The Effect of Concrete Footing Shape in Differential

Research ArticleThe Effect of Concrete Footing Shape in DifferentialSettlement A Seismic Design

Abdoullah Namdar Yun Dong and Yin Deyu

Faculty of Architecture and Civil Engineering Huaiyin Institute of Technology Huairsquoan China

Correspondence should be addressed to Yun Dong hadyun163com

Received 30 December 2018 Accepted 21 February 2019 Published 10 April 2019

Guest Editor Eden Bojorquez

Copyright copy 2019 Abdoullah Namdar et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

is paper presents the numerical results of concrete footing-soil foundation seismic interaction mechanisme concrete footinghas beenmade with two different shapes but with the equal volume of concrete materiale concrete footing-soil foundation hasbeen analyzed using nonlinear finite elements with the fixed-base state e simulated near-fault ground motions have beenapplied to the concrete footing-soil foundatione problem has been formulated based on the settlement controlled analysiselocal geotechnical conditions of all configurations have been analyzed e numerical analysis results indicate that the shape of aconcrete footing alters seismic response revises inertial interaction enhances damping ratio improves load carry capacitymodifies cyclic differential settlement revises failure patterns minimizes nonlinear deformation and changes cyclic strain energydissipation e novelty of this research work is the strain energy has more been dissipated with artistic concrete footing design

1 Introduction

A number of the buildings have been collapsed due toimproper soil-footing interaction it has occurred whendynamic or seismic forces have been applied to them eimprovement of soil-footing seismic interaction mechanismis an art in geotechnical earthquake engineering design andneeds to select appropriate footing shape to enhance thesafety of the structure

ere are many experimental numerical and theoreticalresearch studies which mainly focus on differential settle-ment and bearing capacity of the soil when the soil has beensubjected to simulated seismic loading liquefaction andlandslide e outcome of these research studies has beenrealizing failure mitigation of soil foundation and in-troducing different methods for improving soil foundationstability [1ndash12] Using research idea from different branchesof science and applying them in geotechnical earthquakeengineering is an acceptable research methodology In thisregard there is an investigation on quantitative shapeevaluation of graphite particles in ductile iron [13] withattention to this research work the effect of concrete footingshape in minimizing differential settlement of soil

foundation needs to be investigated However the geo-technical earthquake engineering is a young field and theconcept of the seismic stress response of concrete footing-soil foundation model is a complicated mechanism andneeds more investigation In the present study the seismicdesign of concrete footing with considering the configura-tion of concrete footing to minimize differential settlementat the base of concrete footing has been investigatedEarthquake includes differential settlement but the shape ofconcrete footing in producing differential settlement has notbeen studied with considering seismic response at the base ofa concrete footing energy dissipation hysteretic soildamping strain travel paths inertial interaction nonlineardeformation patterns and footing-soil seismic interactionmechanism We hope all we have done could support theseismic design of concrete footing in considering the safetyof concrete footing and soil foundation to support solvinggeotechnical earthquake engineering problems

2 Problem Definition

In the previous studies many investigations have been madein understanding the differential settlement of soil when the

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 9747896 8 pageshttpsdoiorg10115520199747896

soil has been subjected to dynamic loading [2 3 6 12] epresent investigations analyzed the soil foundation-concretefooting seismic interaction mechanism and stability withconsidering concrete shape ere is no investigation on theeffect of concrete footing geometry to soil foundation-concrete footing seismic interaction present in the litera-ture and the associated simulation indirectly even cannot befound in the literaturee idea to do this research work is tounderstand the effect of concrete footing shape on (i) soilfoundation-concrete footing seismic interaction mecha-nism (ii) the differential settlement (iii) the nonlineardeformation (iv) the strain paths and (v) the failure pat-terns Two types of concrete foundations have been con-sidered and have been analyzed numerically e concretefooting and soil foundation simultaneously have beensubjected to seismic loading In all configurations singleconcrete footing has been analyzed In the present study thespecific geometry of concrete footing may increase or reducesoil-footing interaction From the theoretical concept pointof view to provide an appropriate solution for this problemand for solving and demonstrating this elasticity problemthe ABAQUS software has been employed e ABAQUShas been employed to solve and explain many engineeringproblems in the various fields through numerical simulation[12 14ndash18] e ABAQUS has the ability to solve nonlinearproblems in high quality To design the concrete footing withmaximum safety and minimum cost two different config-urations of concrete footing have numerically been in-vestigated In both configurations the same volume andgrade of concrete have been used e method of embeddedconcrete footing in the soil foundation is adopted and alsothe interaction method for soil foundation with concretefooting in ABAQUS environment has been adopted efooting and soil have been loaded e problem has beenformulated based on the settlement controlled analysis eseismic response of concrete footing and soil foundation inall models has been compared

