Upper bound solutions of bearing capacity of strip footing by pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis of seismic bearing capacity of a strip footing using upper bound limit analysis. However, in the literature, the pseudo-static approach was frequently used by several researchers to compute the seismic bearing capacity factor theoretically, where the real dynamic nature of the earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of bearing capacity factor N _γE are determined for different magnitudes of soil friction angle, soil amplification and seismic acceleration coefficients both in the horizontal and vertical directions. The results obtained from the present study are shown both graphically as well as in the tabular form. It is observed that the bearing capacity factor N _γE decreases significantly with the increase in seismic accelerations and amplification. The results are thoroughly compared with the existing values in the literature and the significance of the present methodology for designing the shallow footing is discussed.     

Bearing capacity of a strip foundation on a sand layer overlying a smooth rigid stratum

The effect of a smooth rigid stratum, located beneath a dense sand layer, on the bearing capacity and settlement of surface and shallow strip footings is investigated using an advanced experimental model. A theoretical analysis is presented for the bearing capacity of surface footings. The results indicate that the bearing capacity reaches a minimum value at a specific sand-layer thickness. Any increase in the layer thickness above this value causes an increase in the bearing capacity up to that corresponding to a continuous media.Notation H= thickness of the sand layer - B= foundation width - N _q and N = bearing capacity factors for a semi-infinite layer - N _qs and N _s= bearing capacity factors for a finite layer - H _o /B= limiting depth - D _r= relative density - = angle of soil internal friction - M= model width - D= depth of surcharge - q= bearing stress, pressure applied on the footing - q _u= bearing capacity - = unit weight of sand     

Reliability analysis of seismic bearing capacity of strip footing by stochastic slip lines method

In this research, the reliability analysis of seismic ultimate bearing capacity of strip footing is assessed with implementing slip lines method coupled with random field theory. The probability density functions of seismic and static bearing capacities which are log-normal and nearly normal distribution respectively are compared to each other. The predicted Probability Density Function (PDF) of the seismic bearing capacity by slip line method is verified, with those of the Terzaghi equation and Monte Carlo simulation (MCs). For uncertainties analysis by Terzaghi equation the N_c, N_q and N_γ are assessed stochastically.     

A Simple Limit Equilibrium Approach for Calculation of Ultimate Bearing Capacity of Shallow Foundations on Two-Layered Granular Soils

The bearing capacity of shallow foundations in a non-homogeneous soil profile has been a challenging task in geotechnical engineering. In this paper, a limit equilibrium method is used for calculating bearing capacity factors of shallow foundations constructed on a two-layered granular soil profile. The main objective has been to determine the ultimate bearing capacity computed from equivalent bearing capacity factors N_q and N_γ and comparing that with numerical analysis using finite element methods. It will be shown that the data obtained form the developed method are well comparable with those obtained from FE approach, specially when the difference between shear strength parameters of layers is low which is a practical case for sedimentary soil profiles and also for artificially compacted soils. A computer program has been developed to investigate the influence of various parameters on bearing capacity factors.     

Influence of random heterogeneity of the friction angle on bearing capacity factor Nγ

ABSTRACT

Probabilistic methods in geotechnical engineering have received a lot of attention during the last decade and different methodologies are used to capture the inherent variability of soil in different geotechnical engineering problems. In this paper, numerical simulations are conducted to obtain the bearing capacity factor, N_γ, for a purely frictional heterogenous soil where the friction angle is modelled as randomly distributed throughout the domain and the effect of its spatial variability on N_γ is investigated. A finite element method, based on the upper bound limit analysis was combined with random field theory and linear programming to develop a probabilistic analysis. Monte Carlo simulations were performed and the effect of the variability of the friction angle defined by statistical parameters on the bearing capacity factor was investigated. Results show that the mean bearing capacity factor N_γ of a footing on a spatially variable cohesionless soil is generally higher than the deterministic N_γ obtained from a constant mean value. Increasing the heterogeneity of the friction angle by an increase in the coefficient of variation generally increases this deviation. This can be explained by the nonlinearity of the relationship between N_γ and the friction angle.     

