Ultimate Bearing Capacity of a Footing Considering the Interference of an Existing Footing on Sand

The ultimate bearing capacity of a new strip footing placed on a cohesionless soil medium, in the presence of an existing strip footing, the load on which is assumed to be known, has been determined. Both the footings are assumed to be perfectly rigid and rough. The analysis is carried out by using an upper bound finite element limit analysis. For different clear spacing (S) between the footings, the values of the efficiency factor (ξ_γ) were determined; where ξ_γ is defined as the ratio of the failure load for an interfering new footing of a given width (B) to that for a single isolated footing having the same width. For ϕ < 30°, it is generally noted that the magnitude of ξ_γ increases continuously with a decrease in S/B. For ϕ > 30°, on the other hand if the applied load on the existing footing is approximately greater than half the failure load for a single isolated footing having the same width, the peak magnitude of ξ_γ was found to occur at around S/B ≈ 0.1 rather than at S/B = 0. The increase in ξ_γ becomes further significant with an increase in the magnitude of the load on the existing footing.     

Horizontal Pullout Capacity of a Group of Two Vertical Strip Anchors Plates Embedded in Sand

The horizontal pullout capacity of a group of two vertical strip anchor plates placed along the same vertical plane in sand, has been determined by using the lower bound finite element limit analysis. The effect of vertical spacing (S) between the anchor plates on the magnitude of the total group horizontal failure load (P_uT) has been determined for different combinations of H/B, δ/ϕ and ϕ. The magnitude of P_uT has been obtained in terms of a group efficiency factor, η_γ, with respect to the failure load for a single vertical plate with the same H/B. The magnitude of η_γ becomes maximum corresponding to a certain critical S/B, which has been found to lie between 0.5 and 0.8. The value of η_γ for a given S/B has been found to become larger for greater values of H/B, ϕ, and δ.     

Three-dimensional numerical analysis of the keying of vertically installed plate anchors in clay

Plate anchors, such as suction embedded plate anchors and vertically driven plate anchors, offer economically attractive anchoring solutions for deep/ultra-deep water offshore developments. The rotation/keying processes of plate anchors will cause embedment losses, which lead to decreases of the uplift resistances of the anchors in normally consolidated soil. In the present paper, the keying processes of vertically installed strip and square plate anchors are simulated using the 3-D large deformation finite element method. The effects of loading eccentricity and pullout angle on the embedment loss during keying are investigated. Both the development of the uplift resistance and the soil flow mechanisms are presented. The numerical results show that the loading eccentricity e/B has a much larger effect on the embedment loss than the pullout angle does. The anchor shape has a minimal effect on the loss in anchor embedment. The shape factors (square/strip) are 1.05–1.09 for loss of embedment and 1.10–1.19 for capacity.     

Uplift capacity of pile group anchors

Experimental investigations on model single pile anchor and pile group anchors of configuration 2 × 2 subjected to uplift loads were conducted on dry Ennore sand, obtained from Madras, India. The embedment length to shaft width ratios, L/d = 20 and L/d = 30, and enlarged base width to shaft width ratios, B/d = 1,2,3, center to center spacing of pile anchors in the groups, 3d, 4d, 6d and 8d were used. The load displacement response, ultimate resistance and variation of group efficiency with L/d, B/d and spacing have been studied quantitatively and qualitatively. For short pile group anchors (L/d = 20), the isolation spacing appears to be at a spacing of about 4d to 6d and 8d for B/d = 1 and B/d = 2 and 3, respectively. For long pile group anchors (L/d = 30), the isolation spacing appears to be at a spacing of about 4d, 6d and 8d for B/d = 1, 2 and 3, respectively. The analytical model of limit equilibrium method has been proposed to predict the net uplift capacity of pile group anchors. The predicted results compare reasonably well with the experimental results.     

