Article

# The Ultimate Bearing Capacity of Foudations

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## Abstract

Synopsis In the first part of the article a theory of bearing capacity is developed, on the basis of plastic theory, by extending the previous analysis for surface footings to shallow and deep foundations in a uniform cohesive material with fntemal friction. The theoretical results are represented by bearing capacity factors in terms of the mechanical properties of the soil, and the physical characteristics of the foundation. The base resistance of foundations in purely cohesive material is found to increase only slightly with foundation depth; for deep foundations the skin friction is, therefore, large compared with the base resistance. In cohesionless material, however, the base resistance increases rapidly with foundation depth and depends to a considerable extent on the earth pressure coefficient on the shaft; for deep foundations the base resistance is the predominant feature and the shin friction is relatively small. In the second part of the article the main results of laboratory and field loading tests on buried and driven foundations are analysed and compared with the theoretical estimates. The observed base resistance of foundations in clay is in good agreement with the estimates; for deep foundations in soft clay the actual base resistance is somewhat less than estimated, on account of local sheer failure, and an empirical compressibility factor is introduced by which the shearing strength is reduced. The skin friction is found to depend largely on the method of installing the foundation. The observed bearing capacity of shallow foundations in sand is in reasonable agreement with the theory; for deep foundations, however, the actual base resistance is considerably less than estimated on account of local shear failure, and anempirical compressibility factor is introduced as before. Since the earth pressure coefficient on the shaft can at present only be deduced from tho shin friction of penetrating tests, it is frequently more convenient to estimate the bearing capacity of deep foundations in cohesionless soil from an extrapolation of the results of cone penetration tests. Dans la première par-tie de l‘article on expose une théorie sur la capacité de portage, basée sur la théorie de la plasticité, par extension de l'analyse préalable des empattements de surface aux fondations faibles et profondes dans une matiére cohésive uniforme avec friction inteme. Les résultats théoriques sont repésentéb par les facteurs de capacité de portage en fonction des propriétés méaniques du sol et des caractériques physiques de la fondation. La réstance de base des fondations dans un sol vraiment cohésif ne s'accrott que faiblement avec la profondeur des fondations; pourles fondations profondes le frottement superflciel est donc grand par comparaison avec la résistance de base. Cependant, dans des matiéres sans cohésion, la résistance de base s'accrott rapidement avec la profondeur de fondation et déend pour une grande mesure du coefficient de pression de la terre sur la souche; pour les fondations profondes la résistance de base est un facteur de premiére importance et le frottement superiiciel n'a que peu d'importance. Dans la deuxième partie de l'article, on peut voir l'analyse des principaux réhats d'essais de charge en laboratoire et sur le terrain, sur fondations enterrées et enfoncées, et la comparaison avec les prévisions thémiques. La résistance de base observée des fondations dans l'argile Concorde bien avec les évaluations; pour les fondations profondes dans l'argile molle, la résistance de base réelle est quelque peu moindre que celle estimée en raison du man ue de résistance locale au-cisaillement, et on introduit un facteur empirique de compressibilité par lequel la résistance au cisaillement est ré;duite. On trouve que le frottement superficiel dépend beaucoup sur la méthode d'installation des fondations. La capacité de portage observée pour les fondations peu profondes dans le sable concorde raisonnablement avec la théorie; pour les fondations profondes, cependant, la résistance de base réelle est bien moindre que celle estimée en raison du manque de résistance locale au cisaillement et un facteur empirique de compressibilité est introduit comme ci-dessus. Comme le coefficient de pression de la terre sur la souche ne peut à l'heure actuelle étre déluit que d'aprés le frottement superficiel des essais de pénétration. il est souvent lus commode d'estimer la capacité de portage des fondations profondes en terrain sans cohésion d'aprés une extrapolation des résultats des essais de pé;né;tration au cône.

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... Figure 9 Three different methodologies were used to estimate the ultimate capacity of the two LDBP cases utilized in this study. ECP 202/4 2005 [3], DIN 4014 1990 [4], and Meyerhof, 1951 [21] classical method are the used to determine the ultimate capacity of both Alzey and Damitta cases, the obtained results of ultimate bearing and friction resistances will be compared with the in-situ measurements of the two loading tests to assess the reliability of the three methodologies. ...
... In 1976, Meyerhof utilized the empirical data obtained from field observations alongside some theoretical considerations in developing his classic formula for the bearing capacity of a pile in a soil possessing both cohesion and friction. As presented in Equation 1, the foundation's physical characteristics and the soil's mechanical properties were represented in this formula through bearing capacity factors (Nc, Nq, and Nɣ ). Figure 14 compares the obtained ultimate capacities using the Meyerhof [21], and the field measurements of two tests. ...
... Where, ca: soil adhesion per unit area; Based on the comparative analysis performed, it was found that the Egyptian code's calculated ultimate LDBP capacity was apparently more conservative than DIN 4014 and Meyerhof, 1951 [21] results. The pile capacity obtained using ECP202/4 2005 [3] criteria for the second case study was 48% and 83% obtained from the Meyerhof, 1951 and DIN 4014, respectively. It also was about 60% of the average value estimated from modified Chin 1970 [10] and Hansen 1963 [9] methods. ...
Article
... In the same line, Meyerhof 's capacity-based classic formula is endorsed in several international design standards for estimating the ultimate pile capacity. Meyerhof 30 developed his theory of bearing capacity of foundations based on the plastic theory by extending the previous analysis for surface footings to shallow and deep foundations in a uniform, cohesive material that exposed internal friction (c-Ø soil). Meyerhof 31 utilized the empirical data obtained from field observations alongside some theoretical considerations in developing his classic formula for the bearing capacity of a pile in a soil possessing both cohesion and friction. ...
