Search results for: strip footing
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 233

Search results for: strip footing

233 The Effect of Jet Grouting on the Behavior of Strip Footing Adjacent to Slope Crest

Authors: Ahmed M. El-Tuhami, Ahmed A. Mohamed

Abstract:

This paper studies the behavior of strip footing adjacent to slope crest and the effect of jet grouting under the footing. This problem is investigated numerically in the present study. Two dimensional plane strain program PLAXIS is used in this study. 15 nodes triangular element is used to idealize soil with hardening soil model. Five nodes isoperimetric beam element is used to idealize stripe footing. Interface element is used to represent the contact between beam element and soil. Two parameters were studied, the first is the foundation depth and the second is the Stripe footing distance from the slope crest. Settlement and horizontal displacement of strip footing were obtained and studied from the analyzed finite element model results. The reduction influence of jet grouting on footing displacement were studied and investigated. The results indicate that the inclusion of jet grouting under strip footing adjacent to slope crest has significant effect in improving the response of the strip footing and the slope.

Keywords: strip footing, jet grouting, slope, PLAXIS, relative distance

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232 Effect of Cavities on the Behaviour of Strip Footing Subjected to Inclined Load

Authors: Ali A. Al-Jazaairry, Tahsin T. Sabbagh

Abstract:

One of the important concerns within the field of geotechnical engineering is the presence of cavities in soils. This present work is an attempt to understand the behaviour of strip footing subjected to inclined load and constructed on cavitied soil. The failure mechanism of strip footing located above such soils was studied analytically. The capability of analytical model to correctly expect the system behaviour is assessed by carrying out verification analysis on available studies. The study was prepared by finite element software (PLAXIS) in which an elastic-perfectly plastic soil model was used. It was indicated, from the results of the study, that the load carrying capacity of foundation constructed on cavity can be analysed well using such analysis. The research covered many foundation cases, and in each foundation case, there occurs a critical depth under which the presence of cavities has shown minimum impact on the foundation performance. When cavities are found above this critical depth, the load carrying capacity of the foundation differs with many influences, such as the location and size of the cavity and footing depth. Figures involving the load carrying capacity with the affecting factors studied are presented. These figures offer information beneficial for the design of strip footings rested on underground cavities. Moreover, the results might be used to design a shallow foundation constructed on cavitied soil, whereas the obtained failure mechanisms may be employed to improve numerical solutions for this kind of problems.

Keywords: axial load, cavity, inclined load, strip footing

Procedia PDF Downloads 255
231 Application of Particle Image Velocimetry in the Analysis of Scale Effects in Granular Soil

Authors: Zuhair Kadhim Jahanger, S. Joseph Antony

Abstract:

The available studies in the literature which dealt with the scale effects of strip footings on different sand packing systematically still remain scarce. In this research, the variation of ultimate bearing capacity and deformation pattern of soil beneath strip footings of different widths under plane-strain condition on the surface of loose, medium-dense and dense sand have been systematically studied using experimental and noninvasive methods for measuring microscopic deformations. The presented analyses are based on model scale compression test analysed using Particle Image Velocimetry (PIV) technique. Upper bound analysis of the current study shows that the maximum vertical displacement of the sand under the ultimate load increases for an increase in the width of footing, but at a decreasing rate with relative density of sand, whereas the relative vertical displacement in the sand decreases for an increase in the width of the footing. A well agreement is observed between experimental results for different footing widths and relative densities. The experimental analyses have shown that there exists pronounced scale effect for strip surface footing. The bearing capacity factors rapidly decrease up to footing widths B=0.25 m, 0.35 m, and 0.65 m for loose, medium-dense and dense sand respectively, after that there is no significant decrease in . The deformation modes of the soil as well as the ultimate bearing capacity values have been affected by the footing widths. The obtained results could be used to improve settlement calculation of the foundation interacting with granular soil.

