Vertical uplift resistance of circular plate anchors in clays under undrained condition

The vertical uplift resistance of circular plate anchors, embedded horizontally in a clayey stratum whose cohesion increases linearly with depth, has been obtained under undrained ( = 0) condition. The axi-symmetric static limit analysis formulation in combination with finite elements proposed recently by the authors has been employed. The variation of the uplift factor (F_c) with changes in the embedment ratio (H/B) has been computed for several rates of increases of soil cohesion with depth. It is noted that in all the cases, the magnitude of F_c increases continuously with depth up to a certain value of H_cr/B beyond which the uplift factor becomes essentially constant. The proposed static limit analysis formulation is seen to provide acceptable results even for the two other simple chosen axi-symmetric problems.     

Performance of embankments with rigid columns embedded in an inclined underlying stratum: centrifuge and numerical modelling

Rigid columns penetrating a firm underlying stratum have often been used to enhance the stability and improve the settlement of embankments over soft ground. Furthermore, an inclined underlying stratum is commonly encountered in engineering practice. This investigation experimentally and numerically studies the performance of embankments over soft ground reinforced by rigid columns with various embedment depths. In centrifuge tests, a tilting failure occurs for columns with an embedment depth L_e of 2D (D is the diameter of columns), whereas the embankments remain stable for L_e of 7D. This result indicates that the inclined underlying stratum weakens the restraint effect at the column base and that a greater embedment depth is required to ensure the stability of embankments. Parametric studies numerically reveal that there exists a critical embedment depth, which represents a shift in the failure mechanism. The optimum column layout is determined based on the contributions of columns in different locations beneath an embankment. Finally, the influence of the embedment depth on the distribution of the bending moment of the columns and the soil reaction are discussed.

     

Effect of Slope on <Emphasis Type="Italic">p</Emphasis>-<Emphasis Type="Italic">y</Emphasis> Curves for Laterally Loaded Piles in Soft Clay

Pile foundations are often subject to lateral loading due to various forces on a variety of structures like high rise buildings, transmission towers, power stations, offshore structures and highway and railway structures. The present investigation is to study the effect of slopes on p-y curves (where p is the static soil reaction and y is the pile deflection) due to static lateral loading in soft clay (Consistency index I_c = 0.42). A series of laboratory model tests were carried out on the instrumented model pile on sloping ground (slopes of 1V:1H, 1V:1.5H, 1V:2H, 1V:3H and 1V:5H) and with varying embedment length to diameter ratio (L/D) of 20, 25 and 30. From the experimental results, the bending moment curves along the pile shaft are double differentiated to obtain the soil resistance (p) and double integrated to obtain the deflection (y) using curve fitting method. New p-y curves for piles located on crest of soft clay with different sloping ground surface under static lateral loading are developed. Moreover, the effect of sloping angles on proposed p-y curves was studied.     

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.     

Stability of long circular tunnels in sloping ground

Assessment of tunnel stability has become increasingly crucial as more and more tunnels are built in difficult terrains such as sloping ground. The required support pressure on the tunnel walls associates both tunnel stability and liner design considerations. The present analysis attempts to find a uniform internal pressure which can support a circular tunnel built in a sloping ground with a particular level of stability in cohesive-frictional soils. The lower bound finite element limit analysis has been applied to find the required minimum uniform internal support pressure presented as a non-dimensional term p/c; where p is the minimum normal internal pressure on the tunnel boundary to avoid collapse and c is the cohesion of soil. The variation of p/c is presented for a range of normalised embedment depth of tunnel (H/D), stability number (γD/c), internal friction angle of soil (?) and slope angle (β); where H is the crown depth of the tunnel, D is the tunnel diameter and γ is the unit weight of soil. Appropriate comparisons have been carried out with available literature. Failure patterns of the tunnel have also been studied to understand the extent and the type of failure zone which may generate during the collapse.     

Observed and predicted test pile behaviour

The results obtained from a loading test on a bored, cast-in-place pile instrumented with six pairs of load cells at different levels are compared with the results obtained from a non-linear finite element analysis based on the geotechnical parameters of the cohesive soils in which the pile was bored. Settlements computed using deformability parameters obtained by a standard laboratory test were much larger than the measured settlements. Satisfactory results are instead obtained assuming E_i=1000c_u and c_α=c_u. The distribution of the vertical stresses within the pile and of the shear stresses in the soil adjacent to the pile obtained by the numerical analysis are compared with the measured values. A fair agreement is found at loads below failure but differences between experimental and computed values are found at loads close to failure.     

