Non-dimensional Charts Research Articles

Seismic Bearing Capacity of a Footing on Sloping Frictional Soil

This study presents the analysis of surficial strip footing on sloping frictional ground for an easy estimation of its seismic bearing capacity (by means of a seismic slope coefficient) to be used in conjunction with any other analytical solution provided for the static case. The influence of the slope angle and height, proximity of the slope to the crest, and value of the pseudo-static seismic coefficient is presented. A parametric study performed for the range of these geometrical and geotechnical parameters is conducted by the finite element method, also presenting the analysis of failure modes. The results are summarized in the form of non-dimensional charts that could be easily used for the estimation of the seismic bearing capacity by practitioners. An example of the application of charts is presented. It can be concluded that there is no influence of the sloping ground when the distance of the footing is greater than four times the width. For the horizontal seismic coefficients greater than 0.3 g, the shallow foundations should not be placed near the slope.

Ultimate bearing capacity of strip footings on Hoek-Brown rock slopes – A stress characteristics solution

The present study addresses the ultimate bearing capacity of strip footings on rock slopes under seismic conditions. The stress characteristics method (SCM) is combined with the modified pseudo-dynamic (MPD) approach for the intended purpose. Unlike the solutions available in the literature, the generation of the stress characteristics network within the framework of the SCM automates the potential failure mechanism of the slope medium at the limiting state of collapse. The MPD approach enables the analysis to capture realistic earthquake inertia forces induced in the slope, considering the material damping properties of the slope. The non-linear nature of the rock mass strength is captured using the generalized Hoek-Brown failure criterion. The seismic ultimate bearing capacity of strip footings is reported as non-dimensional charts. Additionally, the impact of relevant dynamic characteristics of seismic waves and rock mass properties is thoroughly assessed by conducting a detailed parametric investigation. The results reveal a substantial reduction in the ultimate bearing capacity of footings resting on rock slopes under earthquake conditions. The efficacy of the proposed methodology is validated with the existing solutions reported by various researchers.

Seismic Bearing Capacity of Strip Footings Placed Adjacent to Rock Slopes

ABSTRACT The bearing capacity of strip footings placed adjacent to the rock slopes subjected to pseudo-static horizontal earthquake body forces has been investigated by using the upper bound (UB) finite element limit analysis (FELA) in combination with a mesh adaptive strategy. The generalized Hoek–Brown (GHB) failure criterion is applied to describe the strength properties of rock masses, which can be treated as its native form without the smoothing of the yield surface while employing the second-order cone and power cone programming to solve the optimization models. Based on the UB FELA method, the seismic bearing capacity factor is determined considering the effect of different governing parameters, namely the horizontal earthquake acceleration coefficient k h , the normalized slope height H/B, the rock strength ratio σ ci /γB, the geological strength index GSI and the material constant m i . For design purpose, a series of non-dimensional charts are provided, and typical failure mechanisms are also discussed in detail.

Seismic bearing capacity of a strip footing on rock media

The bearing capacity factors for a rough strip footing placed on rock media, which is subjected to pseudo-static horizontal earthquake body forces, have been determined using the lower bound finite element limit analysis in conjunction with the power cone programming (PCP). The rock mass is assumed to follow the generalized Hoek-Brown (GHB) yield criterion. No assumption needs to be made to smoothen the GHB yield criterion and the convergence is found to achieve quite rapidly while performing the optimization with the usage of the PCP. While incorporating the variation in horizontal earthquake acceleration coefficient (kh), the effect of changes in unit weight of rock mass (γ), ground surcharge pressure (q0) and the associated GHB material shear strength parameters (geological strength index (GSI), yield parameter (mi), uniaxial compressive strength (σci)) on the bearing capacity factors has been thoroughly assessed. Non-dimensional charts have been developed for design purpose. The accuracy of the present analysis has been duly checked by comparing the obtained results with the different solutions reported in the literature. The failure patterns have also been examined in detail.

Development of Non-dimensional Design Chart Incorporating the Effect of Raker Piles in Pile Groups Under Lateral Load

Development of Non-dimensional Design Chart Incorporating the Effect of Raker Piles in Pile Groups Under Lateral Load

Droplet breakup of a high-viscosity-ratio system in a nonuniform temperature field under laser irradiation

This study conducted experimental and simple numerical studies to investigate the effect of change in viscosity ratio on the dispersion progress in a two-phase immiscible fluid. The viscosity ratio of the fluid was successfully modified by supplying direct heat radiation from an infrared laser. In the experiment, polybutenes and polydimethylsiloxane silicone oils were used as the dispersed droplet and matrix phases, respectively, and the radiation from an infrared laser with an intensity ranging from 10.9 to 87.3 W/cm2 was applied. The results show that the selective radiation-heating method using different radiation absorption coefficients against the infrared laser wavelength caused significant deformation of the droplet phase, reaching even the breakup point of the droplet. We further performed a numerical simulation of three-dimensional thermal conduction, including radiation heating, to estimate the temperature changes in the droplet phase. The results show that the droplet size significantly affects the heat absorption and temperature distribution of the system. Finally, we discuss a suitable radiation intensity on a nondimensional chart using the modified viscosity ratio and critical capillary number.