... Ultimate bearing resistance of the LDBP. Prandtl 39 , Reissner 40 , Terzaghi 41 , Meyerhof 30 and Vesic 42 have studied the bearing capacity of shallow and deep foundations. They all built their theories based on plasticity wedge failure mechanism but with different shear patterns and rupture lines reverting to the shaft. ...
... Meyerhof 's analytical solutions 30,31 ignored the effect of arching action that occurs around the pile's base at the failure state. With that in mind, it was proven in several studies 37,[43][44][45] that this arching action is affecting the vertical and horizontal stresses around the pile's shaft and base. ...
Article
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... As a reminder, all the results obtained for Nc are compared with the case of Terzaghi [28]. When it is β=0 it can be seen in Equation (1) above (Nc=5.7, ...
... Plastic regions and slip surfaces near rough strip foundation on upper of inclination, Meyerhof[28] ...
Article
this poses a danger to the structure due to failures that occur in slopes. Therefore, a solution or improvement should be determined for these issues of the collapse of the structure as a result of the failure of the slopes. A laboratory model has been built to test the impact of some variables on the bearing capacity factor. The variables include the magnitude of static axial load applied at the center of footing, the depth of embedment, the spacing between geogrid reinforcement layer and the numbering of the geogrid sheet under the footing, the inclination angle of slope clayey soil (β), the spacing between the footing's edge and the slope's end (b/H). The results show that the critical case of reduction in bearing capacity is mobilized at (b/H˂ 0.25) and (β˃ 30°). A design chart has been obtained to the case of unreinforced slope soil under a footing to describe the reduction in (Nc) when increasing the inclination angle and another design chart of the case of reinforced slope soil with (N=1, 2 and 3) has been obtained to show the increase in value of (Nc) with increasing the number of the reinforced layer at different values of (β) and finally simple equations have been obtained in order to calculate the ultimate bearing capacity of foundation on sloped clayey soil at different number of reinforcement. Copyright © 2022 Praise Worthy Prize S.r.l. - All rights reserved.
... As a reminder, all the results obtained for Nc are compared with the case of Terzaghi [28]. When it is β=0 it can be seen in Equation (1) above (Nc=5.7, ...
... Plastic regions and slip surfaces near rough strip foundation on upper of inclination, Meyerhof[28] ...
Article
Full-text available
The placement of buildings and structures on/or adjacent to slopes is possible, but this poses a danger to the structure due to failures that occur in slopes. Therefore, a solution or improvement should be determined for these issues of the collapse of the structure as a result of the failure of the slopes. A laboratory model has been built to test the impact of some variables on the bearing capacity factor. The variables include the magnitude of static axial load applied at the center of footing, the depth of embedment, the spacing between geogrid reinforcement layer and the numbering of the geogrid sheet under the footing, the inclination angle of slope clayey soil (β), the spacing between the footing's edge and the slope's end (b/H). The results show that the critical case of reduction in bearing capacity is mobilized at (b/H˂ 0.25) and (β˃ 30°). A design chart has been obtained to the case of unreinforced slope soil under a footing to describe the reduction in (Nc) when increasing the inclination angle and another design chart of the case of reinforced slope soil with (N=1, 2 and 3) has been obtained to show the increase in value of (Nc) with increasing the number of the reinforced layer at different values of (β) and finally simple equations have been obtained in order to calculate the ultimate bearing capacity of foundation on sloped clayey soil at different number of reinforcement
... There are several theories to evaluate the bearing capacity of a shallow foundation. The models presented by Terzaghi [22], Meyerhof [23], and Vesic [24] are the most commonly used for evaluating the bearing capacity of cohesive soils. For the bearing capacity computation in cohesive soils, the ϕ = 0 condition is considered [4,25,26]. ...
... ULS and SLS requirements were used as the design optimization constraints. Additionally, some practical restrictions were applied to the design variables as given in Equations (23) and (24). ...
Article
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This study presents a cost-based optimization model for the design of isolated foundations in cohesive soils. The optimization algorithm not only incorporates safety requirements in the form of ultimate limit state (ULS) and serviceability limit state (SLS) criteria but also deals with the economics simultaneously. In that regard, the generalized reduced gradient (GRG) method is used for the optimization purpose to achieve the least construction cost of an isolated foundation along with the integration of design parameters as optimization variables. The optimization technique is elaborated using a design example in silty clayey soil and the results of the optimized design are compared with those of the conventional design. The optimization model shows that the optimized design can reduce the construction cost by up to 44% as compared to the conventional design cost for the particular example. Moreover, a sensitivity analysis is also performed to evaluate the quantitative impact of cohesive soil properties, design load, and groundwater table on the construction cost. The results indicate that the construction cost majorly depends on the combined effect of four key parameters: Young’s modulus, recompression index, design load, and groundwater table.
... For strip footing, the analytical expressions derived from the theory of plasticity provide the factors N c and N q which remain unchanged with respect to roughness variations of the footing-soil interface (Bolton and Lau 1993;Griffiths 1982;Meyerhof 1951Meyerhof , 1955. However, there is a considerable difference in the magnitudes of N γ between smooth and rough footings (Bolton and Lau 1993;Griffiths 1982;Meyerhof 1951Meyerhof , 1955Michalowski 1997). ...
... For strip footing, the analytical expressions derived from the theory of plasticity provide the factors N c and N q which remain unchanged with respect to roughness variations of the footing-soil interface (Bolton and Lau 1993;Griffiths 1982;Meyerhof 1951Meyerhof , 1955. However, there is a considerable difference in the magnitudes of N γ between smooth and rough footings (Bolton and Lau 1993;Griffiths 1982;Meyerhof 1951Meyerhof , 1955Michalowski 1997). Consequently, numerous methods have been proposed to calculate the magnitude of N γ . ...