Keywords: DPIV, granular mechanics, scale effect, upper bound analysis

Procedia PDF Downloads 152
230 Influence Zone of Strip Footing on Untreated and Cement Treated Sand Mat Underlain by Soft Clay (2nd reviewed)

Authors: Sharifullah Ahmed

Abstract:

Shallow foundation on soft soils without ground improvement can represent a high level of settlement. In such a case, an alternative to pile foundations may be shallow strip footings placed on a soil system in which the upper layer is untreated or cement-treated compacted sand to limit the settlement within a permissible level. This research work deals with a rigid plane-strain strip footing of 2.5m width placed on a soil consisting of untreated or cement treated sand layer underlain by homogeneous soft clay. Both the thin and thick compared the footing width was considered. The soft inorganic cohesive NC clay layer is considered undrained for plastic loading stages and drained in consolidation stages, and the sand layer is drained in all loading stages. FEM analysis was done using PLAXIS 2D Version 8.0 with a model consisting of clay deposits of 15m thickness and 18m width. The soft clay layer was modeled using the Hardening Soil Model, Soft Soil Model, Soft Soil Creep model, and the upper improvement layer was modeled using only the Hardening Soil Model. The system is considered fully saturated. The value of natural void ratio 1.2 is used. Total displacement fields of strip footing and subsoil layers in the case of Untreated and Cement treated Sand as Upper layer are presented. For Hi/B =0.6 or above, the distribution of major deformation within an upper layer and the influence zone of footing is limited in an upper layer which indicates the complete effectiveness of the upper layer in bearing the foundation effectively in case of the untreated upper layer. For Hi/B =0.3 or above, the distribution of major deformation occurred within an upper layer, and the function of footing is limited in the upper layer. This indicates the complete effectiveness of the cement-treated upper layer. Brittle behavior of cemented sand and fracture or cracks is not considered in this analysis.

Keywords: displacement, ground improvement, influence depth, PLAXIS 2D, primary and secondary settlement, sand mat, soft clay

Procedia PDF Downloads 93
229 Design Charts for Strip Footing on Untreated and Cement Treated Sand Mat over Underlying Natural Soft Clay

Authors: Sharifullah Ahmed, Sarwar Jahan Md. Yasin

Abstract:

Shallow foundations on unimproved soft natural soils can undergo a high consolidation and secondary settlement. For low and medium rise building projects on such soil condition, pile foundation may not be cost effective. In such cases an alternative to pile foundations may be shallow strip footings placed on a double layered improved soil system soil. The upper layer of this system is untreated or cement treated compacted sand and underlying layer is natural soft clay. This system will reduce the settlement to an allowable limit. The current research has been conducted with the settlement of a rigid plane-strain strip footing of 2.5 m width placed on the surface of a soil consisting of an untreated or cement treated sand layer overlying a bed of homogeneous soft clay. The settlement of the mentioned shallow foundation has been studied considering both cases with the thicknesses of the sand layer are 0.3 to 0.9 times the width of footing. The response of the clay layer is assumed as undrained for plastic loading stages and drained during consolidation stages. The response of the sand layer is drained during all loading stages. FEM analysis was done using PLAXIS 2D Version 8.0. A natural clay deposit of 15 m thickness and 18 m width has been modeled using Hardening Soil Model, Soft Soil Model, Soft Soil Creep Model, and upper improvement layer has been modeled using only Hardening Soil Model. The groundwater level is at the top level of the clay deposit that made the system fully saturated. Parametric study has been conducted to determine the effect of thickness, density, cementation of the sand mat and density, shear strength of the soft clay layer on the settlement of strip foundation under the uniformly distributed vertical load of varying value. A set of the chart has been established for designing shallow strip footing on the sand mat over thick, soft clay deposit through obtaining the particular thickness of sand mat for particular subsoil parameter to ensure no punching shear failure and no settlement beyond allowable level. Design guideline in the form of non-dimensional charts has been developed for footing pressure equivalent to medium-rise residential or commercial building foundation with strip footing on soft inorganic Normally Consolidated (NC) soil of Bangladesh having void ratio from 1.0 to 1.45.

Keywords: design charts, ground improvement, PLAXIS 2D, primary and secondary settlement, sand mat, soft clay

Procedia PDF Downloads 123
228 Effect of Reinforcement Density on the Behaviour of Reinforced Sand Under a Square Footing

Authors: Dhyaalddin Bahaalddin Noori Zangana

Abstract:

This study involves the behavior of reinforced sand under a square footing. A series of bearing capacity tests were performed on a small-scale laboratory model, which filled with a poorly-graded homogenous bed of sand, which was placed in a medium dense state using sand raining technique. The sand was reinforced with 40 mm wide household aluminum foil strips. The main studied parameters was to consider the effect of reinforcing strip length, with various linear density of reinforcement, number of reinforcement layers and depth of top layer of reinforcement below the footing, on load-settlement behavior, bearing capacity ratio and settlement reduction factor. The relation of load-settlement generally showed similar trend in all the tests. Failure was defined as settlement equal to 10% of the footing width. The recommended optimum reinforcing strip length, linear density of reinforcement, number of reinforcement layers and depth of top layer of reinforcing strips that give the maximum bearing capacity improvement and minimum settlement reduction factor were presented and discussed. Different bearing capacity ration versus length of the reinforcing strips and settlement reduction factor versus length of the reinforcing strips relations at failure were showed improvement of bearing capacity ratio by a factor of 3.82 and reduction of settlement reduction factor by a factor of 0.813. The optimum length of reinforcement was found to be 7.5 times the footing width.