Seismic Bearing Capacity of Shallow Strip Footing with Coulomb Failure Mechanism using Limit Equilibrium Method

In this paper, an effort is made to evaluate the seismic bearing capacity of shallow strip footing resting on c–ф soil. The formulation is developed to get a single coefficient of bearing capacity for simultaneous resistance of weight, surcharge and cohesion. Limit equilibrium method in Pseudo-static approach with Coulomb mechanism is applied here to evaluate the seismic bearing capacity. The seismic bearing capacity of footing (q_uE) is expressed in terms of single coefficient N_γE. The effect of various parameters viz. angle of internal friction of soil (ф), angle of wall friction (δ), cohesion (c), ratio of depth to width of footing (d_f/B₀), seismic acceleration (k_h, k_v) are studied on the variation of seismic bearing capacity co-efficients.     

Variations in shear wave velocity and soil site class in Kolkata city using regression and sensitivity analysis

The detrimental effects of an earthquake are strongly influenced by the response of soils subjected to dynamic loading. The behavior of soils under dynamic loading is governed by the dynamic soil properties such as shear wave velocity, damping characteristics and shear modulus. Worldwide, it is a common practice to obtain shear wave velocity (V _s in m/s) using the correlation with field standard penetration test (SPT) N values in the absence of sophisticated dynamic field test data. In this paper, a similar but modified advanced approach has been proposed for a major metro city of eastern India, i.e., Kolkata city (latitudes 22°20′N–23°00′N and longitudes 88°04′E–88°33′E), to obtain shear wave velocity profile and soil site classification using regression and sensitivity analyses. Extensive geotechnical borehole data from 434 boreholes located across 75 sites in the city area of 185 km² and laboratory test data providing information on the thickness of subsoil strata, SPT N values, consistency indices and percentage of fines are collected and analyzed thoroughly. A correlation between shear wave velocity (V _s) and SPT N value for various soil profiles of Kolkata city has been established by using power model of nonlinear regression analysis and compared with existing correlations for other Indian cities. The present correlations, having regression coefficients (R ²) in excess of 0.96, indicated good prediction capability. Sensitivity analysis predicts that significant influence of soil type exists in determining V _s values, for example, typical silty sand shows 30.4 % increase in magnitude of V _s as compared to silt of Kolkata city. Moreover, the soil site classification shows Class D and Class E category of soil that exists typically in Kolkata city as per NEHRP (Recommended provisions for seismic regulations for new buildings and other structures—Part 1: Provisions. Prepared by the Building Seismic Safety Council for the Federal Emergency Management Agency (Report FEMA 450), Washington, DC, 2003) guidelines and thereby highlighting the seismic vulnerability of the city. The results presented in this study can be utilized for seismic microzonation, ground response analysis and hazard assessment for Kolkata city.

     

Failure modes and bearing capacity of strip footings on soft ground reinforced by floating stone columns

This study evaluates the failure modes and the bearing capacity of soft ground reinforced by a group of floating stone columns. A finite difference method was adopted to analyze the performance of reinforced ground under strip footings subjected to a vertical load. The investigation was carried out by varying the aspect ratio of the reinforced zone, the area replacement ratio, and the surface surcharge. General shear failure of the reinforced ground was investigated numerically without the surcharge. The results show the existence of an effective length of the columns for the bearing capacity factors N _c and N _γ. When certain surcharge was applied, the failure mode of the reinforced ground changed from the general shear failure to the block failure. The aspect ratio of the reinforced zone and the area replacement ratio also contributed to this failure mode transition. A counterintuitive trend of the bearing capacity factor N _q can be justified with a shift in the critical failure mode. An upper-bound limit method based on the general shear failure mode was presented, and the results agree well with those of the previous studies of reinforced ground. Equivalent properties based on the area-weighted average of the stone columns and clay parameters were used to convert the individual column model to an equivalent area model. The numerical model produced reasonable equivalent properties. Finally, a theoretical method based on the comparison of the analytical equations for different failure modes was developed for engineering design. Good agreement was found between the theoretical and numerical results for the critical failure mode and its corresponding bearing capacity factors.     

Bearing capacity of foundations on rock mass using the method of characteristics

The method of stress characteristics has been used for computing the ultimate bearing capacity of strip and circular footings placed on rock mass. The modified Hoek‐and‐Brown failure criterion has been used. Both smooth and rough footing‐rock interfaces have been modeled. The bearing capacity has been expressed in terms of nondimensional factors N_σ0 and N_σ, corresponding to rock mass with (1) γ = 0 and (2) γ ≠ 0, respectively. The numerical results have been presented as a function of different input parameters needed to define the Hoek‐and‐Brown criterion. Slip line patterns and the pressure distribution along the footing base have also been examined. The results are found to compare generally well with the reported solutions.     