... Depending on the development of the slip lines from either side of the footing, two different types of failure mechanisms were considered in the current study. In the early research pertaining to this area, the shape of the non-plastic wedge was assumed to be a triangular in shape [5,9,35,51]. However, later it was found that this nonplastic wedge is actually curvilinear which results in a lower magnitude of the collapse loads [21,23,25,26,30,32]. ...
... Substituting Eqs. (35) and (1) in Eqs. (6) and (7), the values of R and r can be given as: ...
Article
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Experimental studies indicate that the yield parameters for soils remain generally stress dependent, in which case, the internal friction angle reduces continuously with an increase in the normal stress. Such a yield behaviour cannot be modelled correctly by using a linear failure envelope for which case the friction angle does not depend on the stress level such as the Mohr–Coulomb failure criterion. In the current manuscript, a nonlinear yield criterion, considering pure-frictional as well as cohesive-frictional power-type failure envelope, has been employed to compute the bearing capacity of a rough strip footing placed horizontally on sloping ground surface in the presence of pseudo-static seismic inertial forces. The analysis has been performed by using the method of stress characteristics approach. The variation of the seismic bearing capacity factor Nσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}_{\sigma }$$\end{document}, with an increase in horizontal earthquake acceleration coefficient (αh)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha}_{\mathrm{h}})$$\end{document} for various ground inclinations (β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}), has been provided. The obtained solutions have been compared with different available numerical and experimental results. The factor Nσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}_{\sigma }$$\end{document} reduces continuously with increases in earthquake acceleration as well as slope inclination. It has been clearly noted that the power-type failure criterion provides a much better prediction of the bearing capacity as compared to the conventional Mohr–Coulomb yield criterion.
... For strip footing, the analytical expressions derived from the theory of plasticity provide the factors N c and N q which remain unchanged with respect to roughness variations of the footing-soil interface (Bolton and Lau 1993;Griffiths 1982;Meyerhof 1951Meyerhof , 1955. However, there is a considerable difference in the magnitudes of N γ between smooth and rough footings (Bolton and Lau 1993;Griffiths 1982;Meyerhof 1951Meyerhof , 1955Michalowski 1997). ...
... For strip footing, the analytical expressions derived from the theory of plasticity provide the factors N c and N q which remain unchanged with respect to roughness variations of the footing-soil interface (Bolton and Lau 1993;Griffiths 1982;Meyerhof 1951Meyerhof , 1955. However, there is a considerable difference in the magnitudes of N γ between smooth and rough footings (Bolton and Lau 1993;Griffiths 1982;Meyerhof 1951Meyerhof , 1955Michalowski 1997). Consequently, numerous methods have been proposed to calculate the magnitude of N γ . ...
Article
This paper presents the computations of vertical bearing capacity factors Nc, Nq, and Nγ, of the smooth and rough strip, circular and ring footings resting on soil with a friction angle (ϕ) ranging from 5° to 45° using a finite element viscoplastic strain method obeying the Mohr-Coulomb yield criterion. The numerical difficulty could be improved to some extent by using the proper magnitude of soil dilation angle (ψ) in the analysis of high non-associative flow. The effects of domain and mesh size are presented thoroughly. The factors are calculated individually and found to be in close agreement with the existing solutions. However, differences are also reported and discussed. The magnitude of bearing capacity factors increases with increasing ϕ. Moreover, the factors with a rough base are significantly greater than the smooth base at high values of ϕ. Moreover, this work also indicates that the shape factors may depend on ϕ.
... The ESA requires effective soil parameters and uses c' (effective cohesion) and ∅' (effective internal friction angle), whereas the TSA is based on the ∅u = 0 analysis and is used for undrained conditions. Until recently, UBC values for footings on unsaturated soil layers were determined based on the assumption of saturated soil [1][2][3]. However, this assumption is not always accurate and can lead to non-economical solutions. ...
Article
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In general, the ultimate bearing capacity (UBC) of shallow foundations on unsaturated soils is characterized by the conventional shear strength (SS) parameters in which saturated theories are applied. However, in this case, it is clear that the foundations designed using the obtained values from the saturated cases not be economical. In recent years, procedures have been developed to estimate the UBC of foundations on unsaturated soils, that take into account drained and undrained loading conditions. However, these studies generally concentrate on sandy soils. The validity of the results proposed in the literature should be tested for other soils. Therefore, this paper includes a conventional direct shear box (DSB) test to determine the unsaturated SS of statically compacted silty soil, and a series of model tests were performed to determine the foundation's UBC. In the experimental model setup, the UBC values of different types and sizes of model foundations on silty soil layers with a different soil saturation degrees (SSDs)/matric suctions (MSs) and different void ratio values were measured. In addition, the soil-water characteristic curves (SWCCs) and SS parameters of unsaturated silt were obtained. Using the experimental results, a new equation is proposed for the characterization of the UBC of shallow foundations on unsaturated silty soils. Using this equation, the UBC of unsaturated soils can be determined based on the results of unconfined compressive strength tests (UC) measured on unsaturated soil samples and based on the degree of saturation and the fitting parameter. The results indicate that the measured bearing capacity values obtained via the model footing test, shows a good consistency with those obtained by the proposed equation.
... However, for screw piles in the IBF mode, much controversy exists about the failure law of the soil under the screw teeth, and the method for calculating the bearing capacity of the screw teeth is still unclear. Relevant scholars have proposed various failure modes following the bearing theory of strip foundations, such as the Terzaghi, Meyerhof, and cavity expansion failure modes [23][24][25]; however, determination of the failure type requires further investigation. ...