Keywords: square footing, relative density, linear density of reinforcement, bearing capacity ratio, load-settlement behaviour

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227 Punching Shear Behavior of RC Column Footing on Stabilized Ground

Authors: Sukanta K. Shill, Md. M. Hoque, Md. Shaifullah

Abstract:

An experiment on the punching of RC column footing, comparison of test result to established different codes for punching shear calculation of column footings is presented in the paper. The principal aim of this study is to investigate the punching shear behavior of an isolated column footing using brick aggregate as coarse aggregate. Consequence, a RC model footing was constructed on a stabilized soil and tested the footing under field condition. The test result yields that the experimental punching shear capacity is greater than all the theoretical punching shear capacities obtained by using different codes of practices. It can be stated that BNBC 1993, as well as ACI 318, 2002 code formulae are very conservative in predicting the punching shear resistance of RC footing, whereas the CEB-FIP MC, 1990 formula and Eurocode2 formula are less conservative in predicting the punching shear resistance of footing.

Keywords: footing, punching shear, field condition, stabilized soil, brick aggregate

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226 Displacement Fields in Footing-Sand Interactions under Cyclic Loading

Authors: S. Joseph Antony, Z. K. Jahanger

Abstract:

Soils are subjected to cyclic loading in situ in situations such as during earthquakes and in the compaction of pavements. Investigations on the local scale measurement of the displacements of the grain and failure patterns within the soil bed under the cyclic loading conditions are rather limited. In this paper, using the digital particle image velocimetry (DPIV), local scale displacement fields of a dense sand medium interacting with a rigid footing are measured under the plane-strain condition for two commonly used types of cyclic loading, and the quasi-static loading condition for the purposes of comparison. From the displacement measurements of the grains, the failure envelopes of the sand media are also presented. The results show that, the ultimate cyclic bearing capacity (qultcyc) occurred corresponding to a relatively higher settlement value when compared with that of under the quasi-static loading. For the sand media under the cyclic loading conditions considered here, the displacement fields in the soil media occurred more widely in the horizontal direction and less deeper along the vertical direction when compared with that of under the quasi-static loading. The 'dead zone' in the sand grains beneath the footing is identified for all types of the loading conditions studied here. These grain-scale characteristics have implications on the resulting bulk bearing capacity of the sand media in footing-sand interaction problems.

Keywords: cyclic loading, DPIV, settlement, soil-structure interactions, strip footing

Procedia PDF Downloads 167
225 The Effect of Geogrid Reinforcement Pre-Stressing on the Performance of Sand Bed Supporting a Strip Foundation

Authors: Ahmed M. Eltohamy

Abstract:

In this paper, an experimental and numerical study was adopted to investigate the effect geogrid soil reinforcement pre-stressing on the pressure settlement relation of sand bed supporting a strip foundation. The studied parameters include foundation depth and pre-stress ratio for the cases of one and two pre-stressed reinforcement layers. The study reflected that pre-stressing of soil reinforcement resulted in a marked enhancement in reinforced bed soil stiffness compared to the reinforced soil without pre-stress. The best benefit of pre-stressing reinforcement was obtained as the overburden pressure and pre-straining ratio increase. Pre-stressing of double reinforcement topmost layers results in further enhancement of stress strain relation of bed soil.

Keywords: geogrid reinforcement, prestress, strip footing, bearing capacity

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224 Study of the Behavior of Geogrid Mechanically Stabilized Earth Walls Under Cyclic Loading

Authors: Yongzhe Zhao, Ying Liu, Zhiyong Liu, Hui You

Abstract:

The soil behind retaining wall is normally subjected to cyclic loading, for example traffic loading. Geotextile has been widely used to reinforce the soil for the purpose of reducing the settlement of the soil. A series of physical model tests were performed to investigate the settlement of footing under cyclic loading. The settlement of the footing, ground deformation and the vertical earth pressure in subsoil were presented and discussed under different types of geotextiles. The results indicate that including geotextiles significantly decreases the footing settlement and the stiffer the geotextile, the less the settlement. Under cyclic loading, the soil below the footing shows dilation within certain depths and beyond that it experiences contraction. The location of footing relative to the retaining wall has important effects on the deformation behavior of the soil in the ground, and the closer the footing to the retaining wall, the greater the contraction soil shows. This is because the retaining wall experienced greater lateral displacement.