A simplified model of layered soil for analyzing vertical vibration of loaded foundations

Numerous physical models using frequency-independent elements have been developed to reproduce impedance functions for the purposes of time-domain soil–foundation interaction analysis. Most of the models have been developed to simulate homogeneous soils. However, the physical models developed in past research for layered soils are mostly focused on surface foundations only. Accordingly, this study proposes a representative simplified model to simulate the three-dimensional layered soil for square foundations embedded in a non-uniform layer, overlying a uniform half-space, subjected to vertical forced vibrations. The non-uniform layer has shear-wave velocities linearly varying with depth. Non-dimensional charts are presented to determine the model parameters as per foundation embedment ratios, layer depth ratios, and shear-wave velocity ratios of layered soil. The capability of the proposed model is demonstrated through the analysis of frequency-response curves of the foundation to a constant-force type oscillator in the frequency domain and of the displacement history of the foundation to a non-periodic loading in the time domain. The proposed model is found to give results consistent with those obtained from a dynamic soil-structure interaction analysis program. The proposed model may be of practical value for analysis of dynamically loaded foundations.

Stress-dependent method for calculating the modulus improvement factor in geocell-reinforced soil layers

This paper presents an analytical method for determining the modulus improvement factor (MIF) in geocell-reinforced soil layers. Using a modified version of the hyperbolic soil model as a constitutive model, the method is developed based on the soil-reinforcement interaction relating nonlinear elastic soil behavior to the linear elastic response of the reinforcement. The proposed method, in an original way, explicitly takes into account the geometry of the geocell pocket, effects of soil and geocell-reinforcement stiffness, compaction-induced stresses, soil strength and strain compatibility. The method can be used both analytically and using simple and presented non-dimensional charts. Parametric analyses show that the reinforcement, soil relation and the stresses induced during the compaction procedure are the major factors influencing MIF. An evaluation using data from several laboratory, full-scale and field experiments in works is presented showing good predictive capability of proposed method. An application procedure for calculating MIF is presented.

Effect of Adjacent Axle Loads on Uplift of Rails on Geocell-Stone Column Improved Tensionless Foundation

Rails resting over tensionless or unilateral foundation (responds to compressive forces only) has an uplift tendency ahead and behind the applied load. The presence of train of loads on such foundations may result in greater upward deflection of the rail. The current study investigates this possibility for rails on geocell-stone column improved tensionless foundations. Lumped parameter modelling approach has been used to idealize the rail on reinforced foundation. Granular layer has been placed between two infinite beams, one representing the rail and other the geocell with infill soil, and modelled as Pasternak shear layer. Stone columns and soft foundation soil beneath the beams have been idealized by Winkler springs of different stiffnesses. Mathematical model in the form of governing differential equations has been developed with due consideration to damping in the system. Finite difference method in combination with Gauss–Seidel iterative scheme has been used to arrive at their solution based on employed loading and the boundary conditions. Effect of adjacent axle loads and inclusion of stone columns on the response of the rail has been investigated. Influence of variations in input parameters of soil-foundation system has been studied in detail and presented in the form of non-dimensional charts along with a sensitivity study.

Seismic loading on cantilever retaining walls: Full-scale dynamic analysis

The assessment of realistic seismic loading on cantilever retaining wall requires modeling of actual seismic events to act on an integral cantilever wall. In this sense, an analysis is carried out to simulate eight candidate earthquake time histories. Scaling effect on seismic motions is taken into consideration through a one-dimensional numerical calculation using SHAKE2000 software. Two-dimensional PLAXIS finite element analysis is carried out through a full-scale seismic analysis of a typical cantilever retaining wall. Results of the analysis quantified seismic earth pressure in terms of magnitude and point of application. These results are presented in a non-dimensional chart to be compared with up-to-date seismic loading propositions. In conclusion, a relationship is proposed to relate the horizontal seismic inertial coefficient with a representative lateral seismic active earth pressure coefficient.

Analysis and design of two layered flexible pavement systems: A new mechanistic approach

Analysis of two layered flexible pavements is considered as a significant aspect for design of low volume roads, which typically consist of a thick granular base course directly laid over subgrade with or without a thin asphalt-wearing course. Permanent deformation or rutting has been observed to be the major distress mode in thin surfaced or unsurfaced low volume roads. In the present study, a new formulation has been proposed to determine the surface and interface deflections for both single and standard axle dual wheel assembly for a two layered pavement system. The present formulation has been developed based on mechanistic approach and the solutions obtained from 3-dimensional finite element program, using ABAQUS taking into account the influence of rectangular tire imprint, modulus of granular base course, pavement thickness and ratio of modulus of pavement and subgrade. The effect of Poisson’s ratio of granular base and subgrade is observed to be very insignificant. For the estimation of surface and interface deflections, deflection factors have been generated in the form of non-dimensional charts as a function of ratio of modulus of pavement and subgrade, and ratio of pavement thickness and tire width.