Article
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A screw pile is a special-shaped pile with several advantages, including good bearing capacity, economy, and rapid construction. The calculation of the screw piles’ ultimate bearing capacity in the individual bearing failure state remains controversial. To address the problems of an unclear failure mechanism and the pile–soil contact relationship in screw piles, we conducted large-scale direct shear tests using a partial amplification method. The variation law for soil stress and the failure pattern of soil around the screw teeth were analyzed. The bearing capacity of the screw shear plate with screw teeth was found to be significantly higher than that of the plane shear plate, while that of the screw pile first increased and then decreased with an increase in the screw pitch. The optimal screw pitch allowed the determination of the maximum bearing capacity. Furthermore, the optimal screw pitch was generally equal to the critical screw pitch, which distinguished the individual bearing failure from the cylindrical shearing failure. A new calculation method for the critical screw pitch and ultimate bearing capacity in the individual bearing failure state was presented, and its rationality was proved using the direct shear test results. The calculation of the critical screw pitch considers the shear strength of soil and the geometric parameters of the screw teeth, making it more widely applicable. These results can provide a theoretical basis for the subsequent design of screw piles.
... The boundary-value problem of footing penetration in soil involves the determination of the displacement and stress fields in the soil domain. The bearing capacity equation (Brinch Hansen 1970;Meyerhof 1951Meyerhof , 1963Terzaghi 1943) is one of the tools that geotechnical engineers typically use to estimate the limit unit bearing capacity q bL (resistance to plunging) of footings in sand (Sakleshpur et al. 2021a, b). Fig. 1 shows the classical failure (collapse) mechanism for a footing with a level base embedded in a uniform sand deposit. ...
Article
Bearing capacity calculation is an important part of shallow foundation design. The expressions for the shape and depth factors available in the literature for bearing capacity calculation are mostly empirical and are based on results obtained using limit analysis or the method of characteristics assuming a soil that is perfectly plastic following an associated flow rule. This paper presents the results of an experimental program in which load tests were performed on model strip and square footings in silica sand prepared inside a half-cylindrical calibration chamber with a transparent visualization window. The results obtained from the model footing load tests show a significant dependence of footing penetration resistance on embedment depth. The load test results were subsequently used to determine experimentally the shape and depth factors for model strip and square footings in sand. To obtain the displacement and strain fields in the sand domain, the digital image correlation (DIC) technique was used to analyze the digital images collected at different stages during loading of the model footing. The DIC results provide insights into the magnitude and extent of the vertical and horizontal displacement and maximum shear strain contours below and around the footing base during penetration.
... The model domain is extended to a depth equals 5 times the external radius and extends laterally 10 times the external radius from the centerline of ring footing to make the "boundary influence" on the estimation of the collapse load neglectable. To obtain accurate results from the numerical analysis, the finite element mesh size, the number, and the distribution of element are chosen to satisfy both of the following two requirements [15]. ...
Conference Paper
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A ring footing is very importance in supporting symmetrical constructions for instance tall transmission towers, silos, oil storage container etc. These structures are susceptible to seismic loads in addition to their dead weight. There is a lack of knowledge in studying the behavior of ring foundation subjected to seismic loading resting on layered soils. Also, the impact of different diameter of ring footing is seemed a valuable field of studying the performance of ring footing. The current study focused on achieving these goals. In this paper, PLAXIS 3D software used to investigate the load-settlement of a ring footing rest on different layers of soil such as clay, sand, and clay over sand soils under seismic loading. The performance of four types of ring footings with four diameter ratios (inner diameter, R1/outer diameter, R2) and rest on the three-types of soils are investigated. The results of this study identified that the maximum settlement value is less in clay and much higher in sand for different ratios of (R1/R2) of footing models under seismic load. Also, in sandy soil, the seismic settlements always more than other soils by about double value at the same foundation dimension and conditions. The results of this study can be considered as data base for geotechnical to control footing design and to avoid all affecting factors.
... This initial establishment undergoes several modifications, as it considers linear relationship (Cheng and Au 2005). Among these modifications, the work of (Vesic 1973;Meyerhof 1951;Hansen 1970) were found to be the most well-known due to their consideration of relevant non-linearity conditions, such as non-linear peak strength envelope, continuous failure due to strain localization, softening to critical states, and depth/width ratio modification by including allowances for increase in depth under loading. ...
Article
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There are challenges associated with determining the actual behaviour of soil foundation due to its heterogeneous nature especially when subjected to an imposed loading. This has led to deployment of various soft-computing approaches as an alternative to field experiments for measuring the resistance level of the soil caused by imposed loading. Therefore, this research work was aimed at modelling the soil bearing capacity with specific consideration of index properties parameters of soil, shear strength parameters and relative varied depths, by employing Terzaghi's equations. To considerably overcome complexities, and spontaneous variabilities associated with natural soil foundation, a relatively larger set (45) of data were sourced and used for the modelling. Multiple linear regression (MLR) was used to develop the model using 30 set of data and natural bearing capacity was determined as output with relatively high level of accuracy. The model developed was validated using remaining 15 set of data by employing normal probability plots, which indicates a low level of variance between experimental, and modelled values. Likewise, the corresponding R 2 values of strip, square, and circular footings were found to be 96.98%, 96.93%, and 96.90%, this indicates a high reliability of the model developed.
... As this method considers the equilibrium conditions only, so the solutions obtained are mostly approximate. Many researchers namely Terzaghi (1943), Meyerhof (1951), Zhu et al. (2001), Silvestri (2003), Bishnoi (1968) and Kulhawy and Goodman (2005) have developed bearing capacity solutions using this methodology. ...
Article
... Note that the linearity implicit in the Mohr-Coulomb equation is just a convenient approximation and in reality, the σ s (p n ) relation is often curved, in particular, at a small p n (e.g., [36]). Nevertheless, linear MC is the basis for engineering soil mechanics [37][38][39][40], which adopts the so-called limit equilibrium method to identify the ultimate bearing capacity of the ground. The general shear failure of the soil is determined as part of the analysed scenario in which multiple slip faces are generated. ...