Keywords: physical model tests, reinforced retaining wall, cyclic loading, footing

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223 Numerical Modeling of Geogrid Reinforced Soil Bed under Strip Footings Using Finite Element Analysis

Authors: Ahmed M. Gamal, Adel M. Belal, S. A. Elsoud

Abstract:

This article aims to study the effect of reinforcement inclusions (geogrids) on the sand dunes bearing capacity under strip footings. In this research experimental physical model was carried out to study the effect of the first geogrid reinforcement depth (u/B), the spacing between the reinforcement (h/B) and its extension relative to the footing length (L/B) on the mobilized bearing capacity. This paper presents the numerical modeling using the commercial finite element package (PLAXIS version 8.2) to simulate the laboratory physical model, studying the same parameters previously handled in the experimental work (u/B, L/B & h/B) for the purpose of validation. In this study the soil, the geogrid, the interface element and the boundary condition are discussed with a set of finite element results and the validation. Then the validated FEM used for studying real material and dimensions of strip foundation. Based on the experimental and numerical investigation results, a significant increase in the bearing capacity of footings has occurred due to an appropriate location of the inclusions in sand. The optimum embedment depth of the first reinforcement layer (u/B) is equal to 0.25. The optimum spacing between each successive reinforcement layer (h/B) is equal to 0.75 B. The optimum Length of the reinforcement layer (L/B) is equal to 7.5 B. The optimum number of reinforcement is equal to 4 layers. The study showed a directly proportional relation between the number of reinforcement layer and the Bearing Capacity Ratio BCR, and an inversely proportional relation between the footing width and the BCR.

Keywords: reinforced soil, geogrid, sand dunes, bearing capacity

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222 Effect of Footing Shape on Bearing Capacity and Settlement of Closely Spaced Footings on Sandy Soil

Authors: A. Shafaghat, H. Khabbaz, S. Moravej, Ah. Shafaghat

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The bearing capacity of closely spaced shallow footings alters with their spacing and the shape of footing. In this study, the bearing capacity and settlement of two adjacent footings constructed on a sand layer are investigated. The effect of different footing shapes including square, circular, ring and strip on sandy soil is captured in the calculations. The investigations are carried out numerically using PLAXIS-3D software and analytically employing conventional settlement equations. For this purpose, foundations are modelled in the program with practical dimensions and various spacing ratios ranging from 1 to 5. The spacing ratio is defined as the centre-to-centre distance to the width of foundations (S/B). Overall, 24 models are analyzed; and the results are compared and discussed in detail. It can be concluded that the presence of adjacent foundation leads to the reduction in bearing capacity for round shape footings while it can increase the bearing capacity of rectangular footings in some specific distances.

Keywords: bearing capacity, finite element analysis, loose sand, settlement equations, shallow foundation

Procedia PDF Downloads 256
221 Influence of Intermediate Principal Stress on Solution of Planar Stability Problems

Authors: M. Jahanandish, M. B. Zeydabadinejad

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In this paper, von Mises and Drucker-Prager yield criteria, as typical ones that consider the effect of intermediate principal stress σ2, have been selected and employed for investigating the influence of σ2 on the solution of a typical stability problem. The bearing capacity factors have been calculated under plane strain condition (strip footing) and axisymmetric condition (circular footing) using the method of stress characteristics together with the criteria mentioned. Different levels of σ2 relative to the other two principal stresses have been considered. While a higher σ2 entry in yield criterion gives a higher bearing capacity; its entry in equilibrium equations (axisymmetric) causes substantial reduction.

Keywords: intermediate principal stress, plane strain, axisymmetric, yield criteria

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220 Effect of Slope Height and Horizontal Forces on the Bearing Capacity of Strip Footings near Slopes in Cohesionless Soil

Authors: Sven Krabbenhoft, Kristian Krabbenhoft, Lars Damkilde

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The problem of determining the bearing capacity of a strip foundation located near a slope of infinite height has been dealt with by several authors. Very often in practical problems the slope is of limited height, and furthermore the resulting load may be inclined at an angle to the horizontal, and in such cases the bearing capacity of the footing cannot be found using the existing methods. The present work comprises finite element based upper- and lower-bound calculations, using the geotechnical software OptumG2 to investigate the effect of the slope height and horizontal forces on the total bearing capacity, both without and with using superposition as presupposed in the traditional bearing capacity equation. The results for friction angles 30, 35 and 40 degrees, slope inclinations 1:2, 1:3 and 1:4, for selfweight and surcharge are given as charts showing the slope inclination factors suitable for design.