On the Study of Pile Driving Formula Based on Blow Counts

Accuracy of predicting pile capacities by pile driving formulas have been investigated. Five test piles were driven up to a depth of about 9 m of clay deposit and the penetrations due to final blows were recorded. The pile bearing capacity of each pile was predicted using 6 different pile driving formulas and the predicted pile capacity was compared with measured pile capacity from the pull up tests. Hiley formula, Modified Engineering News Record (ENR) formula, Janbu formula, Dutch formula, Danish formula, and Gates formula were used. The performance and accuracy of each formula was evaluated and the correlation coefficient of each pile driving formula was determined for a more accurate pile capacity prediction. Methods used to evaluate the performance of each formula were; (1) the best fit line for Q _p versus Q _m (2) cumulative probability for Q _p/Q _m and (3) the arithmetic mean and standard deviation for Q _p/Q _m. From the study, it was found that using Dutch formula provided the most accurate pile capacity estimate compared to the other formulas with an average of 7% deviation from value obtained from the field pull up test. It was followed by the Danish formula, Janbu formula, Hiley formula, Modified ENR formula, and Gates formula. The ability to predict the accuracy of estimating pile capacity using an appropriate method is very important and valuable to contractors, developers, geotechnical engineers, and manufacturers.     

Interpretation of load tests on bored piles in the city of Matera

This paper briefly reviews several calculation methods to evaluate the bearing capacity expressed in terms of undrained strength (c_u) of piles bored in clay for their entire length and of piles whose tip is embedded into weak rock. The scope of the paper is to compare the results obtained with those from full-scale pile tests. These tests were carried out within the city of Matera which is well studied from a geotechnical point of view and for which there are statistically significant data on the geomechanical properties of the Subapennine Blue clays and the underlying Gravina Calcarenites. This represents the first attempt to show, on the basis of laboratory and field data, the influence of variability of the above mentioned soils and rocks on the real behaviour of deep foundations.For piles completely bored into Matera clay, the calculation in terms of total stress are able to interpret sufficiently well the bearing capacity of the piles. For piles having their toe embedded in calcarenite, the variability of the strength of the weak rock presents greater uncertainties in the calculation of base and soft resistance.     

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 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.     

Response of rigid piles during passive dragging

This paper develops a three‐layer model and elastic solutions to capture nonlinear response of rigid, passive piles in sliding soil. Elastic solutions are obtained for an equivalent force per unit length p_s of the soil movement. They are repeated for a series of linearly increasing p_s (with depth) to yield the nonlinear response. The parameters underpinning the model are determined against pertinent numerical solutions and model tests on passive free‐head and capped piles. The solutions are presented in non‐dimensional charts and elaborated through three examples. The study reveals the following:

• On‐pile pressure in rotationally restrained, sliding layer reduces by a factor α, which resembles the p‐multiplier for a laterally loaded, capped pile, but for its increase with vertical loading (embankment surcharge), and stiffness of underlying stiff layer: α = 0.25 and 0.6 for a shallow, translating and rotating piles, respectively; α = 0.33–0.5 and 0.8–1.3 for a slide overlying a stiff layer concerning a uniform and a linearly increasing pressure, respectively; and α = 0.5–0.72 for moving clay under embankment loading.
• Ultimate state is well defined using the ratio of passive earth pressure coefficient over that of active earth pressure. The subgrade modulus for a large soil movement may be scaled from model tests.
• The normalised rotational stiffness is equal to 0.1–0.15 for the capped piles, which increases the pile displacement with depth.

The three‐layer model solutions well predict nonlinear response of capped piles subjected to passive loading, which may be used for pertinent design. Copyright © 2016 John Wiley & Sons, Ltd.     

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 rectangular footings in uniform clay with deep embedment

This letter is concerned with the undrained bearing capacity of rectangular footings with various aspect ratios and embedment ratios in uniform clay. It covers thin plate foundations with low aspect ratios and high embedment depth with embedment ratio up to 150. The work is based on small strain finite element analysis (FEA). After verification of the FEA model against existing solutions of the bearing capacity factors of rectangular footings, a series of FEA results are obtained. Based on the FEA results, a simple formulation is proposed to calculate the bearing capacity factor for rectangle footing with different aspect ratio in any embedment depth, extending the existing solutions to cover a wider ranges of footing aspect ratios and embedment ratios.     

Analysis of compressible axially loaded piles in rock

Analytical solutions are developed for the prediction of the load–settlement response of a compressible axially loaded cast in situ pile in rock. The principal input parameters are derived from the τ–z curve which applies to the contact zone between the pile shaft and the embedment material. For larger diameter piles in rock, these τ–z curves can differ markedly from curves that apply to piles in clay and may include a significant strain hardening region prior to reaching peak strength. In addition to the complete analyses which would normally require the use of a computer, simplified solutions suitable for hand calculations have been derived for the peak load and the pile head displacement to peak. An example of the application of these simplified design calculations is presented.     

