Research

Stability of rock tunnels in anisotropic rock mass

In this study, a new conic optimization technique, hybrid second-order exponential cone programming (HSOECP) in the framework of lower bound finite-element limit analysis, has been developed. This framework combines the specific features of a second-order cone and an exponential cone to capture the nonlinearity of the modified Hoek–Brown criterion developed for anisotropic rock masses recently. In the modified Hoek–Brown criterion, both inherent strength anisotropy owing to the variation of the uniaxial compressive strength of intact rock (σcβ) and structural anisotropy based on the anisotropic rock mass rating (ARMR) classification system were considered. The proposed methodology has been applied to study the stability of unlined circular tunnels in anisotropic rock masses. The maximum ground surcharge (σs) for which the tunnel is at its failure state has been obtained and presented in nondimensional form considering the influence of σcβ, ARMR, material constants (mi), inherent strength anisotropy parameter (kβ), unit weight (γ), and tunnel cover depth (C) and diameter (D). The computations were carried out using self-developed codes in MATLAB 2022b version. For C/D = 1 with mi = 5 and [(σcβ)/(γD)] = 50, the value of [(σs)/(γD)] with ARMR = 40 and kβ = 0.2 is approximately 283 times lower than that for ARMR = 100 and kβ = 1. Moreover, at ARMR = 40, the value of [(σs)/(γD)] for kβ = 0.2 is 18.33 times lower than that for kβ = 1. Increasing the tunnel cover depth significantly enhances tunnel stability, with a higher rate of improvement for lower C/D values. The influence of inherent strength anisotropy is found to be lower compared to the structural anisotropy of rock mass on the stability of unlined tunnels. 

Sahu, S., Sahoo, J.P., and Tiwari, G. (2025). A Hybrid Second-Order Exponential Cone Programming–Based Lower Bound Finite-Element Limit Analysis Framework for Rock Tunnels in Anisotropic Rock Masses. International Journal of Geomechanics. 25(8). https://doi.org/10.1061/IJGNAI.GMENG-10937 

Seismic stability of tunnels in soils

The space–time dependent horizontal and vertical seismic accelerations in a soil medium owing to the inhomogeneity in the shear and primary wave propagation velocities were analytically derived, satisfying the boundary conditions on the ground surface and the base. The developed analytical formulations were applied to study the influence of wave velocity heterogeneity on the support pressure required for the circular tunnel stability placed in granular soils using the stress-based limit analysis in conjunction with finite elements. The support pressure was determined as the maximum normal stress exerted by the surrounding earth at its ultimate failure on the tunnel boundary. Further, the effect of frequency of seismic waves on the seismic accelerations, magnitude of tunnel support pressure and the variation of normal stress around the tunnel periphery has been presented in detail. The support pressure was found to be higher considering the heterogeneous wave velocity than the uniform one. A lower dimensionless frequency resulted in higher support pressures for a lower wave velocity ratio and a higher power parameter of the power law used to model the wave velocity profile. Otherwise, for a higher wave velocity ratio, the effect of the power parameter diminishes, and the support pressure is higher for a higher dimensionless frequency.

Stability of tunnels in anisotropic saturated clay and sand below water bodies

In this paper, the internal pressure required to be offered by a support system to support the periphery of circular tunnels excavated in granular soils in the presence of groundwater seepage towards the tunnel has been computed. The optimal value of support pressure is computed with the application of finite element limit analysis based on lower bound theorem of plasticity and second order cone programming. The seepage forces generated due to flow of ground water towards tunnel periphery are computed from the distribution of total head in the ground by solving the two-dimensional flow equation under steady state seepage condition. The forces acting on the support system due to effective overburden pressure and seepage are incorporated as body forces in the analysis. The solutions are presented in the form of non-dimensional charts which will be used in practice to estimate the required support pressure in terms of soil properties, elevation of groundwater table, and diameter and cover of tunnel. For the tunnel driven under water table, a significant increase in the magnitude of required support pressure has been observed as compared to that excavated in dry soil from the solutions obtained in the present analysis.

Stability of foundations and plate anchors in unsaturated clays

Numerous studies have been reported in literature for plate anchors in saturated or dry clays. However, in practical scenario the soil overlying the anchor plate in most of the cases is in unsaturated state, and even then, no study seems to be available for anchors in unsaturated soil. The uplift capacity depends on the resistance of soil overlying the anchor plate, which is in turn affected by the shear strength of soil and varies with variation in the matric suction owing to changes in surface flux conditions and position of the water table. Hence, it has been planned to study the uplift capacity of horizontal strip plate anchors buried in unsaturated clay in this paper. The stress-based limit analysis with the help of finite elements and second-order cone programming has been used for performing the analysis considering the variation of matric suction with depth above the water table under various surface flow conditions (evaporation, no flow and infiltration). Unified effective stress approach-based modified Mohr–Coulomb yield criterion was used to include the influence of stress due to matric suction to the ultimate failure state. The uplift capacity was expressed in terms of a non-dimensional uplift capacity factor, which has been found to be dependent on the embedment depth-to-width ratio of anchor, shear strength parameters of soil, water table position, various flow conditions and their flow rate. The effect of other parameters like air-entry pressure and pore-size distribution parameters, degree of saturation, specific gravity of soil solids, and soil–anchor interface roughness has also been examined and was found to be insignificant. The solutions were presented for an immediate breakaway condition, i.e., considering that the contact between anchor and underlying soil mass is separated at ultimate failure.