Keywords: footings, bearing capacity, slopes, cohesionnless soil

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219 Advanced Approach to Analysis the Thin Strip Profile in Cold Rolling of Pair Roll Crossing and Shifting Mill Using an Arbitrary Lagrangian-Eulerian Technique

Authors: Abdulrahman Aljabri, Essam R. I. Mahmoud, Hamad Almohamedi, Zhengyi Jiang

Abstract:

Cold rolled thin strip has received intensive attention through technological and theoretical progress in the rolling process, as well as researchers have focused on its control during rolling as an essential parameter for producing thinner strip with good shape and profile. An advanced approach has been proposed to analysis the thin strip profile in cold rolling of pair roll crossing and shifting mill using Finite Element Analysis (FEA) with an ALE technique. The ALE (Arbitrary Lagrangian-Eulerian) techniques to enable more flexibility of the ALE technique in the adjustment of the finite element mesh, which provides a significant tool for simulating the thin strip under realistic rolling process constraint and provide accurate model results. The FEA can provide theoretical basis for the 3D model of controlling the strip shape and profile in thin strip rolling, and deliver an optimal rolling process parameter, and suggest corrective changes during cold rolling of thin strip.

Keywords: pair roll crossing, work roll shifting, strip shape and profile, finite element modeling

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218 Influence of Footing Offset over Stability of Geosynthetic Reinforced Soil Abutments with Variable Facing under Lateral Excitation

Authors: Ashutosh Verma, Satyendra MIttal

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The loss of strength at the facing-reinforcement interface brought on by the seasonal thermal expansion/contraction of the bridge deck has been responsible for several geosynthetic reinforced soil abutment failures over the years. This results in excessive settlement below the bridge seat, which results in bridge bumps along the approach road and shortens abutment's design life. There are surely a wide variety of facing configurations available to designers when choosing the sort of facade. These layouts can generally be categorised into three groups: continuous, full height rigid (FHR) and modular (panels/block). The current work aims to experimentally explore the behavior of these three facing categories using 1g physical model testing under serviceable cyclic lateral displacements. With configurable facing arrangements to represent these three facing categories, a field instrumented GRS abutment prototype was modelled into a N scaled down 1g physical model (N = 5) to reproduce field behavior. Peak earth pressure coefficient (K) on the facing and vertical settlement of the footing (s/B) for footing offset (x/H) as 0.1, 0.2, 0.3, 0.4 and 0.5 at 100 cycles have been measured for cyclic lateral displacement of top of facing at loading rate of 1mm/min. Three types of cyclic displacements have been carried out to replicate active condition (CA), passive condition (CP), and active-passive condition (CAP) for each footing offset. The results demonstrated that a significant decrease in the earth pressure over the facing occurs when footing offset increases. It is worth noticing that the highest rate of increment in earth pressure and footing settlement were observed for each facing configuration at the nearest footing offset. Interestingly, for the farthest footing offset, similar responses of each facing type were observed, which indicates that the upon reaching a critical offset point presumably beyond the active region in the backfill, the lateral responses become independent of the stresses from the external footing load. Evidently, the footing load complements the stresses developed due to lateral excitation resulting in significant footing settlements for nearer footing offsets. The modular facing proved inefficient in resisting footing settlement due to significant buckling along the depth of facing. Instead of relative displacement along the depth of facing, continuous facing rotates around the base when it fails, especially for nearer footing offset causing significant depressions in the backfill area surrounding the footing. FHR facing, on the other hand, have been successful in confining the stresses in the soil domain itself reducing the footing settlement. It may be suitably concluded that increasing the footing offset may render stability to the GRS abutment with any facing configuration even for higher cycles of excitation.

Keywords: GRS abutments, 1g physical model, footing offset, cyclic lateral displacement

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217 Numerical Study of Modulus of Subgrade Reaction in Eccentrically Loaded Circular Footing Resting

Authors: Seyed Abolhasan Naeini, Mohammad Hossein Zade

Abstract:

This article is an attempt to present a numerically study of the behaviour of an eccentrically loaded circular footing resting on sand to determine ‎its ultimate bearing capacity. A surface circular footing of diameter 12 cm (D) was used as ‎shallow foundation. For this purpose, three dimensional models consist of foundation, and medium sandy soil was modelled by ABAQUS software. Bearing capacity of footing was evaluated and the ‎effects of the load eccentricity on bearing capacity, its settlement, and modulus of subgrade reaction were studied. Three different values of load eccentricity with equal space from inside the core on the core boundary and outside the core boundary, which were respectively e=0.75, 1.5, and 2.25 cm, were considered. The results show that by increasing the load eccentricity, the ultimate load and the ‎modulus of subgrade reaction decreased.