Ultimate bearing capacity of equally spaced multiple strip footings on cohesionless soils without surcharge

The ultimate bearing capacity of a group of equally spaced multiple rough strip footings was determined due to the contribution of soil unit weight. The analysis was performed by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. Along the interfaces of all the triangular elements, velocity discontinuities were considered. The value of ξ_γ was found to increase continuously with a decrease in S/B, where (i) ξ_γ is the ratio of the failure load of an interfering strip footing of a given width (B) to that of a single isolated strip footing having the same width and (ii) S is the clear spacing between any two adjacent footings. The effect of the variation of spacing on ξ_γ was found to be very extensive for small values of S/B; ξ_γ approaches infinity at S/B=0. In all the cases, the velocity discontinuities were found to exist generally in a zone only around the footing edge. Copyright © 2008 John Wiley & Sons, Ltd.     

Horizontal Pullout Resistance for a Group of Two Vertical Plate Anchors in Clays

The horizontal pullout capacity of a group of two rigid strip plate anchors embedded along the same vertical plane in clays, under undrained condition, has been determined. An increase of cohesion with depth has also been incorporated. The analysis has been performed by using an upper bound finite element limit analysis in combination with linear optimization. For different clear spacing (S) between the anchors, the efficiency factor (η_cγ) has been determined to evaluate the group failure load for different values of (1) embedment ratio (H/B), (2) the normalized rate (m) which accounts for a linear increase of cohesion with depth, and (3) normalized unit weight (γH/c_o). The magnitude of the group failure load (1) becomes maximum corresponding to a certain spacing (S_cr) between the anchors, and (2) increases with an increase in the γH/c_o up to a certain value before attaining a certain maximum magnitude. The value of S_cr/B has been found to vary generally between 0.7 and 1.2. The maximum magnitude of η_cγ, associated with the critical spacing, (1) increases generally with increases in H/B, and (2) decreases with an increase in m. For a greater spacing between the anchors, the analysis reveals the development of a local shear zone around the lower anchor plate. The numerical results developed are expected to be useful for purpose of design.     

Effect of Geotextile Ties on Uplift Capacity of Anchors Embedded in Sand

This paper presents the results of experimental investigation on the effect of geotextile ties on uplift capacity of anchors embedded in sand. Uplift capacity of anchor increases with increase in embedment depth to base diameter (H/D) ratio irrespective of type of anchor. With the introduction of tie to anchors, uplift capacity of anchors increases and optimum number of layers of ties is found to be 2. A non linear power model has been developed to predict the uplift capacity at any settlement (Q _R) of anchors with tie in terms of uplift capacity at any settlement (Q _URs) of anchor without tie, H/D ratio, number of layers of tie and displacement to base diameter ratio (Δ/D). The model is applicable for predicting Q _R having the values of Q _RS, H/D, N and Δ/D in the range of 0.257 ≤ Q _URs ≤ 1.420, 1.5 ≤ H/D ≤ 3.0, 1 ≤ N ≤ 4, 0.8 ≤ Δ/D ≤ 8.     

Bearing capacity of two interfering footings

By using an upper bound limit analysis in conjunction with finite elements and linear programming, the ultimate bearing capacity of two interfering rough strip footings, resting on a cohesionless medium, was computed. Along all the interfaces of the chosen triangular elements, velocity discontinuities were employed. The plastic strains were incorporated using an associated flow rule. For different clear spacing (S) between the two footings, the efficiency factor (ξ_γ) was determined, where ξ_γ is defined as the ratio of the failure load for a strip footing of given width in the presence of the other footing to that of a single isolated strip footing having the same width. The value of ξ_γ at S/B = 0 becomes equal to 2.0, and the maximum ξ_γ occurs at S/B = S_cr/B. For S/B?S_cr/B, the ultimate failure load for a footing becomes almost half that of an isolated footing having width (2B + S), and the soil mass below and in between the two footings deforms mainly in the downward direction. In contrast, for S/B>S_cr/B, ground heave was noticed along both the sides of the footing. As compared to the available theories, the analysis provides generally lower values of ξ_γ for S/B>S_cr/B. Copyright © 2007 John Wiley & Sons, Ltd.     