Bearing capacity of strip foundations reinforced with geogrid sheets by using upper bound finite‐element limit analysis

By using the upper bound finite‐elements limit analysis, with an inclusion of single and two horizontal layers of reinforcements, the ultimate bearing capacity has been computed for a rigid strip footing placed over (i) fully granular, (ii) cohesive‐frictional, and (iii) fully cohesive soils. It is assumed that (i) the reinforcements are structurally strong so that no axial tension failure can occur, (ii) the reinforcement sheets have negligible resistance to bending, and (iii) the shear failure can take place between the reinforcement and soil mass. It is expected that the different approximations on which the analysis has been based would generally remain applicable for reinforcements in the form of geogrid sheets. A method has been proposed to incorporate the effect of the reinforcement in the analysis. The efficiency factors, η_c and η_γ, to be multiplied with N_c and N_γ , for finding the bearing capacity of reinforced foundations, have been established. The results have been obtained (i) for different values of ? in case of fully granular and cohesive‐frictional soils, and (ii) for different rates at which the cohesion increases with depth for a fully cohesive soil. The optimum positions of the reinforcements' layers have also been determined. The effect of the reinforcements' length on the results has also been analyzed. As compared to cohesive soils, the granular soils, especially with higher values of ?, cause a much greater increase in the bearing capacity. The results compare reasonably well with the available theoretical and experimental data from literature. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical analysis under seismic loads of soils improvement with floating stone columns

Geotechnical Engineering has developed many methods for soil improvement so far. One of these methods is the stone column method. The structure of a stone column generally refers to partial change of suitable subsurface ground through a vertical column, poor stone layers which are completely pressed. In general terms, to improve bearing capacity of problematic soft and loose soil is implemented for the resolution of many problems such as consolidation and grounding problems, to ensure filling and splitting slope stability and liquefaction that results from a dynamic load such as earthquake. In this study, stone columns method is preferred as an improvement method, and especially load transfer mechanisms and bearing capacity of floating stone column are focused. The soil model, 32 m in width and 8 m in depth, used in this study is made through Plaxis 2D finite element program. The clay having 5° internal friction angle with different cohesion coefficients (c 10, c 15, c 20 kN/m²) are used in models. In addition, stone columns used for soil improvement are modeled at different internal friction angles (? 35°, ? 40°, ? 45°) and in different s/D ranges (s/D 2, s/D 3), stone column depths (B, 2B, 3B) and diameters (D 600 mm, D 800 mm, D 1000 mm). In the study, maximum acceleration (a _max = 1.785 m/s²) was used in order to determine the seismic coefficient used. In these soil models, as maximum acceleration, maximum east–west directional acceleration value of Van Muradiye earthquake that took place in October 23, 2011 was used. As a result, it was determined that the stone column increased the bearing capacity of the soil. In addition, it is observed that the bearing capacity of soft clay soil which has been improved through stone column with both static and earthquake load effect increases as a result of increase in the diameter and depth of the stone column and decreases as a result of the increase in the ranges of stone column. In the conducted study, the bearing capacity of the soil models, which were improved with stone column without earthquake force effect, was calculated as 1.01–3.5 times more on the average, compared to the bearing capacity of the soil models without stone column. On the other hand, the bearing capacity of the soil models with stone columns, which are under the effect of earthquake force, was calculated as 1.02–3.7 times more compared to the bearing capacity of the soil models without stone column.     

Bearing capacity of foundations on slopes

By applying the lower bound finite element limit analysis in conjunction with non-linear optimisation, the bearing capacity factors, N_c, N_q and N_γ, due to the components of cohesion, surcharge and unit weight, respectively, have been estimated for a horizontal strip footing placed along a sloping ground surface. The variation of N_c, N_q and N_γ with changes in slope angle (β) for different soil friction angle (φ) have been computed for smooth as well as rough strip footings. The analysis reveals that along a sloping ground surface, in addition to N_γ, the factors N_c and N_q also vary considerably with changes in footing roughness. Compared to the smooth footing, the extent of the plastic zone around the footing becomes greater for the rough footing. The results obtained from the analysis are found to compare well with those previously reported in literature.     