Keywords: circular foundation, sand, eccentric loading, modulus of subgrade reaction

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216 The Behavior of Polypropylene Fiber Reinforced Sand Loaded by Squair Footing

Authors: Dhiaadin Bahaadin Noory

Abstract:

This research involves the effect of both sizes of reinforced zone and the amount of polypropylene fiber reinforcement on the structural behavior of model-reinforced sand loaded by square footing. The ratio of the side of the square reinforced zone to the footing width (W/B) and the ratio of the square reinforced zone depth to footing width (H/B) has been varied from one to six and from one to three, respectively. The tests were carried out on a small-scale laboratory model in which uniform-graded sand was used as a fill material. It was placed in a highly dense state by hitting a thin wooden board placed on the sand surface with a hammer. The sand was reinforced with randomly oriented discrete fibrillated polypropylene fibers. The test results indicated a significant increase in the bearing capacity and stiffness of the subgrade and a modification of load–the settlement behavior of sand with the size of the reinforced zone and amount of fiber reinforcement. On the basis of the present test results, the optimal side width and depth of the reinforced zone were 4B and 2B, respectively, while the optimal percentage of fibers was 0.4%.

Keywords: square footing, polypropylene fibers, bearing capacity, stiffness, load settlement behavior, relative density

Procedia PDF Downloads 65
215 Evaluation of Stone Column Behavior Strengthened Circular Raft Footing under Static Load

Authors: R. Ziaie Moayed, B. Mohammadi-Haji

Abstract:

Stone columns have been widely employing to improve the load-settlement characteristics of soft soils. The results of two small scale displacement control loading tests on stone columns were used in order to validate numerical finite element simulations. Additionally, a series of numerical calculations of static loading have been performed on strengthened raft footing to investigate the effects of using stone columns on bearing capacity of footings. The bearing capacity of single and group of stone columns under static loading compares with unimproved ground.

Keywords: circular raft footing, numerical analysis, validation, vertically encased stone column

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214 Circular Raft Footings Strengthened by Stone Columns under Dynamic Harmonic Loads

Authors: R. Ziaie Moayed, A. Mahigir

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Stone column technique has been successfully employed to improve the load-settlement characteristics of foundations. A series of finite element numerical analyses of harmonic dynamic loading have been conducted on strengthened raft footing to study the effects of single and group stone columns on settlement of circular footings. The settlement of circular raft footing that improved by single and group of stone columns are studied under harmonic dynamic loading. This loading is caused by heavy machinery foundations. A detailed numerical investigation on behavior of single column and group of stone columns is carried out by varying parameters like weight of machinery, loading frequency and period. The result implies that presence of single and group of stone columns enhanced dynamic behavior of the footing so that the maximum and residual settlement of footing significantly decreased. 

Keywords: finite element analysis, harmonic loading, settlement, stone column

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213 Solution to Riemann Hypothesis Critical Strip Zone Using Non-Linear Complex Variable Functions

Authors: Manojkumar Sabanayagam

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The Riemann hypothesis is an unsolved millennium problem and the search for a solution to the Riemann hypothesis is to study the pattern of prime number distribution. The scope of this paper is to identify the solution for the critical strip and the critical line axis, which has the non-trivial zero solutions using complex plane functions. The Riemann graphical plot is constructed using a linear complex variable function (X+iY) and is applicable only when X>1. But the investigation shows that complex variable behavior has two zones. The first zone is the transformation zone, where the definition of the complex plane should be a non-linear variable which is the critical strip zone in the graph (X=0 to 1). The second zone is the transformed zone (X>1) defined using linear variables conventionally. This paper deals with the Non-linear function in the transformation zone derived using cosine and sinusoidal time lag w.r.t imaginary number ‘i’. The alternate complex variable (Cosθ+i Sinθ) is used to understand the variables in the critical strip zone. It is concluded that the non-trivial zeros present in the Real part 0.5 are because the linear function is not the correct approach in the critical strip. This paper provides the solution to Reimann's hypothesis.