3 Domain Theoretical Concept forPresent Analysis

e nonlinear deformation develops due to six componentsof stresses applied to a body element the six components ofstresses are σx σy σz τxy τxz and τyz

Two types of distortions arise (i) direct strainεx εy and εyz from σx σy and σz and (ii) angular distor-tions exy exz and eyz from τxy τxz and τyz e strains androtation components for each tensor may be expressed interms of their respective displacements gradients

eij

zu

zx

zu

zy

zu

zz

zv

zx

zv

zy

zv

zz

zw

zx

zw

zy

zw

zz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(1)

e strain matrix is

εij

zu

zx

12

zu

zy+

zv

zx1113888 1113889

12

zu

zz+

zw

zx1113888 1113889

12

zu

zy+

zv

zx1113888 1113889

zv

zy

12

zv

zz+

zw

zy1113888 1113889

12

zu

zz+

zw

zx1113888 1113889

12

zv

zz+

zw

zy1113888 1113889

zw

zz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)

e rotation matrix is

ωij minus

012

zu

zyminus

zv

zx1113888 1113889

12

zu

zzminus

zw

zx1113888 1113889

12

zu

zyminus

zv

zx1113888 1113889 0

12

zv

zzminus

zw

zy1113888 1113889

minus12

zu

zzminus

zw

zx1113888 1113889 minus

12

zv

zzminus

zw

zy1113888 1113889 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ex exy exz

eyx ey eyz

ezx ezy ez

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

εx εxy εxz

εyx εy εyz

εzx εzy εz

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦ +

ωx ωxy ωxz

ωyx ωy ωyz

ωzx ωzy ωz

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦ (3)

Consequently the complete distortion of a volume el-ement may be expressed as the sum of corresponding strainsand rotations in the matrix form [19] In this study thenonlinear finite element analysis has been applied to analyzeseismic behavior of concrete footing-soil foundation in-teraction Accordingly the soil foundation and concretefooting have numerically been investigated e six straincomponents will not act independently they have a directrelationship with the displacements Under earthquakefunction due to loading unloading and reloading processan element can translate rotate compress or elongate

4 Materials and Modeling

e concrete footing-soil foundation has been modeledusing nonlinear finite elements with the fixed-base statee soil foundation is 18lowast18lowast 09 (m) e concretefooting for configuration-1 and configuration-2 are06lowast 06lowast 04 (m) and 04lowast 09lowast 04 (m) respectively Forboth models the concrete foundation of 02lowast 02lowast 02 (m) isinstalled on center of concrete footing e soil foundation-concrete footing seismic interaction has been evaluated econcrete footing configuration is with two different shapesand equal volume In the numerical analysis the typicalmesh has been used e concrete footing is placed on ahorizontal surface of the soil foundation it is shown inFigures 1 and 2 e simulated near-fault ground motionswith equal magnitude have numerically been applied toconcrete footing and soil foundation e accelerationhistory of the earthquake occurred in Norcia Italy has beenused in numerical analysis and is shown in Figures 3 and 4From 22 to 28 seconds of the earthquake the main seismicexcitation has been observed In comparing E N and Zcomps the E comp has maximum acceleration history and

2 Advances in Civil Engineering

nonlinearity tolerance in Norcia Earthquake However due tothese reasons the E comp has been selected for numericalanalysis e mechanical properties of materials have beenused in this analysis extracted from those reported in theliterature and are shown in Table 1e soil is often discretizedwith solid finite elements Nonlinear numerical analysis hasbeen performed based on realistic seismic data e earth-quake data have been used in numerical analysis and arereported by AMATRICE station with 89 (km) distance fromthe epicenter of the earthquake e Norcia Earthquake

occurredwith 62magnitude at the location of 4271N 1317Eand depth of 100 km on 1 36 33 UTC 24 August 2016

5 Numerical Analysis Discussion andVerification of the Result

Enhancement geometry of a concrete footing considerablychanges soil-footing seismic interaction mechanism andthis process leads to develop a new concept for the satis-factory seismic design of a concrete footingemorphology

(a) (b)

Figure 1 Soil models (a) Configuration-1 (b) Configuration-2

(a) (b)