Bearing capacity of strip and circular footings in sand using finite elements

Design of shallow foundations relies on bearing capacity values calculated using procedures that are based in part on solutions obtained using the method of characteristics, which assumes a soil following an associated flow rule. In this paper, we use the finite element method to determine the vertical bearing capacity of strip and circular footings resting on a sand layer. Analyses were performed using an elastic–perfectly plastic Mohr–Coulomb constitutive model. To investigate the effect of dilatancy angle on the footing bearing capacity, two series of analyses were performed, one using an associated flow rule and one using a non-associated flow rule. The study focuses on the values of the bearing capacity factors N_q and N_γ and of the shape factors s_q and s_γ for circular footings. Relationships for these factors that are valid for realistic pairs of friction angle and dilatancy angle values are also proposed.     

Seismic hazard assessment in Jordan and its vicinity

The earthquake hazard in Jordan and its vicinity is assessed on the basis of probabilistic methods. For this purpose, an updated earthquake catalog is compiled which covers the period between AD 1–1989. The earthquakes lie between latitudes 27.0°-35.5° N and longitudes 32.0°-39.0° E. Thirteen seismic zones are defined on a regional seismic and tectonic map presented for the area. Point-source and line-source models are used. The seismic hazard parameters, namely, theb-parameter (of the Gutenberg-Richter relation),m ₁ (the upper bound magnitude), and ₄ (the annual rate of occurrence of earthquakes with local magnitudeM _L 4.0) are calculated for each zone. The results of the seismic hazard assessment are displayed as iso-acceleration contours expected to be exceeded during typical economic life times of structures, i.e. 50 and 100 years. For each model, two seismic hazard maps are derived. In order to determine the importance of the South-eastern Mediterranean zone and the north part of the Red Sea zone from a seismic hazard point of view for Jordan, one seismic hazard map which corresponds to 50 years' economic life for every model, excluding the seismicity of these zones, is derived.     

Computation of the seismic stability of rock wedges

Summary Newmark's concept of computing the permanent displacement under seismic loads has been combined with the conventional limit equilibrium analysis to compute the displacements of a rock wedge. The rock wedge formed by the intersecting planes may or may not have a tension crack in the upper slope surface. As the static analysis of a rock wedge is available from the literature, only the seismic problem is treated theoretically in more details.A computer program has been developed to compute the displacements from the digitised input data of the acceleration-time-history. The program can take into account the water pressure on the intersecting planes and on the planes of the tension crack. The effect of rock anchors if present is also taken care of in addition to static surcharge loads. The program calculates the conventional static factor of safety, remaining resistance against sliding, the critical acceleration, exciting force, relative velocity with time and the cumulative displacements.Two model examples are presented: one with simple sinusoidal acceleration and the other one with actual earthquake data considering the different systems of forces acting on the wedge. The results are critically discussed with respect to the different parameters e. g. anchor forces, water pressure and cohesion influencing the magnitude of displacements under seismic loads. It is shown that the critical acceleration is a better index for the seismic stability than the conventional factor of safety.The critical acceleration presented in this paper serves as a very handy tool for a site engineer to get the first hand information about the stability of the wedge for a given acceleration-time-history without going into the details of dynamic analysis.Notations A, B Inclined intersecting planes - C, D Geometric points on the intersection ofA andB - a _cr Critical acceleration - a _h Horizontal acceleration - a _v Vertical acceleration - a _r Relative acceleration of the wedge - DF Driving force - DF _dyn Dynamic driving force - DF _st Static driving force - FS Factor of safety - g Acceleration due to gravity - m Mass of the wedge - RF Resisting force - RF _dyn Dynamic resisting force - RF _st Static resisting force - RS Remaining resisting force against sliding - RS _dyn Total seismic induced force - RS _st Remaining static resisting force against sliding - s _r Cumulative relative displacement of the wedge - TRS Total remaining resisting force against sliding - v _r Relative velocity of the wedge - W Weight of the wedge - W _A ,W _B Weight of the wedge in the planeA andB - Dip of line of intersection of the planesA andB - Average friction angle - _A , _B Friction angle of planeA andB - I, II, III, IV Points in the curve shown in Fig. 6     