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     

Heat capacity of γ-Fe2SiO4 between 5 and 303 K and derived thermodynamic properties

A multi-anvil device was used to synthesize 24 mg of pure γ-Fe₂SiO₄ crystals at 8.5 GPa and 1,273 K. The low-temperature heat capacity (C _p) of γ-Fe₂SiO₄ was measured between 5 and 303 K using the heat capacity option of a physical properties measurement system. The measured heat capacity data show a broad λ-transition at 11.8 K. The difference in the C _p between fayalite and γ-Fe₂SiO₄ is reduced as the temperature increases in the range of 50–300 K. The gap in C _p data between 300 and 350 K of γ-Fe₂SiO₄ is an impediment to calculation of a precise C _p equation above 298 K that can be used for phase equilibrium calculations at high temperatures and high pressures. The C _p and entropy of γ-Fe₂SiO₄ at standard temperature and pressure (S°₂₉₈) are 131.1 ± 0.6 and 140.2 ± 0.4 J mol⁻¹ K⁻¹, respectively. The Gibbs free energy at standard pressure and temperature (ΔG° _f,298) is calculated to be −1,369.3 ± 2.7 J mol⁻¹ based on the new entropy data. The phase boundary for the fayalite–γ-Fe₂SiO₄ transition at 298 K based on current thermodynamic data is located at 2.4 ± 0.6 GPa with a slope of 25.4 bars/K, consistent with extrapolated results of previous experimental studies.     

The effects of solid solution and diffusion on infiltration-driven metamorphism with application to metaperidotite,Val d’Efra,Central Swiss Alps

The complication introduced by solid solutions in the analysis of infiltration-driven mineral reactions is that the mole fraction of tracer component i in fluid (X _i) changes with reaction progress (ξ). The effect was incorporated into transport models for coupled fluid flow and mineral reaction by parameterizing the relation between X _i and ξ. With specific reference to carbonation and hydration during regional metamorphism of the peridotite body in Val d’Efra, whose constituent minerals are all solid solutions, infiltration of a disequilibrium fluid produces a single sharp reaction front if rock is assumed uniform in composition. The reaction front separates completely unreacted rock downstream from rock upstream with ξ at a steady-state limit (ξ_ss ≤ ξ_max) that depends on input fluid composition (ξ_max is the maximum possible value). Novel phenomena develop, however, if the flow medium, like the metaperidotite body, is composed of many small domains that differ in initial mineral modes and compositions but with X _i homogenized at a spatial scale larger than the size of the domains (e.g., by diffusion). In this case, infiltration of a disequilibrium fluid produces up to as many different reaction fronts along the flow path as there are domains with 0 ≤ ξ < ξ_ss in all domains except upstream from the slowest moving front where ξ = ξ_ss in all domains. Measured values of ξ in the metaperidotite, (all 0 < ξ < ξ_max) are best reproduced by down-temperature infiltration of a disequilibrium fluid with X_\textCO2 =  0. 1 9 6 X_{{{\text{CO}}_{2} }} = \, 0. 1 9 6 into a multi-domain medium with uniform X_\textCO2 X_{{{\text{CO}}_{2} }} at each spatial point along the flow path (homogenized across the domains at the m-scale by diffusion), and time-integrated fluid flux ≥1,836 mol fluid/cm² rock. Results resolve the paradox of the widespread spatial distribution of reactants and products of infiltration-driven decarbonation/dehydration reactions in regional metamorphic terrains (which in the absence of solid solution and compositional domains indicate up-temperature flow) and the prediction of hydrodynamic models that regional metamorphic fluid flow normally is directed vertically upward and down temperature.     

Influence of overburden pressure and soil rigidity on uplift behavior of square plate anchor in uniform clay

A numerical study incorporating three-dimensional Eulerian large deformation finite element analyses is performed to investigate the pullout process of horizontal square plate anchors in both hypothetical weightless soil and soil with self-weight. The validity of the numerical model is established through verification against published experimental and numerical results. The failure mechanisms during the pullout process under different conditions are then investigated. Three types of failure mechanism are observed; of which only two have been reported in the literature. The third mechanism identified in this study, which is a partially localized flow mechanism, is operative when the soil overburden ratio is not high enough to mobilize the full flow mechanism. The influence of soil self-weight is directly investigated by incorporating the density of the soil in the finite element model and maintaining the gravitational acceleration field throughout the analysis. The critical overburden ratio corresponding to the full transition to a localized plastic flow mechanism is identified in this study. The effect of the soil rigidity index (E/s_u) on the anchor uplift capability has not been systematically investigated in earlier studies. Contrary to the general failure mechanism and the full flow mechanism described in the literature, the capacity factor corresponding to this new mechanism increases with increasing E/s_u. The capacity factors for square plate anchors corresponding to different anchor embedment ratios, overburden ratios and E/s_u are provided in the form of design charts.     