Stability of an unsupported vertical circular excavation in clays under undrained condition

By using the axisymmetric finite elements static limit analysis formulation, proposed recently by the authors, the stability numbers (γH/c_o) for an unsupported vertical circular excavation in clays, whose cohesion increases with depth, have been determined under undrained condition; γ = unit weight, H = height of the excavation and c_o = cohesion along ground surface. The results are obtained for various values of H/b and m; where b = the radius of the excavation and m = a non-dimensional parameter which accounts for the rate of the increase of cohesion with depth. The values of the stability numbers increase continuously both with increases in H/b and m. The results obtained in this study compare well with those available in literature.     

Load–Deflection response of transversely isotropic piles under lateral loads

In general, pile materials are assumed to be isotropic during the analysis of the load–deflection response of piles under lateral loads. However, commonly used materials such as reinforced concrete and timber as well as potentially promising new pile materials such as fiber reinforced polymers are typically transversely isotropic materials. Experimental studies have shown that transversely isotropic materials have a high ratio of section longitudinal modulus to the section in‐plane shear modulus (E_zz/G_xz) compared to the value for isotropic materials. The high modulus ratio leads to a more significant shear deformation effect in beam bending. To account for the shear deformation effect, the Timoshenko Beam Theory has been adopted in deriving the solutions for the load–deflection response of transversely isotropic piles under lateral loads instead of the Classical (Euler–Bernoulli) Beam Theory. The load–deflection responses depend on the shear effect coefficient, the lateral soil resistance, the embedment ratio, and the boundary conditions. The deflection of the pile, if the shear deformation effect is considered, is always larger than if it is neglected. Copyright © 2000 John Wiley & Sons, Ltd.     

A comparison between Shields' threshold criterion and the movement of loosely packed gravel in a tidal channel

Observations of the threshold of movement of loosely packed gravel in a tidal current are described. For gravel with equivalent ‘spherical’ diameters D in the range 0.2 ?D? 5.0cm the critical friction velocity u*_c, corresponding to the initiation of sediment transport, is given by u*_c=7.0 D^0.2. At large values of D within the quoted range, the value u*_c is significantly lower than would be obtained by a Shields experiment (u*_c∞D^0.5). By comparing our values of u*_c with those obtained under well-controlled laboratory conditions, the discrepancy with Shields is shown to be due to the open spacing between, and exposure of, individual pebbles on the seabed. By comparing our results with those from upland gravel streams and flume experiments, it is suggested that Shields assumed an excessively large water depth to particle size ratio as a constraint within which the critical sediment entrainment number 0_c is valid.     

Shaft and base resistance of non-displacement piles in sand

This paper presents the results of three-dimensional, finite element analyses performed with an advanced, two-surface-plasticity, constitutive sand model to investigate the response of non-displacement piles to axial loading. The analysis domain is carefully meshed such that the formation and evolution of shear bands next to the pile shaft and near the pile base can be properly captured. Analyses considering various soil profiles and pile geometries show that the mobilized lateral earth pressure coefficient K along the pile shaft increases with increasing relative density and decreasing initial confining stress. The ultimate unit base resistance is independent of pile diameter, increasing with increasing relative density and increasing initial confining stress at the pile base. Based on the analysis results, design equations are proposed to estimate the limit shaft resistance and ultimate base resistance of non-displacement piles in sandy soil. In proposing these relationships, the pile slenderness ratio is considered. The effect of layer proximity to the base of the pile or pile base embedment in a layer is also considered.     

Site characterization model using least‐square support vector machine and relevance vector machine based on corrected SPT data (Nc)

Statistical learning algorithms provide a viable framework for geotechnical engineering modeling. This paper describes two statistical learning algorithms applied for site characterization modeling based on standard penetration test (SPT) data. More than 2700 field SPT values (N) have been collected from 766 boreholes spread over an area of 220 sqkm area in Bangalore. To get N corrected value (N_c), N values have been corrected (N_c) for different parameters such as overburden stress, size of borehole, type of sampler, length of connecting rod, etc. In three‐dimensional site characterization model, the function N_c=N_c (X, Y, Z), where X, Y and Z are the coordinates of a point corresponding to N_c value, is to be approximated in which N_c value at any half‐space point in Bangalore can be determined. The first algorithm uses least‐square support vector machine (LSSVM), which is related to a ridge regression type of support vector machine. The second algorithm uses relevance vector machine (RVM), which combines the strengths of kernel‐based methods and Bayesian theory to establish the relationships between a set of input vectors and a desired output. The paper also presents the comparative study between the developed LSSVM and RVM model for site characterization. Copyright © 2009 John Wiley & Sons, Ltd.