Figure 2 Concrete footing-soil configurations (a) Configuration-1 (b) Configuration-2

ndash4ndash2

02

ndash4ndash2

02

0 10 20 30 40 50ndash4ndash2

02

Endashcomp

Nndashcomp

Acc

eler

atio

n (m

s2 )

Time (sec)

Zndashcomp

Figure 3 Acceleration history of Norcia Earthquake [20]

22 23 24 25 26 27 28

E-comp

N-comp

Z-comp

Time (sec)

ndash4ndash2

02

ndash4ndash2

02

ndash4ndash2

02A

ccel

erat

ion

(ms

2 )


Advances in Civil Engineering 3

of concrete footing influences on the shear strain travel pathsand seismic energy distributionemeaningful relationshipshave been observed between simulated near-fault ground-shaking and energy dissipation mechanism at each config-uratione characteristics of seismic waves are altered as it isfacing different simulated geomorphological conditions eseismic wave dispersion modifies damping ratio and governsnonlinear deformation patterns of soil foundation andfooting-soil seismic interaction mechanism However themorphology of concrete footing significantly affects theamplitude of earthquake groundmotions it may be known asldquogeomorphological conditions effectrdquo in concrete footing-soilfoundation seismic design e numerical analysis resultshave confirmed that the geomorphological condition influ-ence to strain energy dissipation and this process leads todeveloping nonlinear deformation patterns and differentialsettlement with the specific shape at each configuration andsubsequently it is understood that the geomorphologicalconditions are important in the distribution of earthquakedamage e flexible soil foundation area-to-ridge concretefooting area interaction is responsible for the failure mech-anism of soil foundation at each configuration However thedesign of concrete footing shape at each configuration isimportant in the stability of concrete footing and soilfoundation as well e modified shape of concrete footingleads to change in the concrete footing center of gravity andshape of cyclic load distribution this phenomenon results inthe modification of concrete footing-soil foundation seismicinteractionmechanism and seismic load response And on theother hand the geomorphological conditions and mor-phology of concrete footing are responsible for developingcharacteristics of strain paths and the strain path is a factor indeveloping a differential settlement failure mechanism de-formation and bearing capacity e seismic site response ishighly variable with respect to concrete footing morphologywhile the volume of used concrete is equal in both config-urations and cost effectiveness of the project is consideredwith seismic design of concrete footing e geotechnicalcondition is another factor in ground motion behaviorprediction e geomorphological condition affects theseismic response of an infrastructure It can suggest beyondthe theoretical seismic design it requires to numericallysimulate the influence of geomorphological conditions topredict seismic stability of the infrastructure e near-faultground motions change strain energy dissipation via travelpath of seismic wave propagation e hysteretic behavior ofsoil significantly affects the concrete footing seismic responseis process affects concrete footing and soil foundationinertial interaction and leads to stress response of the soilfoundation Cyclic seismic load response has been developeddue to concrete footing morphology and it is shown inFigures 5 and 6 e seismic loading and concrete footing

morphology are responsible for soil compaction modify soilfoundation shear strength and alter concrete footing-soilfoundation seismic interaction mechanism e geo-morphological conditions affect wave motion behavior and itcauses differential ground deformation and differential ro-tations of concrete footing along its base to interact with soilfoundation e wave energy propagates in different di-rections and results in forming cyclic volumetric strain andproduces nonlinear deformation for each configuration it isshown in Figures 7 and 8 In configurations 1 and 2 thedifferent ground motions response has been observed it

Table 1 Mechanical properties of materials [21 22]

Materials Modulus elasticity E(MPa)

Poissonrsquosratio (])

Friction angle ϕ(degree)

Dilatancy angle ψ(degree)

Cohesion c(kPa)

Unit weight c

(kNm3) Ref

Soil 120 035 53 21 001 2268 [21]Concrete 49195 024 mdash mdash mdash 24405 [22]

ndash4 ndash2 0 2 4ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Seism

ic lo

ad (k

Pa)

Cyclic displacement (mm)

Figure 5 Seismic load (kPa) vs cyclic displacement (mm) at thebase of a concrete footing configuration-1

Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10




developed with respect to concrete footing shape and thisphenomenon supports in earthquake damage estimationwhen the movement of seismic wave radiates along thebase and sides of the concrete footing e seismic waveradiate dislocates the concrete footing at any possibledirections and this phenomenon results in acceleratingmodel and releasing cyclic strain energy e hystereticenergy dissipation is scattered in all configurations withthe critical mechanism in respect to the flexible the soilfoundation area-to-the ridge concrete footing area in-teraction this mechanism is responsible for failuremechanism of soil foundation at each configuration In-ertia has been developed due to near-fault ground mo-tions applied to each configuration it has appeared in theform of base shear moment and torsional excitation andcauses differential displacements and nonlinear de-formation rotation with a different magnitude in respectto the soil foundation flexibility and concrete footing

shape e damping ratio in configuration-2 is reduced by15 compared to configuration-1 e shape of concretefooting governs hysteretic soil damping and inertial in-teraction this process occurs based on kinematic interactionof concrete footing-soil foundation characteristics and causesconcrete foundation motions in soil foundation e non-linear deformation significantly influences the overall con-crete footing seismic behavior especially with respect todamping and seismic degrees of damage

e stress third invariant behavior is depicted inFigures 9ndash12 A comparative numerical analysis of theseismic response between two differently shaped and equalvolume of concrete footing under significantly invariantstresses through establishing nonlinear finite elementanalysis has been made e stress third invariant at the baseof concrete footing for configuration-1 is formed with higherstrain energy and lower energy dissipation magnitudecompared to configuration-2 is complex mechanisminfluences load carry capacity of soil foundation and types ofearthquake damage e evaluated results show that theshearing resistance at configuration-2 is improved due tolower degradation of soil by cyclic loading e nonlinearseismic load-cyclic strain curve expresses the variation ofstiffness and shear strength at the base of the concretefooting e cyclic strain energy causes increasing nonlinearshear deformation and soil foundation failure if cyclic shearstress increases more than the shear strength of the soilfoundation Figure 9 shows the stress invariant at the base ofconcrete footing for configurations 1 and 2 As a result thecyclic strain behavior would be expected to provide a morereliable prediction of differential settlement in consideringconcrete footing-soil foundation seismic interaction enonlinear seismic load-cyclic strain relationship at bothconfigurations shows the higher strain energy concentrationis developed at the base of the configuration-1 with respectto the magnitude and shape of the seismic loading Howeverthe differential settlement is significantly minimized inconfiguration-2 e higher cyclic strain energy concen-tration has a direct relationship with nonlinear shear de-formation and nonlinear volume change e failurepatterns are plotted in Figure 9 in such a way that red andblue zone implies a fully plastic state Due to the nature ofcyclic loading nonplastic deformation occurred in anypossible direction e geometry of the failure patternsshows the plastic slice has been occupied more area inconfiguration-1 e plastic deformation morphology showsthat the differential settlement for both models is not thesame and a higher magnitude of differential settlementoccurred in configuration-1

Figures 10 and 11 show the cyclic stress behavior of theconfigurations 1 and 2 in respect to the size and shape of theplastic deformation And it describes increment of cyclicstress invariant e stronger response of earthquakeshaking in the configuration-1 has been observed Howeverit is a possibility for permanent deformation inconfiguration-1 e strong strain in several parts of theconfiguration-1 results in permanent nonlinear shear de-formations and nonlinear volume change e nonlinearvolumetric strain often refers to ground failure It is the

Seism

ic lo

ad (k

Pa)

ndash4 ndash3 ndash2 ndash1 0 1 2 3 4ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Cyclic strain

Figure 7 Seismic load (kPa) vs cyclic strain at the base of aconcrete footing configuration-1

Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Cyclic strain



possibility of ground failure in the form of lateral grounddisplacement and it can contribute to the failure of the soilfoundation

Color map surface projection techniques are used inmatrix analysis to simulate results of ABAQUS softwarewhich is reported in cyclic stress invariant According toFigure 12 by using the matrix in numerical simulation thedevelopment of cyclic stress invariant due to seismic ac-celeration load response at the base of the soil foundation isillustrated Figure 12 shows the seismic load travel paths andseismic load directions e loading and reloading processhas been depicted in different colors e load distributionamong two soil foundations is varied configuration-2 issubjected to more distributed cyclic load compared toconfiguration-1 it is a result of increasing stable soil-concrete footing interaction in configuration-2 It can be

concluded that the stability of configuration-2 is higher thanconfiguration-1

e minimum strain energy density allows the influenceof the T-stress on the mixed modes III fracture strength[23] And the specimen geometry can strongly influence themode-I fracture strength [24] e hysteretic energy dissi-pation influences the flexible soil foundation area-to-theridge concrete footing area interaction and governs failuremechanism e configurations 1 and 2 affect strain energydissipation according to their geometry e results of thenumerical analysis show good agreements with those re-ported in the literature

e different types of loads can store elastic energybefore damage and this energy storage accelerates anddevelops damage mechanism [25ndash33] In the present nu-merical analysis it has been observed that the shape of