Article
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Mechanical properties, in particular, strength (tensile, shear, compressive) and porosity, are important parameters for understanding the evolution and activity of comets. However, they are notoriously difficult to measure. Unfortunately, neither Deep Impact nor other comet observations prior to Rosetta provided firm data on the strength of cometary material. This changed with the Rosetta mission and its detailed close observation data and with the landing(s) of Philae in 2014. There are already many articles and reviews in the literature that derive or compile many different strength values from various Rosetta and Philae data. In this paper, we attempt to provide an overview of the available direct and indirect data; we focus on comet Churyumov–Gerasimenko/67P but include a discussion on the Deep Impact strength results. As a prerequisite, we start by giving precise definitions of ‘strength’, discuss soil mechanics based on the Mohr–Coulomb ‘law’ of micro-gravity, and discuss bulk density and porosity, sintering, and the physics of the strength of a cohesive granular medium. We proceed by discussing the scaling of strength with the size and strain rate, which is needed to understand the observational data. We show how measured elastic properties and thermal (conductivity) data can be correlated with strength. Finally, a singular very high strength value is reviewed as well as some particularly small-strength values inferred from the bouncing motion of Philae, data from its collisions with the surface of the comet, and scratch marks it left, allegedly, on the surface close to its final resting site. The synthesis is presented as an overview figure of the tensile and compressive strength of cometary matter as a function of the size scale; conclusions about the size dependence and apparent natural variability of strength are drawn.
... A reasonable prediction of the bearing capacity of shallow foundations has therefore been the most important issue for geotechnical engineers during the past several years. Several researchers, basing their studies on the limit equilibrium approach (Terzaghi, 1943;Meyerhof, 1951Meyerhof, , 1963Hansen, 1970;Vesic, 1973) and limit analysis (Michalowski, 1997;Chakraborty and Kumar, 2014) have attempted to solve the problem of bearing capacity. However, one inherent limitation for all their solutions is that in all the analyses the soil was assumed to exist either in dry or fully saturated conditions, thus neglecting the infl uence of matric suction on the overall bearing capacity response of a foundation. ...
Article
The present study proposes a novel and simplified methodology to assess the seismic bearing capacity (SBC) of a shallow strip footing by incorporating strength non-linearity arising due to partial saturation of a soil matrix. Furthermore, developed methodology incorporates the modal response analysis of soil layers to assess SBC. A constant matric suction distribution profile has been considered throughout the depth of the soil. The Van Genuchten equation and corresponding fitting parameters have been considered to quantify matric suction in the analysis. SBC has been obtained for three different geomaterials; viz. sand, fly ash and clay, based on their predominant grain size and diverse soil water characteristics curve (SWCC) attributes. Variation of SBC with different modes of vibration and damping ratio are reported for ranges of matric suction pertinent to the geomaterials considered in the study. The relative significance of matric suction on SBC has been reported for suction values within the transition zone of each geomaterial. It is observed that the SBC of sand is drastically reduced, with matric suction reaching beyond the residual suction value. The SBC of fly ash remains constant beyond the residual suction value, whereas the SBC of clay shows an increasing trend toward the practical range of matric suction values.
... Solutions to the bearing capacity problems of ring footing are attempted by the limit equilibrium methods, the upper bound plastic limit analysis method and the method of characteristics. Griffiths (1982Griffiths ( , 1989 (Terzaghi, 1943;Meyerhof, 1951;Vesic, 1973). when the soil displays high non-associativity for  > 30, the dilation angle of the soil has a major influence on the value of N'. ...
Thesis
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Open caissons are deep foundations sunk in the ground by the removal of the soil within the caisson shaft. A cutting edge with a tapered inner face is used at the bottom of the caisson to allow the bearing failure of the soil and hence the continued sinking. In the present study, the bearing capacity factors of the cutting edge for the wide range of radii ratio (ri/ro = 0.35 to 0.95), varying friction angles of the soil ( = 5 to 35) and different tapered angles of the cutting edge ( = 30 and 45) are evaluated using finite element (FE) analysis. Before evaluating the bearing capacity of the cutting edge, the preliminary investigations are carried out considering the strip and ring footing problems to frame the guidelines for the FE evaluation of the open caisson problem. A series of 1g model tests have also been performed to investigate the load penetration response of the cutting edge at different stages of the sinking and the soil flow mechanism in the soil beneath the cutting edge. Using strip footing problem, the sensitivity analysis is carried out to examine the ultimate capacity of the strip footing considering the strength parameters, width of the footing, unit weight of the soil, surcharge at the base level of the footing, and deformation parameters as the variables. Then the effect of different material models on the ultimate capacity of the strip footing is examined. A few suggestions are given in regard to the FE analysis of the ring footing and open caisson problems to assess their bearing capacities. The bearing capacity factors N'c, N'q and N' of the smooth and rough base ring footing are evaluated using the finite element method (FEM). In the analyses, the radius ratio is varied from 0 to 0.75 with an increment of 0.25 and friction angle of the soil is varied from 5 to 35. The Mohr-Coulomb yield criterion and non-associative flow rule are used in the analyses. Then the superposition of the three components of the bearing capacity equation is assessed, i.e., cohesion, surcharge and unit weight of the soil. The methodology adopted for the ring footing is used for the open caisson problem. A series of 1g model tests are performed to investigate the load-penetration response and soil flow mechanism in the soil during different stages of the sinking of the caisson. The effect of smooth and rough base conditions, varying tapered angles, different types of penetration of the cutting edge, and varying depths of sinking on the load-penetration response of the cutting edge is investigated. The soil flow mechanism corresponding to the varying tapered angles of the cutting edge, varying magnitudes of the penetration, and varying depths of sinking is examined using the image processing technique. The values of bearing capacity factor, N' of the cutting edge of the circular open caisson are also evaluated using the results of the experimental studies. The experimental studies have been performed for the embedded and rough base conditions of the cutting edge and the same are simulated in the FE analysis of the circular open caisson. The formation of influence zone in the soil beneath the cutting edge of the caisson is termed as failure zone. The extent of the failure zone in the vertical and radial directions is evaluated using the FE analysis. The effects of variation in the tapered angles and radii ratio of the cutting edge, unit weight, friction angle and cohesion of the soil, and magnitude of the surcharge on the extent of the failure zone are studied. Using the results of FE analysis, multivariate linear regression analysis is performed and easy to use predictive equations are developed to estimate the extent of the failure zone in the soil beneath the cutting edge. The predictive equations are assessed for their practical applicability using the results of the 1g model tests. The vertical bearing capacity factors, N'c, N'q and N' of the cutting edge of the open caisson are evaluated using the FEM. Two tapered angles of the cutting edge,  = 30 and 45, varying radii ratio = 0.35 to 0.95, and  = 5 to 35 are considered in the analyses. The applicability of the methodology used for the ring footing problem is examined by evaluating the bearing capacity factors for the varying values of cohesion, surcharge and unit weight of the soil. The bearing capacity factors evaluated using the FE analyses are compared with those available in the literature. The FE results are presented in the form of design charts and tables for the practical use. A complete understanding of the different aspects of the open caisson, such as load penetration response, soil flow mechanism beneath the cutting edge, and bearing capacity of the cutting edge will help in planning and controlled sinking operation of the open caisson.