Al,Ge cation ordering in BaAl2Ge2O8-feldspar: monodomain ordering kinetics

The kinetics of monodomain order-disorder processes in monoclinic (I2/c) BaAl₂Ge₂O₈-feldspar have been investigated by X-ray powder diffraction, Hard Mode IR Spectroscopy, and TEM darkfield imaging on quenched samples. Compared to the behaviour predicted by the TDGL approximation ordering kinetics observed at low temperatures slow down significantly when equilibrium is approached. Such a delay is not observed in disordering experiments starting from essentially ordered cation distributions. The deviation from TDGL behaviour is interpreted in terms of partial order parameter conservation in a non-uniformly ordered phase. Modifications to the uniform TDGL rate equation are tested against the available data. An activation energy of 352 ± 28 kJ/mol is obtained for Al,Ge ordering. The mixing coefficient ξ_c ²/ξ², which describes the degree of order parameter conservation, is obtained as a function of temperature. While this coefficient vanishes in the vicinity of the transformation temperature T _tr, it saturates towards a level of ξ_c ²/ξ²≈0.4 for T→0. ξ _c ²/ξ² determines the kinetic stability of ordered clusters quenched from T≈T _tr. Received: 21 April 1999 / Revised, accepted: 19 July 1999     

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (ξ_γ) is determined. On account of interference, the magnitude of ξ_γ is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.     

Seismic interference of two nearby horizontal strip anchors in layered soil

In the present analysis, an attempt is made to explore the seismic response of two nearby horizontal strip anchors embedded in non-homogenous c-? soil deposit at different depths. The analysis is performed by using two-dimensional finite-element software PLAXIS 2D. Each anchor carries equal static safe-working load without violating the ultimate uplift capacity under static condition. The soil is assumed to obey the Mohr?CCoulomb failure criterion. The behavior of single isolated anchor subjected to an earthquake loading is determined first to study the interference effect between two anchors. The horizontal acceleration response obtained from the Loma Prieta Gilroy Earthquake (1989) is considered as the input excitation in the analysis. A parametric study is performed by varying the clear spacing (S) between the anchors at different embedment ratios (??). The magnitude of vertical displacement, shear stress, and shear strain developed at different locations of the failure domain is determined for different clear spacings between the anchors.     

Low-temperature heat capacities,entropies and enthalpies of Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> polymorphs,and α−β−γ and post-spinel phase relations at high pressure

The low-temperature isobaric heat capacities (C _p) of β- and γ-Mg₂SiO₄ were measured at the range of 1.8–304.7 K with a thermal relaxation method using the Physical Property Measurement System. The obtained standard entropies (S°₂₉₈) of β- and γ-Mg₂SiO₄ are 86.4 ± 0.4 and 82.7 ± 0.5 J/mol K, respectively. Enthalpies of transitions among α-, β- and γ-Mg₂SiO₄ were measured by high-temperature drop-solution calorimetry with gas-bubbling technique. The enthalpies of the α−β and β−γ transitions at 298 K (ΔH°₂₉₈) in Mg₂SiO₄ are 27.2 ± 3.6 and 12.9 ± 3.3 kJ/mol, respectively. Calculated α−β and β−γ transition boundaries were generally consistent with those determined by high-pressure experiments within the errors. Combining the measured ΔH°₂₉₈ and ΔS°₂₉₈ with selected data of in situ X-ray diffraction experiments at high pressure, the ΔH°₂₉₈ and ΔS°₂₉₈ of the α−β and β−γ transitions were optimized. Calculation using the optimized data tightly constrained the α−β and β−γ transition boundaries in the P, T space. The slope of α−β transition boundary is 3.1 MPa/K at 13.4 GPa and 1,400 K, and that of β−γ boundary 5.2 MPa/K at 18.7 GPa and 1,600 K. The post-spinel transition boundary of γ-Mg₂SiO₄ to MgSiO₃ perovskite plus MgO was also calculated, using the optimized data on γ-Mg₂SiO₄ and available enthalpy and entropy data on MgSiO₃ perovskite and MgO. The calculated post-spinel boundary with a Clapeyron slope of −2.6 ± 0.2 MPa/K is located at pressure consistent with the 660 km discontinuity, considering the error of the thermodynamic data.     