+5442e + 00+4535e + 00+3628e + 00+2721e + 00+1814e + 00+9070e ndash 01+3576e ndash 07ndash9070e ndash 01ndash1814e + 00ndash2721e + 00ndash3628e + 00ndash4535e + 00ndash5442e + 00

(a)


(b)

Figure 9 Cyclic stress invariant at the base of the concrete footing (a) Configuration-1 (b) Configuration-2


(a)


(b)

Figure 10 Cyclic stress invariant at the base of the soil foundation (a) Configuration-1 (b) Configuration-2

(a) (b)

Figure 11 Cyclic stress invariant for configurations 1 and 2 (a) Configuration-1 (b) Configuration-2


concrete footing causes storage strain energy mechanismand strain energy dissipation as welle cyclic strain energycauses deformation with respect to the shape of the concretefooting e soil foundation was subjected to the seismicexcitation and deforms is deformation occurs accordingto an internal energy mechanism and concrete footingshape is internal energy is known as strain energy In thepresent study the strain energy has more been dissipatedwith artistic concrete footing design e configuration ofsoil foundation-concrete footing significantly modifiedstrain energy storage and damage patterns e stresscomponent distribution due to the external forces dependson the strain energy function However the shape of con-crete footing directly affects seismic acceleration responsedamping mechanism energy dissipation load carry ca-pacity differential settlement nonlinear deformationstrain-stress travel paths and inertial interaction

6 Conclusion

e nonlinear finite elements are applied in the analysis ofconcrete footing-soil seismic interaction mechanism econcrete footing is built up with two different shapes andequal volume e simulated near-fault ground motionshave been applied to each configuration In the presentstudy the following aims have been achieved

(i) It has been found that the concrete footing-soilinteraction and morphology of differential settle-ment have been changed with respect to the shape ofthe concrete footing

(ii) e local geotechnical conditions have been mod-ified ground-shaking characteristics e anoma-lous damage distributions may not derive with theselect appropriate shape of a concrete footingconsidering local site conditions

(iii) emorphology of concrete footing affects the seismicenergy travel paths andmeaningful relationships have

been observed between simulated near-fault ground-shaking and energy dissipationmechanisme strainenergy has more been dissipated with artistic concretefooting design

(iv) e shape of concrete footing governs hysteretic soildamping and inertial interaction these processeshave occurred based on kinematic interaction ofconcrete footing-soil foundation characteristics

(v) e higher strain energy concentration has beenobserved at the base of the configuration-1 withrespect to the magnitude and shape of the seismicloading response e differential settlement issignificantly minimized in configuration-2

(vi) e cyclic strain causes plastic cyclic deformationwith respect to the shape of concrete footing andrelated to increment of stress According to thenumerical results this approach supports in fore-casting the seismic stability of concrete footing

Data Availability

No data were used to support this study

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e support by the Major Projects of Natural Science Re-search in Jiangsu Colleges and Universities (grant no17KJA560001) the Science and Technology Planning Projectof Jiangsu Province (grant no BY2016061-29) the JiangsuProvince Six Talent Peak High-Level Talent Project (grant noJZ-011) and the New Wall Materials and Development ofBulk Cement Projects of Jiangsu Economic and InformationCommission (grant no 2017-21) is greatly acknowledged

(a) (b)

Figure 12 3D cyclic stress invariant of soil at the base of soil foundation using matrix for numerical simulation (a) Configuration-1 (b)Configuration-2


References

[1] A Namdar and M K Pelkoo ldquoNumerical analysis of soilbearing capacity by changing soil characteristicsrdquo Frattura edIntegrita Strutturale vol 3 no 10 pp 38ndash42 2009

[2] A Namdar ldquoLiquefaction zone and differential settlement ofcohesionless soil subjected to dynamic loadingrdquo EJGE vol 21no 2 pp 593ndash605 2016

[3] A Namdar and G S Gopalakrishna ldquoSeismic mitigation ofembankment by using dense zone in subsoilrdquo EmiratesJournal for Engineering Research vol 13 no 3 pp 55ndash612008

[4] O F Drbe and M H El Naggar ldquoAxial monotonic and cycliccompression behaviour of hollow-bar micropilesrdquo CanadianGeotechnical Journal vol 52 no 4 pp 426ndash441 2014

[5] A V Rose R N Taylor and M H El Naggar ldquoNumericalmodelling of perimeter pile groups in clayrdquo Canadian Geo-technical Journal vol 50 no 3 pp 250ndash258 2013