... Evaluation of the bearing capacity of shallow foundations dates back to the evolution of classical soil mechanics theories in the early 1940s with the pioneering study of Terzaghi (1943), followed by seminal theoretical contributions of Meyerhof (1951Meyerhof ( , 1963, Hansen (1970) and Vesic (1973). Accordingly, there has been a great number of studies on the ultimate bearing capacity of surface footings adopting a variety of analytical/numerical approaches. ...
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This study investigates the bearing capacity of strip footings resting on unsaturated soils subjected to combined loading using the lower-bound limit analysis coupled with the finite element discretization approach. In this regard, second-order cone programming (SOCP) is exploited to simulate the nonlinear form of the universal Mohr-Coulomb yield criterion during the process of stress field optimization. The significant influence of matric suction induced below the surface footing was accounted for by adopting the suction stress concept under the no-flow and steady-state infiltration/evaporation flow conditions. The eccentricity and inclination of the foundation loading are introduced into the equilibrium equations along the strip footing so as to render various combinations of moment (M), vertical (V) and shear (H) forces. The results stemming from the lower-bound finite element limit analysis are compared with several previous studies throughout the literature for verification of the model. The substantial contribution of suction stress to the evolution of failure loci and the distribution of subsurface stresses for the shallow foundation subjected to inclined and eccentric loadings is thoroughly discussed. A general three-dimensional failure envelope is presented for shallow foundations resting on partially saturated soils under combined vertical, horizontal and moment loadings.
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This paper investigates the validity and shortcomings of the existing analytical solution for the ultimate bearing capacity of a pile embedded in a rock mass using the modified Hoek–Brown failure criterion. Although this criterion is considered a reference value for empirical and numerical calculations, some limitations of its basic simplifications have not been clarified yet. This research compares the analytical results obtained from the novel discontinuity layout optimization (DLO) method and the numerical solutions from the finite difference method (FDM). The limitations of the analytical solution are considered by comparing different DLO failure modes, thus allowing for the first time a critical evaluation of its scope and conditioning for implementation. Errors of up to 40% in the bearing capacity and unrealistic failure modes are the main issues in the analytical solution. The main aspects of the DLO method are also analyzed with an emphasis on the linearization of the rock failure criterion and the accuracy resulting from the discretization size. The analysis demonstrates DLO as a very efficient and accurate tool to address the pile tip bearing capacity, presenting considerable advantages over other methods.
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This study aims to create soil zonation maps (SZM) using a spatial interpolation approach relying on vast geotechnical subsoil data gathered through field and laboratory analysis. Islamabad, a rapidly growing city and capital of Pakistan, is used as a case study. The sub-soil data were evaluated from 210 geotechnical investigation reports in terms of soil type, standard penetration (SPT-N value), undrained shear strength, and consolidation parameters. The data were digitally analyzed in ArcGIS using the ordinary kriging interpolation technique, and SZM were developed based on SPT-N and soil type. For the developed SZM, settlement and allowable bearing capacity (ABC) are evaluated for shallow foundations. The results showed that the study area was divided into three main zones based on SPT-N [i.e., zone-1(4–15), zone-2(16–30), and zone-3(> 30)], and six sub-zones based on lithology. The lean/silty clay is predominant up to 15 m, underlain by gravel and shale/sandstone up to 50 m. Correlations were presented based on linear regression analysis with R2 = 0.98 to predict the SPT-N with depth for expeditious appraisal of stiffness and strength of sub-soils throughout preliminary planning and feasibility studies of several construction projects. The ABC for the shallow foundation in Islamabad found to be above 100 kPa, indicating an excellent safe ABC to support foundations of lightly loaded structures. Moreover, the correlation coefficient to predict SPT-N values is around 85%, while about 94% for soil type. Furthermore, reliable information on geotechnical properties of the subsoil’s layers will work as a complement for the site characterization and identification of hazard for upcoming projects.