Upper bound limit analysis for finding interference effect of two nearby strip footings on sand

The ultimate bearing capacity of two closely spaced strip footings, placed on a cohesionless medium and loaded simultaneously to failure at the same magnitude of failure load, was determined by using an upper bound limit analysis. A logarithmic spiral radial shear zone, comprising of a number of triangular rigid blocks, was assumed to exist around each footing edge. The equations of the logarithmic spiral arcs were based on angles φ_L and φ_R rather than soil friction angle φ; the values of φ_L and φ_R were gradually varied in between 0 and φ. The ultimate bearing capacity was found to become maximum corresponding to a certain critical spacing between the footings. For spacing greater than the critical, the bearing capacity was found to decrease continuously with increase in the spacing. The extent of the spacing corresponding to which the ultimate bearing capacity becomes either maximum or equal to that of a single isolated footing increases with increase in φ. The results compare reasonably well with the available theoretical and experimental data.     

Pullout resistance of single vertical shallow helical and plate anchors in sand

This paper presents analytical models to predict the pullout capacity and the load–displacement relationship for shallow single vertical helical and plate anchors in sand. The models were developed based on the failure mechanism deduced from laboratory testing and utilize the limit equilibrium technique. Expression was given to estimate the critical depth for a given anchor/soil conditions, which separates deep from shallow anchors. Furthermore, the radius of influence of a individual anchor on the ground surface is established, and accordingly, the spacing between anchors can be determined to avoid anchors interactions between anchors. The proposed theory compared well with the theories and the experimental data available in the literature.

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Résumé Cet article présente un model analytique pour prédire la résistance à l’arrachement et la relation charge-diplacement pour les ancrages à vis et plats verticaux superficiels ancrés dans le sable. Le model est basé sur le mécanisme de rupture déduit des essais de laboratoire et utilise la méthode d’analyse à l’équilibre limite. En outre, une expression a été proposé pour éstimer la profondeur critique pour un ancrage donné permettant d’identifier l’ancrage comme superficiel ou profond. Le rayon d’influence d’un ancrage à la surface du sable autour de l’ancrage a été établi, et par conséquent, l’espacement entre ancrages peut être déterminer pour éviter toute interaction. La théorie proposée montre une bonne concordance avec des résultats theoriques et expérimentaux rapports dans la literature.

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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     

Interference effect of two nearby strip footings on layered soil: theory of elasticity approach

In recent times, rapid urbanisation coupled with scarcity of land forces several structures to come up ever closer to each other, which may sometime cause severe damage to the structures from both strength and serviceability point of view, and therefore, a need is felt to devise simplified methods to capture the effect of footing interference. In the present study, an attempt has been made to model the settlement behaviour of two strip footings placed in close spacing on layered soil deposit consisting of a strong top layer underlying a weak bottom layer. Theory of elasticity is employed to derive the governing differential equations and subsequently solved by the finite difference method. The perfectly rough strip footings are considered to be resting on the surface of two-layer soil system, and the soil is assumed to behave as linear elastic material under a range of static foundation load. The effect of various parameters such as the elastic moduli and thickness of two layers, clear spacing between the footings and footing load on the settlement behaviour of closely spaced footings has been determined. The variation of vertical normal stress at the interface of two different soil layers as well as at the base of the failure domain also forms an important part of this study. The results are presented in terms of settlement ratio (ξ_δ), and their variation is obtained with the change in clear spacing between two footings. The present theoretical investigation indicates that the settlement of closely spaced footings is found to be higher than that of single isolated footing, which further reduces with increase in the spacing between the footings.