[6] A Namdar ldquoTsunami and liquefaction resistance of subsoilrdquoElectronic Journal of Geotechnical Engineering vol 18pp 5907ndash5919 2013

[7] H Toyota and S Takada ldquoGeotechnical distinction of land-slides induced by near-field earthquakes in niigata JapanrdquoGeography Journal vol 2015 Article ID 359047 11 pages2015

[8] A Y Abd Elaziz and M H El Naggar ldquoGeotechnical capacityof hollow-bar micropiles in cohesive soilsrdquo Canadian Geo-technical Journal vol 51 no 10 pp 1123ndash1138 2014

[9] A M Alnuaim M H El Naggar and H El Naggar ldquoNu-merical investigation of the performance of micropiled rafts insandrdquo Computers and Geotechnics vol 77 pp 91ndash105 2016

[10] J Kumar and V B K Mohan Rao ldquoSeismic bearing capacityfactors for spread foundationsrdquo Geotechnique vol 52 no 2pp 79ndash88 2002

[11] D Chakraborty and J Kumar ldquoSeismic bearing capacity ofshallow embedded foundations on a sloping ground surfacerdquoInternational Journal of Geomechanics vol 15 no 1 article04014035 2015

[12] A Namdar ldquoA numerical investigation on soil-concretefoundation interactionrdquo Procedia Structural Integrityvol 2 pp 2803ndash2809 2016

[13] A D Santis O D Bartolomeo D Iacoviello andF Iacoviello ldquoQuantitative shape evaluation of graphiteparticles in ductile ironrdquo Journal of Materials ProcessingTechnology vol 196 no 1ndash3 pp 292ndash302 2008

[14] A Namdar E Darvishi X Feng and Q Ge ldquoSeismic re-sistance of timber structuremdasha state of the art designrdquo Pro-cedia Structural Integrity vol 2 pp 2750ndash2756 2016

[15] R Ali Q Z Khan and A Ahmad ldquoNumerical investigationof load-carrying capacity of GFRP-reinforced rectangularconcrete members using CDP model in ABAQUSrdquo Advancesin Civil Engineering vol 2019 Article ID 1745341 21 pages2019

[16] A Namdar Y Dong and Y Liu ldquoe effect of nonlinearly ofacceleration histories to timber beam seismic responserdquoMaterial Design and Processing Communication 2019 Inpress

[17] S Frank O R Ramos J P Reyes and M J PantaleonldquoRelative displacement method for track-structure in-teractionrdquo e Scientific World Journal vol 2014 Article ID397515 7 pages 2014

[18] A S Genikomsou andM A Polak ldquoFinite element analysis ofpunching shear of concrete slabs using damaged plasticity

model in ABAQUSrdquo Engineering Structures vol 98 pp 38ndash48 2015

[19] D W A Rees Basic Engineering Plasticity ElsevierAmsterdam Netherlands 2006

[20] httpsstrongmotioncenterorg[21] Y Yu R J Bathurst and T M Allen ldquoNumerical modelling

of two full-scale reinforced soil wrapped-face wallsrdquo Geo-textiles and Geomembranes vol 45 no 4 pp 237ndash249 2017

[22] J Li C Wu and H Hao ldquoAn experimental and numericalstudy of reinforced ultra-high performance concrete slabsunder blast loadsrdquo Materials amp Design vol 82 pp 64ndash762015

[23] M R Ayatollahi M Rashidi Moghaddam and F Berto ldquoAgeneralized strain energy density criterion for mixed modefracture analysis in brittle and quasi-brittle materialsrdquo e-oretical and Applied Fracture Mechanics vol 79 pp 70ndash762015

[24] M R Ayatollahi M Rashidi Moghaddam S M J Razavi andF Berto ldquoGeometry effects on fracture trajectory of PMMAsamples under pure mode-I loadingrdquo Engineering FractureMechanics vol 163 pp 449ndash461 2016

[25] S You H Ji Z Zhang and C Zhang ldquoDamage evaluation forrock burst proneness of deep hard rock under triaxial cyclicloadingrdquo Advances in Civil Engineering vol 2018 Article ID8193638 7 pages 2018

[26] L Chen L Qiao J Yang and Q Li ldquoLaboratory investigationof energy propagation and scattering characteristics in cy-lindrical rock specimensrdquo Advances in Civil Engineeringvol 2018 Article ID 2052781 7 pages 2018

