solutions are later used as the training dataset for an ANN model. Note that there are four input dimensionless parameters, including the dimensionless overburden factor γD/c′, the cover–depth ratio C/D, the width–depth ratio B/D, and the soil friction angle ϕ. The impacts of these input dimensionless parameters on the stability factor σs/c′ of the stability of shallow elliptical tunnels in sands are comprehensively examined. Some failure mechanisms are carried out to demonstrate the effects of all input parameters. The solutions will reliably and accurately provide a safety assessment of shallow elliptical tunnels.

Application of Artificial Neural Networks for Predicting the Stability of Rectangular Tunnels in Hoek–Brown Rock Masses

An artificial neural network (ANN) model for predicting the stability of rectangular tunnels in rock masses based on the Hoek–Brown (HB) failure criterion is presented in this study. Since the safety assessment of the tunnel stability is one critical issue for civil engineers during the construction, it is very important to develop a reliable and accurate stability analysis of such problems. The finite element limit analysis (FELA) with the HB failure criterion is used to develop the numerical upper and lower bound solutions of the problem of rectangular tunnels in rock masses. A novel machine learning-aided prediction of this problem is then developed based on the datasets of the numerical bound solutions obtained from the FELA. The inputs consist of six dimensionless parameters including the cover-depth ratio of tunnels, the width ratio of tunnels, the normalized uniaxial compressive strength, the geological strength index, the mi parameter, and the degree of disturbance of rock masses. The results show that the optimal ANN models provide very great accuracy in predicting the stability of the rectangular tunnels based on the HB failure criterion. The solutions will provide a prompt assessment of tunnel stability in rock masses for geotechnical engineers during the construction of rock tunnels.

Design equation for stability of a circular tunnel in anisotropic and heterogeneous clay

The safety assessment of tunnel stability is critical to tunnel construction and requires accurate analysis to obtain a reliable prediction. Strength anisotropy is an important aspect of clay behavior, but it is mostly neglected in practical stability analyses. In this study, the effects of undrained strength anisotropy and strength nonhomogeneity on the stability of unlined circular tunnels in clays are investigated. The static approach of lower-bound (LB) analysis using finite-element and second-order cone programming is employed to examine the aforementioned effects. The anisotropic shear strength of clay is modeled by employing an elliptical yield function under plane strain conditions. A complete set of dimensionless parameters covering the cover depth ratios of tunnels, normalized overburden pressure ratios, normalized strength gradient ratios of clays, and anisotropic strength ratios, are systematically investigated. The new LB solutions indicate that the stability load factor of the problem has a nonlinear relationship with the cover depth ratio and the anisotropic strength ratio, and there exists a linear relationship with the normalized overburden pressure and the normalized strength gradient. Their influence on the predicted failure mechanism is parametrically evaluated. A statistically approximate stability equation of unlined circular tunnels in anisotropic and non-homogeneous clay is proposed for the first time, which contains four new stability factors, namely, constant undrained strength, linearly increasing strength gradient, undrained strength anisotropy, and soil unit weight, and it can serve as a fast and accurate tool for predicting the undrained stability of this problem in practice.

Stability of active trapdoors in axisymmetry

Trapdoor stability has been widely studied by many researchers in the field of tunneling engineering. A general question being frequently asked is that why most sinkholes have a near-perfect circular shape on the ground surface. This could be possibly explained by the current numerical study using finite element limit analysis under axisymmetric condition, where upper and lower bound solutions of active circular trapdoors are determined. The failure study of sinkholes and the associated failure mechanisms in this paper are for non-homogeneous clay with a linear increase of strength with depth under various cover depth ratios and dimensionless strength gradients. A design equation for predicting the stability solutions is also developed based on the novel three dimensional solutions using axisymmetry.

Lateral and Uplift Capacity of Pipeline Buried in Seabed of Homogeneous Clay

Buried offshore pipes are prone to upheaval and lateral buckling because of the high temperature and pressure of the materials being transported. An attempt has been made in the present study to evaluate uplift and lateral capacity of buried offshore pipes in a soft clay seabed using finite-element software. The numerical model used in the present study has been validated against results available in the literature. Finite-element analyses are carried out to study the upheaval and lateral buckling behavior of pipes for both the no-tension (NT) condition, i.e., when separation occurs between the pipe and soil, and the full-tension (FT) condition, i.e., when the soil beneath the pipe remains attached to the pipe. The variation of both uplift and lateral normalized capacity factors with soil cover depth ratio is presented for different combinations of soil strength and effective weight. Both uplift and lateral capacity factors have been found to increase and reach a constant peak value with increasing depth of soil cover. A transition from global and local failure mechanisms of a pipe is observed when the capacity factors attain their peak values at a limiting soil cover depth. The critical cases for the design of buried offshore pipe in homogeneous clay are established for both NT and FT conditions.