Effects of ageing and overconsolidation on the elastic stiffness of a remoulded clay

Summary Results of resonant column tests were used to determine values of low amplitude shear modulus (G ₀) of a remoulded kaolinite clay for different durations of ageing and for different values of consolidation stress (₀) and overconsolidation ratio (OCR). It was found that after completion of primary consolidation the values of G ₀ increased linearly with the logarithm of time and after a week of confinement the value of normalized rate of secondary increase of shear modulus (N _G ) could be reliably estimated. Values of N _G were found to derease linearly with the logarithm of OCR and with the logarithm of ageing duration. This similarity of behaviour provided a basis for establishing an equivalency between age and equivalent overconsolidation ratio (OCR)_eq. The effects of ₀ and OCR on the value of G ₀ were also established in a functional form that indicated a stronger influence compared to that predicted by the Hardin Equation.     

Seismic precursors to a 2017 Nuugaatsiaq,Greenland, earthquake–landslide–tsunami event

High-frequency (5–20 Hz) seismic signals precursory to and embedded within the June 17, 2017 M_L?=?4 earthquake–landslide event are analyzed. This event in western Greenland generated a tsunami in Karrat fjord inundating Nuugaatsiaq village 32 km distant. Spectrogram and wavelet analyses of seismic data from the Greenland Ice Sheet Monitoring Network (GLISN) corroborate observations of seismic precursors at Nuugaatsiaq reported by Poli (Geophys Res Lett 44:8832–8836, 2017) and Caplan-Auerbach (in: AGU fall meeting abstracts, 2017) and reveal additional high-frequency arrivals being generated after the apparent initiation of fault rupture. New observations of seismic precursors 181 km from the Event at Upernavik, Greenland are correlated with those seen at Nuugaatsiaq. Wavelet analysis presents?>?100 significant energy peaks accelerating up to and into the earthquake–landslide event. The precursor events show a distinct, power law distribution, characterized by b values of ~?2.4. Results are compared and contrasted with small precursors observed in the studies of a natural chalk cliff landslide at Mesnil-Val, Haute Normandie, France. The earthquake–landslide appears to have been initiated by seismic precursors located at the fault scarp, leading to a small seismic foreshock and small landslide initiation, followed by a larger earthquake at the fault scarp, precipitating the primary landslide into the Karrat Fjord, which caused the subsequent tsunami.

     

Shear wave velocity and attenuation structure for the shallow crust of the southern Korean peninsula from short period Rayleigh waves

We analyzed the short period Rayleigh waves from the first crustal-scale seismic refraction experiment in the Korean peninsula, KCRUST2002, to determine the shear wave velocity and attenuation structure of the uppermost 1 km of the crust in different tectonic zones of the Korean peninsula and to examine if this can be related to the surface geology of the study area. The experiment was conducted with two large explosive sources along a 300-km long profile in 2002. The seismic traces, recorded on 170 vertical-component, 2-Hz portable seismometers, show distinct Rayleigh waves in the period range between 0.2 s and 1.2 s, which are easily recognizable up to 30–60 km from the sources. The seismic profiles, which traverse three tectonic regions (Gyeonggi massif, Okcheon fold belt and Yeongnam massif), were divided into five subsections based on tectonic boundaries as well as lithology. Group and phase velocities for the five subsections obtained by a continuous wavelet transform method and a slant stack method, respectively, were inverted for the shear wave models. We obtained shear wave velocity models up to a depth of 1.0 km. Overall, the shear wave velocity of the Okcheon fold belt is lower than that of the Gyeonggi and Yeongnam massifs by  0.4 km/s in the shallowmost 0.2 km and by 0.2 km/s at depths below 0.2 km. Attenuation coefficients, determined from the decay of the fundamental mode Rayleigh waves, were used to obtain the shear wave attenuation structures for three subsections (one for each of the three different tectonic regions). We obtained an average value of Q_β^− 1 in the upper 0.5 km for each subsection. Q_β^− 1 for the Okcheon fold belt ( 0.026) is approximately three times larger than Q_β^− 1 for the massif areas ( 0.008). The low shear wave velocity in the Okcheon fold belt is consistent with the high attenuation in this region.