[27] Z Wang J Yao N Tian J Zheng and P Gao ldquoMechanicalbehavior and damage evolution for granite subjected to cyclicloadingrdquo Advances in Materials Science and Engineeringvol 2018 Article ID 4312494 10 pages 2018

[28] B H Osman X Sun Z Tian H Lu and G Jiang ldquoDynamiccompressive and tensile characteristics of a new type of ultra-high-molecular weight polyethylene (UHMWPE) and poly-vinyl alcohol (PVA) fibers reinforced concreterdquo Shock andVibration vol 2019 Article ID 6382934 19 pages 2019

[29] A Reyes-Salazar E Bojorquez Juan BojorquezF Valenzuela-Beltran and M D Llanes-Tizoc ldquoEnergydissipation and local story and global ductility reductionfactors in steel frames under vibrations produced by earth-quakesrdquo Shock and Vibration vol 2018 Article ID 971368519 pages 2018

[30] E Bojorquez A Reyes-Salazar A Teran-Gilmore andS E Ruiz ldquoEnergy-based damage index for steel structuresrdquoSteel amp Composite structures vol 10 no 4 pp 331ndash348 2010

[31] B Dadfar M H El Naggar and M Nastev ldquoVulnerability ofburied energy pipelines subject to earthquake-triggeredtransverse landslides in permafrost thawing slopesrdquo Journalof Pipeline Systems Engineering and Practice vol 9 no 4article 04018015 2018

[32] N Bonora D Gentile P P Milella G Newaz andF Iacoviello ldquoDuctile damage evolution under different strainrate conditionsrdquo ASME vol 246 pp 145ndash154 2000

[33] L Susmel F Berto and Z Hu ldquoe strain energy density toestimate lifetime of notched components subjected to variableamplitude fatigue loadingrdquo Frattura ed Integrita Strutturalevol 13 no 47 pp 383ndash393 2019


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soil has been subjected to dynamic loading [2 3 6 12] epresent investigations analyzed the soil foundation-concretefooting seismic interaction mechanism and stability withconsidering concrete shape ere is no investigation on theeffect of concrete footing geometry to soil foundation-concrete footing seismic interaction present in the litera-ture and the associated simulation indirectly even cannot befound in the literaturee idea to do this research work is tounderstand the effect of concrete footing shape on (i) soilfoundation-concrete footing seismic interaction mecha-nism (ii) the differential settlement (iii) the nonlineardeformation (iv) the strain paths and (v) the failure pat-terns Two types of concrete foundations have been con-sidered and have been analyzed numerically e concretefooting and soil foundation simultaneously have beensubjected to seismic loading In all configurations singleconcrete footing has been analyzed In the present study thespecific geometry of concrete footing may increase or reducesoil-footing interaction From the theoretical concept pointof view to provide an appropriate solution for this problemand for solving and demonstrating this elasticity problemthe ABAQUS software has been employed e ABAQUShas been employed to solve and explain many engineeringproblems in the various fields through numerical simulation[12 14ndash18] e ABAQUS has the ability to solve nonlinearproblems in high quality To design the concrete footing withmaximum safety and minimum cost two different config-urations of concrete footing have numerically been in-vestigated In both configurations the same volume andgrade of concrete have been used e method of embeddedconcrete footing in the soil foundation is adopted and alsothe interaction method for soil foundation with concretefooting in ABAQUS environment has been adopted efooting and soil have been loaded e problem has beenformulated based on the settlement controlled analysis eseismic response of concrete footing and soil foundation inall models has been compared

3 Domain Theoretical Concept forPresent Analysis

e nonlinear deformation develops due to six componentsof stresses applied to a body element the six components ofstresses are σx σy σz τxy τxz and τyz

Two types of distortions arise (i) direct strainεx εy and εyz from σx σy and σz and (ii) angular distor-tions exy exz and eyz from τxy τxz and τyz e strains androtation components for each tensor may be expressed interms of their respective displacements gradients

eij

zu

zx

zu

zy

zu

zz

zv

zx

zv

zy

zv

zz

zw

zx

zw

zy

zw

zz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(1)

e strain matrix is

εij

zu

zx

12

zu

zy+

zv

zx1113888 1113889

12

zu

zz+

zw

zx1113888 1113889

12

zu

zy+

zv

zx1113888 1113889

zv

zy

12

zv

zz+

zw

zy1113888 1113889

12

zu

zz+

zw

zx1113888 1113889

12

zv

zz+

zw

zy1113888 1113889

zw

zz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)

e rotation matrix is

ωij minus

012

zu

zyminus

zv

zx1113888 1113889

12

zu

zzminus

zw

zx1113888 1113889

12

zu

zyminus

zv

zx1113888 1113889 0

12

zv

zzminus

zw

zy1113888 1113889

minus12

zu

zzminus

zw

zx1113888 1113889 minus

12

zv

zzminus

zw

zy1113888 1113889 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ex exy exz

eyx ey eyz

ezx ezy ez

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦

εx εxy εxz

εyx εy εyz

εzx εzy εz

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦ +

ωx ωxy ωxz

ωyx ωy ωyz

ωzx ωzy ωz

⎡⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎦ (3)