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Chapter
Most theories of bearing capacity of foundations on or in ground are based on the assumption that soil is incompressible and its stress–strain behavior is rigid-perfectly plastic following Mohr–Coulomb failure criteria. Menard (1957) proposed a theory for estimation of limit pressure for pressure meter that incorporates compressibility of soils in the form of rigidity index, (ratio of shear modulus to undrained shear strength of soils). Vesic (1973) derived compressibility factors for cohesive–frictional soils for the estimation of the ultimate bearing capacity of footings. The present study focuses on the variation of bearing pressure factor for circular footings on soft ground with settlement, for a wide range of rigidity indices . Finite element axisymmetric analysis is carried out to evaluate the bearing pressure, q, versus settlement responses for circular footings for a range of from which is obtained at different settlement ratios (SR). Perfectly rigid plastic response, i.e., incompressible soil is achieved for at SR of 0.25%. Normalized (ratio of of compressible soil to that of incompressible one) are derived as function of rigidity index, for different normalized (ratio of SR of compressible to incompressible soil).
Chapter
Many previous studies analyzed the footing resting on cohesionless soil slopes. The present study focuses on determining bearing capacity on clayey soil slopes through the finite element method associated with limit analysis. The soil consistency has been varied from soft to hard. The bearing capacity and slope factors representing the slope effect on bearing capacity are presented in the study. The bearing capacity factor enhances with an increase in the soil strength, footing depth and setback. The slope factor increases with setback and reduces with footing depth and slope inclination. The increase in bearing capacity with footing depth is relatively less visible in the sloping ground than level ground. Contrary to this, the increase in bearing capacity with soil strength is more visible on slopes.
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The kinematic method of limit analysis theory was adopted in this paper to calculate the seismic bearing capacity of the shallow strip foundation on a rock mass obeying the non-linear modified Hoek-Brown failure criterion. The generalized Prandtl failure mechanism was chosen, which is different from the multi-wedge failure mechanism assumption commonly used in previous research. Three angle parameters were used to control the mechanism shapes, and the equivalent friction angle and equivalent cohesive were adopted to faithfully reflect the shape characteristics of the failure mechanism. The seismic action was considered using the pseudo-static method, which is simplified to the inertial force determined by the horizontal seismic coefficient. The validation of the present method was carried out by comparing with previous analytical results and the finite element model. Subsequently, the influences of the surface overload, the properties of the rock mass, and the seismic action on the shape and ultimate bearing capacity of the failure mechanism were investigated. For the convenience of practical engineering, this paper gives the ultimate bearing capacity of strip foundations on five representative rock foundations, and the variation trend of bearing capacity with the unit weight of rock mass, surface overload, and horizontal seismic coefficient.
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Abstract: One of the constructions that can be used to overcome the problem of soft soil is through pile mattress bamboo construction. This construction consists of bamboo arranged as mattresses and bamboo arranged as cluster of piles. The cluster pile consists of several bamboo culms tied together (cluster pile). Cluster pile capabilities that are not analysed for strength can result in wastage or construction failure. Hence, this study was intended to analyse the ability of clusters pile through recorded direct observation and compare them based on sonder (CPT) data. The method is carried out by direct observation of the model at the research site. The model observed are clusters with a length of 8 m, inserted into soft soil and then vertical loading is carried out until the soil that supports it collapses. There are 3 types of clusters pile, namely cluster piles C3, C4, and C7. The results showed that the ultimate bearing capacity of the cluster based on the direct load test was relatively the same as the calculated with sonder data. Thus, this study established the ultimate bearing capacity (Pult) which can be determined using the equation, Pult = 7.4056Ac, where Pult in (kg), and Ac is cluster area in (cm2). Keywords: Cluster pile, soft soil, bearing capacity, direct load test, CPT (sonder)
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The landing of a probe on the surface of an asteroid can produce a stable operating platform and obtain vital data describing the mechanical response of the asteroid material. The fine-grained regolith area on the asteroid surface is essential in cushioning the probe from impact energy and in avoiding the risk raised by the large protruding rocks during the landing of the probe. Models incorporating macro forces explaining the interaction between the landing terminal of the probe and the regolith on the asteroid surface conclusively reflect the mechanical process and characteristics of the interaction, making them particularly suitable to analyze and control the landing process of the probe. In this paper, we study the macro normal force of the interaction between the footpad of a legged probe and the regolith on the asteroid surface with particular attention paid to the mathematical expression of the force model and the contribution of the most essential soil parameters. The ultimate bearing theory of soil mechanics is extended to discuss the mathematical model of the macro normal force on the asteroid regolith in a micro-gravity environment undergoing different damage modes. Subsequently, a series of discrete element method simulations are implemented to verify the normal force model and to analyze its characteristics under the influence of landing impact. On the basis, the effect modes of several most essential soil parameters of soil porosity, particle size and cohesive strength are revealed through a robust regression analysis of the simulation data. Next, the correlation coefficients of the effects of soil parameters on the macro normal force are researched. The model of macro normal force established in this paper can be used to facilitate an effective performance analysis in the development of the landing-cushioning mechanism of the probe, as well as to conclude a reference for the most essential soil properties parameters of the asteroid regolith via the inverse solution of the interaction data recorded in actual landing missions.
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The performance of shallow foundation constructed in deep clay deposits is poor; as it undergoes large total and differential settlements. Adoption of deep foundations can certainly eliminates the movements within the main structure as the structural loads are transmitted to the great depths. However, providing pile foundation may be uneconomical for the sites with deep soft clay deposits. In the present study, an experimental program was undertaken to propose the appropriate foundation system for light structures on deep clay deposits. In the study, six different foundation systems namely conventional isolated footing [CIF], Rigid Concrete Straight shafted pile [RCP (S)], Rigid Concrete Under-reamed pile [RCP (UR)], Straight shafted cemented stone column [CSC (S)], Under-reamed cemented stone column [CSC (UR)], and an isolated footing on cemented stone column [FOCS] were studied for load-settlement behavior and comparison is made. The testing program was carriedout in two different soils with undrained cohesion 0.46 kg/cm² and 0.36 kg/cm² respectively at 27 % and 30 % moisture content. Laboratory investigation clearly shows that FOCS model is the most suitable foundation system amongst all for deep clay deposits as the stone column helps to transmit applied loads at greater depth.