Cyclic loading response of subgrade soil and mechanistic approach for two-layered flexible pavements

Subgrades that are constructed from fine-grained cohesive soils undergo large settlements; therefore, the study of their deformation behavior is important to avoid early deterioration in the traffic infrastructure. In this study, the deformation behavior of two different types of cohesive subgrade soils at different compaction states has been addressed that considered the effect of influencing factors, such as water content, deviatoric stress, and confining pressure (σ3). The results from the unconsolidated undrained cyclic triaxial tests show that the deformation behavior of soil is highly influenced by the level of applied deviatoric stresses and moisture content on the wet side of optimum (WS) and is slightly affected by σ3 and moisture content on the dry side of optimum (DS). The elastic strain (ɛe) component showed a decreasing trend with an increase in the number of load cycles (N) and then attained a steady value toward a higher N; however, the plastic strain (ɛp) component continuously increased for a given magnitude of applied cyclic deviatoric stresses (σd,c). From the test results, logarithmic strain models were proposed to predict the long-term total (ɛt) strain and ɛp that developed in cohesive subgrade soils, which were subjected to various combinations of variations in moisture content and stresses. The proposed model has been compared with the existing model and shows better prediction ability with a coefficient of correlation (R2) of >95% in most cases.

Singh, A.K., and Sahoo, J.P. (2022). Undrained Cyclic Loading Response of Subgrade Soil Subjected to Varying Moisture Content and Stress Level. International Journal of Geomechanics. 23(2). https://doi.org/10.1061/IJGNAI.GMENG-6536 

Stability of nailed vertical slopes

A vertical cut reinforced with inclined nails subjected to seismic loading was analyzed using the modified pseudodynamic approach, assuming a log-spiral failure surface. A novel calculus-based methodology has been devised to obtain the maximum individual nail force demands and locus of maximum tension, which directly affect nail length in the passive and active zone. The influence of depth of cut to wavelength ratio, nail declination, surcharge, wave amplitudes, soil’s shear strength parameters, and damping ratio were reported. The maximum nail forces required to restrict the failure of a cut have been observed to increase nonlinearly with the depth of nails. The lower angle of shearing resistance, stronger horizontal base acceleration, and closeness of frequency level to fundamental shear wave frequency claimed additional nail lengths in both active and passive zones highlighting their significance in the stability of nailed cut. Practicing engineers can use proposed expressions by employing inexpensive spreadsheet software rather than costly finite element or slices-based commercial software.

Kokane, A.K., Sawant, V.A., and Sahoo, J.P. (2021). Nail Forces and Locus of Maximum Tension of Nailed Cut Subjected to Seismic Excitations: A Calculus Approach with Log-Spiral Failure Surface. International Journal of Geomechanics. 21(11). https://doi.org/10.1061/(ASCE)GM.1943-5622.0002213 

Kinematic limit analysis formulations for geotechnical structures

The reliable estimation of uplift capacity of plate anchors becomes necessary for the safe and cost-effective design of various structures against uplift loads. Uplift capacity studies have traditionally been conducted using semi-analytical methods based on plasticity theories, and the previous research has primarily focused on homogeneous soils and a linear failure criterion. Soils, in general, are nonhomogeneous and exhibit nonlinear shear strength behavior. The present study proposes a novel kinematic horizontal slice method within the context of plasticity theory to determine the vertical uplift capacity of various shapes of plate anchors in nonhomogeneous soils using the nonlinear power-law failure criterion. A linear variation of parameters such as initial cohesion, tensile strength, nonlinear coefficient, and unit weight with depth below the ground surface was considered. The effect of nonassociativity for a general nonlinear material has been examined. A detailed parametric study was conducted to explore the effects of various parameters on the uplift capacity of anchors. The results revealed that increasing initial cohesion while decreasing tensile strength, nonlinear coefficient, and unit weight with depth below the ground surface increases anchor uplift capacity, especially for three-dimensional cases. Anchor failure patterns were also investigated for a few parameter combinations. The results of this study were found to be more consistent with those developed in the literature for some specific cases.

Ganesh, R., and Sahoo, J.P. (2023). Kinematic horizontal slice method for uplift capacity analysis of plate anchors in nonhomogeneous soils with a nonlinear failure criterion. Computers and Geotechnics. 159. https://doi.org/10.1016/j.compgeo.2023.105407