Consequently the complete distortion of a volume el-ement may be expressed as the sum of corresponding strainsand rotations in the matrix form [19] In this study thenonlinear finite element analysis has been applied to analyzeseismic behavior of concrete footing-soil foundation in-teraction Accordingly the soil foundation and concretefooting have numerically been investigated e six straincomponents will not act independently they have a directrelationship with the displacements Under earthquakefunction due to loading unloading and reloading processan element can translate rotate compress or elongate

4 Materials and Modeling

e concrete footing-soil foundation has been modeledusing nonlinear finite elements with the fixed-base statee soil foundation is 18lowast18lowast 09 (m) e concretefooting for configuration-1 and configuration-2 are06lowast 06lowast 04 (m) and 04lowast 09lowast 04 (m) respectively Forboth models the concrete foundation of 02lowast 02lowast 02 (m) isinstalled on center of concrete footing e soil foundation-concrete footing seismic interaction has been evaluated econcrete footing configuration is with two different shapesand equal volume In the numerical analysis the typicalmesh has been used e concrete footing is placed on ahorizontal surface of the soil foundation it is shown inFigures 1 and 2 e simulated near-fault ground motionswith equal magnitude have numerically been applied toconcrete footing and soil foundation e accelerationhistory of the earthquake occurred in Norcia Italy has beenused in numerical analysis and is shown in Figures 3 and 4From 22 to 28 seconds of the earthquake the main seismicexcitation has been observed In comparing E N and Zcomps the E comp has maximum acceleration history and






(a) (b)


(a) (b)


ndash4ndash2

02

ndash4ndash2

02

0 10 20 30 40 50ndash4ndash2

02

Endashcomp

Nndashcomp

Acc

eler

atio

n (m

s2 )

Time (sec)

Zndashcomp


22 23 24 25 26 27 28

E-comp

N-comp

Z-comp

Time (sec)

ndash4ndash2

02

ndash4ndash2

02

ndash4ndash2

02A

ccel

erat

ion

(ms

2 )










Cohesion c(kPa)

Unit weight c

(kNm3) Ref



ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Seism

ic lo

ad (k

Pa)



Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10








Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Cyclic strain


Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Cyclic strain









(a)


(b)



(a)


(b)


(a) (b)




6 Conclusion









Data Availability




Acknowledgments


(a) (b)



References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






(a) (b)


(a) (b)


ndash4ndash2

02

ndash4ndash2

02

0 10 20 30 40 50ndash4ndash2

02

Endashcomp

Nndashcomp

Acc

eler

atio

n (m

s2 )

Time (sec)

Zndashcomp


22 23 24 25 26 27 28

E-comp

N-comp

Z-comp

Time (sec)

ndash4ndash2

02

ndash4ndash2

02

ndash4ndash2

02A

ccel

erat

ion

(ms

2 )










Cohesion c(kPa)

Unit weight c

(kNm3) Ref



ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Seism

ic lo

ad (k

Pa)



Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10








Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Cyclic strain


Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Cyclic strain









(a)


(b)



(a)


(b)


(a) (b)




6 Conclusion









Data Availability




Acknowledgments


(a) (b)



References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









Cohesion c(kPa)

Unit weight c

(kNm3) Ref



ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Seism

ic lo

ad (k

Pa)



Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10








Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Cyclic strain


Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Cyclic strain









(a)


(b)



(a)


(b)


(a) (b)




6 Conclusion









Data Availability




Acknowledgments


(a) (b)



References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Cyclic strain


Seism

ic lo

ad (k

Pa)


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

10

Cyclic strain









(a)


(b)



(a)


(b)


(a) (b)




6 Conclusion









Data Availability




Acknowledgments


(a) (b)



References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








(a)


(b)



(a)


(b)


(a) (b)




6 Conclusion









Data Availability




Acknowledgments


(a) (b)



References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



6 Conclusion









Data Availability




Acknowledgments


(a) (b)



References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

The Effect of Concrete Footing Shape in Differential