Keywords: Reimann hypothesis, critical strip, complex plane, transformation zone

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212 Numerical Approach for Solving the Hyper Singular Integral Equation in the Analysis of a Central Symmetrical Crack within an Infinite Strip

Authors: Ikram Slamani, Hicheme Ferdjani

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This study focuses on analyzing a Griffith crack situated at the center of an infinite strip. The problem is reformulated as a hyper-singular integral equation and solved numerically using second-order Chebyshev polynomials. The primary objective is to calculate the stress intensity factor in mode 1, denoted as K1. The obtained results reveal the influence of the strip width and crack length on the stress intensity factor, assuming stress-free edges. Additionally, a comparison is made with relevant literature to validate the findings.

Keywords: center crack, Chebyshev polynomial, hyper singular integral equation, Griffith, infinite strip, stress intensity factor

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211 Investigation of Several Parameters on Local Scour around Inclined Dual Bridge Piers

Authors: Murat Çeşme

Abstract:

For a bridge engineer to ensure a safe footing design, it is very important to estimate the maximum scour depth around the piers as accurately as possible. Many experimental studies have been performed by several investigators to obtain information about scouring mechanism. In order to examine the effect of inclination of dual bridge piers on scour depth under clear-water conditions for various uniform flow depths, an experimental research on scaled dual bridge piers has been carried over in METU Hydromechanics Lab. Dimensional and non-dimensional curves were developed and presented to show the variation of scour depth with respect to various parameters such as footing angle with the vertical, flow depth and footing dimensions. Results of the study were compared to those obtained from a similar study performed with single inclined piers to see the effect of the second pier on scour depths. Useful equations for the design engineers were developed based on multiple regression analyses to be used for predicting local scour depths around inclined piers in uniform and non-uniform sediments.

Keywords: experimental research, inclined dual bridge piers, footing safety, scour depth, clear water condition

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210 Design of Soil Replacement under Axial Centric Load Isolated Footing by Limit State Method

Authors: Emad A. M. Osman, Ahmed M. Abu-Bakr

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Compacted granular fill under shallow foundation is one of the oldest, cheapest, and easiest techniques to improve the soil characteristics to increase the bearing capacity and decrease settlement under footing. There are three main factors affecting the design of soil replacement to gain these advantages. These factors are the type of replaced soil, characteristics, and thickness. The first two factors can be easily determined by laboratory and field control. This paper emphasizes on how to determine the thickness accurately for footing under centric axial load by limit state design method. The advantages of the method are the way of determining the thickness (independent of experience) and it takes into account the replaced and original or underneath soil characteristics and reaches the goals of replaced soils economically.

Keywords: design of soil replacement, LSD method, soil replacement, soil improvement

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209 Analysis of the Strip Shape and Microstructure with Consideration of Roll Crossing and Shifting

Authors: Z. Y. Jiang, H. B. Tibar, A. Aljabri

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Optimisation of the physical and mechanical properties of cold rolled thin strips is achieved by controlling the rolling parameters. In this paper, the factors affecting the asymmetrical cold rolling of thin low carbon steel strip have been studied at a speed ratio of 1.1 without lubricant applied. The effect of rolling parameters on the resulting microstructure was also investigated. It was found that under dry condition, work roll shifting and work roll cross angle can improve the strip profile, and the result is more significant with an increase of work roll cross angle rather than that of work roll shifting. However, there was no obvious change in microstructure. In addition, effects of rolling parameters on strip profile and microstructure have also been discussed.

Keywords: rolling speed ratio, microstructure, work roll cross angle, work roll shifting

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208 Cooling Profile Analysis of Hot Strip Coil Using Finite Volume Method

Authors: Subhamita Chakraborty, Shubhabrata Datta, Sujay Kumar Mukherjea, Partha Protim Chattopadhyay

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Manufacturing of multiphase high strength steel in hot strip mill have drawn significant attention due to the possibility of forming low temperature transformation product of austenite under continuous cooling condition. In such endeavor, reliable prediction of temperature profile of hot strip coil is essential in order to accesses the evolution of microstructure at different location of hot strip coil, on the basis of corresponding Continuous Cooling Transformation (CCT) diagram. Temperature distribution profile of the hot strip coil has been determined by using finite volume method (FVM) vis-à-vis finite difference method (FDM). It has been demonstrated that FVM offer greater computational reliability in estimation of contact pressure distribution and hence the temperature distribution for curved and irregular profiles, owing to the flexibility in selection of grid geometry and discrete point position, Moreover, use of finite volume concept allows enforcing the conservation of mass, momentum and energy, leading to enhanced accuracy of prediction.