Support pressure for stability of circular tunnels driven in granular soil under water table

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.

Nonlinear lateral stiffness and bearing capacity of suction caissons for offshore wind-turbines

The paper investigates the linear-elastic and nonlinear stiffnesses of a suction caisson used as monopod foundation for an Offshore Wind-Turbine (OWT). Starting from caissons at low working stresses, in which case the linear elastic theory provides an adequate engineering model for soil, analytical expressions for the elastic stiffness matrix of a flexible skirted foundation are proposed and validated. To account for the nonlinear foundation response, the paper proposes a simplified equivalent linear iterative approach where the effective foundation stiffness is expressed in terms of deformation amplitude. To this end, utilizing results from a 3D finite element parametric study, non-dimensional charts have been produced for caissons ranging from perfectly rigid to flexible with variable embedment ratios. To deal with uncertainty on the conditions at the soil-skirt interface, three idealized interface scenarios – “fully-bonded”, “tensionless”, “frictionless” – are implemented. Reduced values of foundation stiffness are computed for a frictionless contact. On the contrary, the impact of a “tensionless” interface, whilst trivial in elastic problems, is intensified with progressing soil inelasticity resulting in severely reduced stiffnesses and capacities. Moreover, with increasing relative skirt flexibility, the elastic stiffnesses of deep suction caissons tend to recede substantially, but the rate of stiffness degradation is fairly attenuated.

Soil–Structure Interaction of Plates on Earth Beds with Geosynthetic Inclusion

A simple model has been presented for the analysis of plates on earth beds with geosynthetic inclusions. Plates simulate the behavior of concrete slabs such as raft foundations, lock type structures, rigid pavements etc., resting on the viscous medium. The foundation soil has been represented by Kelvin–Voigt model. A layer of granular fill, represented by Pasternak model, has been placed on top of this foundation soil and is reinforced with geosynthetic layer. Hyperbolic constitutive relationship has been used to simulate the nonlinearity of foundation soil and the overlying granular soil. An elastic rough membrane sandwiched within the granular layer, on to which the plate is in direct contact, represented the geosynthetic layer. From basic mechanics principles, the mathematical model of the system has been derived and solution has been obtained employing relevant boundary conditions. System of simultaneous equations, so obtained, has been solved using lower–upper decomposition method. An iterative scheme has been adopted to determine the deflection of plate and the tension generated in geosynthetic layer. After validating the proposed model, response of soil–plate system has been studied under the influence of load intensity, flexural rigidity of plate, ultimate bearing resistance of poor subgrade and degree of consolidation. Non-dimensional charts depicting the influence of these parameters have been developed which can be used in the analysis of plates on reinforced earth beds.

A Simplified Method for Prediction of Ultimate Bearing Capacity of Eccentrically Loaded Foundation on Geogrid Reinforced Sand Bed

This study aimed to develop reduction factors for eccentrical ultimate bearing capacity of circular and square footings resting on geogrid-reinforced sand. The process has been simplified with presenting non-dimensional charts for the various load eccentricities, the number of reinforcement layers and footing shape, which can be used by practicing engineers directly. To establish and evaluate this approach a series experimental tests for circular and square shallow footings was considered. Regarding square footing, different ratios of load eccentricity were considered; one-way and two-way. The proposed approach for eccentrical loading in unreinforced and reinforced condition has been validated with Meyerhof’s Effective Width Concept, laboratory model tests and numerical reported data in the literature review. Also, this solution is verified using the results of field tests on actual full scale reinforced soil foundations to study scale effects. New method provides reasonable agreement of the ultimate bearing capacity. Also, the results of laboratory tests conducted by the authors show that the ultimate bearing capacity of circular footing decreases less with increment of load eccentricity in comparison with square footing in reinforced condition. Improvement Index investigated that contribution of reinforcement layers in enhancing the ultimate bearing capacity increases with the load eccentricity. This behaviour followed with the proposed model. Also, finite element method (FEM) in a three-dimensional space is performed for verifying the laboratory tests and studying the stress–strain behaviour of reinforcement layers.