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This paper aims to introduce simple empirical models to describe the nonlinear behavior of shallow foundations under rocking vibration. The model is developed based on parametric numerical investigations of rectangular surface footings on homogenous dense dry sand, taking advantage of a nonlinear macro-element model verified based on a set of experimental results. The proposed empirical expressions include the moment-rotation backbone curve, stiffness degradation and equivalent damping ratio as well as the correlation of the foundation settlements with cumulated rotations. These expressions are provided mainly as a function of the rotation, static factor of safety and aspect ratio of foundation. Similar to previous researches, the uplift reference rotation was introduced as a normalization parameter for the new closed-form expressions to be expressed in a non-dimensional form, whenever possible. The proposed approach aimed to be simple, in order to minimize the dependence on the variable parameters, and to provide physically sound selections for engineering applications.
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A ring foundation is widely used in bridges, water towers, caissons, and other engineering structures, and its ultimate bearing capacity is one of the significant concerns in engineering design. This paper is aimed at exploring the ultimate bearing capacity of ring foundations embedded in undrained clay. Based on the finite element limit analysis, effects of the inside-to-outside radius ratio, embedment depth ratio, cutting face inclination angle, and face roughness on the vertical ultimate bearing capacity of ring foundations are investigated. The results show that the ultimate bearing capacity of the ring foundation increases gradually with the embedment depth ratio. When the embedment depth ratio D / B reaches a critical value, the bearing capacity tends to be stable, and the critical embedment depth ratio is affected by the inside-to-outside radius ratio of the ring foundation, varying from 0.2 to 0.4. The ultimate bearing capacity of the ring foundation decreases with cutting face inclination angle β . When β ≤ 40 ° , the ultimate bearing capacity tends to be stable, and the bearing capacity is reduced by approximately 30%. The influence of the cutting face inclination angle on the bearing capacity is highly dependent on the roughness of the cutting face.
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An Incompletely End Supported Pile (IESP) is a pile in a soft soil layer underlain by a hard soil layer that does not reach the bottom hard layer in practice. This study estimates the end bearing capacity of IESP by using an inhouse Rigid Plastic FEM code (RPFEM), considering shear strength non-linearity of soil against confining pressure, and soil-foundation interaction. The effect of the distance between the pile tip and the bottom hard soil layer (d/B) on the end-bearing capacity of IESP was mainly investigated for three types of soil: cohesive soils, cohesionless soils and intermediate soils. Also, theratio (r) of the end bearing capacity of the pile when it reaches the bottom hard layer to that of the pile when the bottom layer has no influence was was considered. By considering the shear strength non-linearity, the end bearing capacity was accurately estimated. The estimations were consistent with previous analytical, experimental and numerical solutions. It is found that the end bearing capacity inversely decreases with the distance d/B and becomes constant around d/B = 3. Based on the results, a formula for estimating the end bearing capacity of IESP is proposed. Comparisons with methods in existing literature confirmed the reliability of the proposed equation.
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In order to clarify the bearing mechanism of closed-ended and open-ended piles supported by a thin bearing layer, pile-loading tests are conducted on model grounds with different bearing layer thicknesses, and the soil deformation characteristics around the pile tips are observed by X-ray micro CT. In the case of open-ended piles supported by a thin bearing layer, the soil in the pile greatly displaces following the downward displacement of the soil located more deeply than the pile tip, and the soil density in the pile becomes lower than when the bearing layer thickness is sufficiently large. These characteristics probably cause lower inner friction and lower base resistance, resulting in a lower bearing capacity. When the bearing layer thickness is more than three times the pile diameter, the bearing capacity is much higher than when the bearing layer thickness is the same as the pile diameter. In addition, soil deformation which occurs is almost entirely in the bearing layer, and the changes in bearing capacity are hardly affected by the soft layer below the bearing layer. The experimental findings obtained in the present study support the idea that the criterion for the bearing layer thickness, where the influence of a thin bearing layer on the bearing capacity can be ignored, is three times the pile diameter, regardless of whether the pile tip is open or closed.
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An analytical approach to the ultimate bearing capacity qu of strip foundations on rock mass under both smooth and rough base conditions is presented. To consider the three-dimensional (3D) stress state, a 3D version of the Hoek-Brown (HB) criterion is combined with equilibrium equations to derive the governing equations by using the characteristics method. Then, a finite difference-based approach is used to solve the stresses below the foundation. Finally, integration of the vertical stress on the foundation base is performed to determine the qu of a strip foundation with different base conditions. Validation of the proposed approach is performed through comparisons with model test results and the effect of 3D strength is investigated by comparing the proposed approach with a two-dimensional HB criterion-based solution. Finally, parametric analyses are conducted to study the effects of rock constant mi, unconfined compression strength of intact rock, geological strength index, Poisson’s ratio of rock mass, and foundation width on the qu, failure zone, and vertical stress on the base. The results show that ignoring 3D strength and unit weight of rock leads to underestimations of qu and it is important to consider the different factors when designing a strip foundation on rock mass.
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In this paper, an analytical method is proposed for estimating the bearing capacity of soil within the framework of slip line theory. The method incorporates a closed-form solution taking account the transient unsaturated vertical flow conditions. The proposed framework is validated for both level and sloping ground scenarios considering saturated and unsaturated soil conditions. More specifically, the bearing capacity of a strip foundation located on an unsaturated soil slope under the influence of different rainfall infiltration conditions is evaluated. A comprehensive parametric study is also conducted taking account the influence of the rainfall influx, rainfall duration, slope angle, foundation setback distance, soil type, and the depth of the ground water table. In addition, the contribution of matric suction towards the bearing capacity under transient flow conditions is evaluated. Results of this study provide a rigorous understanding of the performance of foundations on sloping ground extending the mechanics of unsaturated soils.
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