Keywords: simulation, modeling, thermal analysis, coil cooling, contact pressure, finite volume method

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207 Evaluation of Bearing Capacity of Vertically Loaded Strip Piled-Raft Embedded in Soft Clay

Authors: Seyed Abolhasan Naeini, Mohammad Hosseinzade

Abstract:

Settlement and bearing capacity of a piled raft are the two important issues for the foundations of the structures built on coastal areas from the geotechnical engineering point of view. Strip piled raft as a load carrying system could be used to reduce the possible extensive consolidation settlements and improve bearing capacity of structures in soft ground. The aim of this research was to evaluate the efficiency of strip piled raft embedded in soft clay. The efficiency of bearing capacity of strip piled raft foundation is evaluated numerically in two cases: in first case, the cap is placed directly on the ground surface and in the second, the cap is placed above the ground. Regarding to the fact that the geotechnical parameters of the soft clay are considered at low level, low bearing capacity is expected. The length, diameter and axe-to-axe distance of piles are the parameters which varied in this research to find out how they affect the bearing capacity. Results indicate that increasing the length and the diameter of the piles increase the bearing capacity. The complementary results will be presented in the final version of the paper.

Keywords: soft clay, strip piled raft, bearing capacity, settlement

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206 Effect of Rolling Parameters on Thin Strip Profile in Cold Rolling

Authors: H. B. Tibar, Z. Y. Jiang

Abstract:

In this study, the influence of rolling process parameters such as the work roll cross angle and work roll shifting value on the strip shape and profile of aluminum have been investigated under dry conditions at a speed ratio of 1.3 using Hille 100 experimental mill. The strip profile was found to improve significantly with increase in work roll cross angle from 0o to 1o, with an associated decrease in rolling force. The effect of roll shifting (from 0 to 8mm) was not as significant as the roll cross angle. However, an increase in work roll shifting value achieved a similar decrease in rolling force as that of work roll cross angle. The effect of work roll shifting was also found to be maximum at an optimum roll speed of 0.0986 m/s for the desired thickness. Of all these parameters, the most significant effect of the strip shape profile was observed with variation of work roll cross angle. However, the rolling force can be a significantly reduced by either increasing the the work roll cross angle or work roll shifting.

Keywords: rolling speed ratio, strip shape, work roll cross angle, work roll shifting

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205 Behaviour of Model Square Footing Resting on Three Dimensional Geogrid Reinforced Sand Bed

Authors: Femy M. Makkar, S. Chandrakaran, N. Sankar

Abstract:

The concept of reinforced earth has been used in the field of geotechnical engineering since 1960s, for many applications such as, construction of road and rail embankments, pavements, retaining walls, shallow foundations, soft ground improvement and so on. Conventionally, planar geosynthetic materials such as geotextiles and geogrids were used as the reinforcing elements. Recently, the use of three dimensional reinforcements becomes one of the emerging trends in this field. So, in the present investigation, three dimensional geogrid is proposed as a reinforcing material. Laboratory scaled plate load tests are conducted on a model square footing resting on 3D geogrid reinforced sand bed. The performance of 3D geogrids in triangular and square pattern was compared with conventional geogrids and the improvement in bearing capacity and reduction in settlement and heave are evaluated. When single layer of reinforcement was placed at an optimum depth of 0.25B from the bottom of the footing, the bearing capacity of conventional geogrid reinforced soil improved by 1.85 times compared to unreinforced soil, where as 3D geogrid reinforced soil with triangular pattern and square pattern shows 2.69 and 3.05 times improvement respectively compared to unreinforced soil. Also, 3D geogrids performs better than conventional geogrids in reducing the settlement and heave of sand bed around the model footing.

Keywords: 3D reinforcing elements, bearing capacity, heavy, settlement

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204 Discrete Element Modeling on Bearing Capacity Problems

Authors: N. Li, Y. M. Cheng

Abstract:

In this paper, the classical bearing capacity problem is re-considered from discrete element analysis. In the discrete element approach, the bearing capacity problem is considered from the elastic stage to plastic stage to rupture stage (large displacement). The bearing capacity failure mechanism of a strip footing on soil is investigated, and the influence of micro-parameters on the bearing capacity of soil is also observed. It is found that the distinct element method (DEM) gives very good visualized results, and basically coincides well with that derived by the classical methods.

Keywords: bearing capacity, distinct element method, failure mechanism, large displacement

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