Pseudo-dynamic analysis of seawall considering non-breaking wave force

This paper presents the stability determination of seawall, supporting submerged cohesion-less backfill under combined actions of earthquake and non-breaking wave forces. The pseudo-dynamic approach is adopted for the calculation of seawall stability using limit equilibrium method against sliding, overturning and bearing failure. Parametric study shows significant effects of B/H ratio, pore water pressure ratio, horizontal seismic acceleration coefficient, ratio of height of water on seaward side to the wall height, ratio of non-breaking wave height to height of water on seaward side, wall friction angle, ratio of height of water on landward side to the wall height on stability of seawall at both restrained and free water cases, against all failure modes. Present result is compared with results available in literature. The results are presented in non-dimensional forms and design charts are provided to calculate factor of safety for design of stability of seawall against different failures under earthquake forces combined with non-breaking wave forces.

Numerical investigation on vibration isolation by softer in-filled trench barriers

This paper deals with a 2-D finite element study in PLAXIS 2D on isolation of steady-state surface vibrations by softer backfilled trenches in an elastic, isotropic, and homogeneous half-space. Effects of barrier geometric features and infill material characteristics on reducing vertical and horizontal components of surface displacements are investigated. This study adopts a non-dimensional approach where the geometric parameters are normalized against the Rayleigh wavelength of vibration in half-space and backfill shear wave velocity is expressed as a ratio of that of parent soil. Softer barriers of shear wave velocity ratios less than unity are considered as they are found significantly effective than stiffer barriers. Effects of the parameters participating on wave isolation are extensively discussed and some guidelines are framed regarding their optimal selection. Non-dimensional charts are developed which would provide a sound basis for designing such barriers in actual engineering practice. The design charts are validated with some documented results and close agreement is obtained.

Nonlinear Response of Lateral Piles with Compatible Cap Stiffness and p-Multiplier

AbstractResponse of lateral pile groups is modeled using the more accurate (than any other numerical modeling) p−y curves–based load transfer model. It is essentially underpinned by limiting force per unit length pmpu, modulus of subgrade reaction pmk, and p-multiplier pm (to cater for pile-pile interaction, pm=1 for single piles). With the model, new closed-form solutions are developed incorporating the cap-rotational stiffness kr. The solutions are presented in nondimensional charts for free-head (kr=0) through fixed-head (kr>10 times the pile bending stiffness). The study reveals that the existing pm (bearing no link to the stiffness kr) is inconsistent with pm=0.25 for capped piles (at limiting state of elastic solutions). This casts doubt about the accuracy of available solutions, and a compatible stiffness kr and pm is required. The compatible normalized stiffness knr is equal to 0.275–0.333 (n=0.7) and 0.333–0.564 (n=1.7) for the associated pm at the design level of (ground-level) bending moment sp...

Seismic Bearing Capacity of Strip Footings Located Close to the Crest of Geosynthetic Reinforced Soil Structures

This paper investigates the performance of geo-reinforced soil structures subjected to loading applied to strip footings positioned close to a slope crest. The kinematic theorem of limit analysis, which is based on the upper bound theory of plasticity, is applied for evaluating the ultimate bearing capacity within the framework of pseudo-static approach to account for earthquake effects. The mechanism considered in this analysis is a logarithmic spiral failure surface, which is assumed to start at the edge of the loaded area far from the slope, consistent with the observed failure mechanisms shown in the experimental tests reported in the literature. A parametric study is then carried out to investigate the influence of various parameters including the geosynthetic configuration, backfill soil friction angle, footing distances from the crest of the slope, slope angles and horizontal seismic coefficients. Attention is paid to the failure mechanism because its maximum depth is the depth at least to which the reinforcements must be placed. Results of the analyses are presented in the form of non-dimensional design charts for practical use. Finally, a simple procedure based on the assessment of earthquake-induced permanent displacements is shown for the design of footing resting on reinforced slopes subjected to earthquake.

Infinite beams on stone column reinforced tensionless earth beds under moving loads

In the present study, an analysis of a rail, idealized as an infinite beam, resting on a granular bed-stone column reinforced earth bed has been carried out under a load moving with constant velocity. The granular fill layer just below the rail has been modeled as the Pasternak shear layer, while stone columns as non-linear Winkler springs and foundation soil as non-linear Kelvin–Voigt body. As the load moves on rail, the rail tends to separate from the ground. This separation has been modeled (tensionless foundation) by means of appropriate deflection and soil reaction conditions. Governing differential equations of the soil–foundation system have been obtained and have been solved with proper boundary and continuity conditions. The Gauss–Siedel iterative method has been employed to obtain the solution of finite difference form of these equations. Detailed parametric study revealed that the velocity of load, the damping of the soil–foundation system, and the ultimate resistance of soft soil and granular fill layer has the least influence on the response of system. However, the magnitude of load, ultimate resistance of stone columns, diameter and spacing of stone columns, and degree of consolidation and relative stiffness of stone columns with respect to the surrounding soil have been found to significantly affect the response of the system. The influence of all these parameters has been quantified and presented in the form of readily usable non-dimensional charts.