Evaluation of Seismic Performance of Buildings

Evaluation of seismic performance of buildingsconstructed on hillside slope of Dronka village Egypt

Ahmed Abdelraheem Farghaly*

Construction on hillside slopes poses more challenges to the structural engineer, especially under

seismic load due to a powerful earthquake in addition to the forces of sliding slope itself. Regarding

to the population growth and narrowness of available lands, people build their houses on hillside

slopes. One of the main sources of seismic vulnerability in Egypt is represented by the instability of

slopes; therefore, this is a subject of great significance, particularly in view of the growing attention

that has been recently dedicated to the reduction of seismic hazard. This paper evaluates the

seismic performance of Dronka city buildings constructed on rocky hillside slopes and its

foundations system by studying base shear, acceleration, and displacements. The stability of the

slope was first evaluated under seismic loads and then the stability of constructed buildings was

checked on the hillside slope. The results of the study show that these buildings will collapse if

subjected to earthquake even if the pick ground acceleration (PGA) magnitude is less than 0?25g

with the hillside slope remaining stable within a high earthquake magnitude.

Keywords: Slope stability, Seismic force, Hillside slope buildings, FE analysis, SAP2000, Dynamic analysis of slopes

IntroductionDronka city located in the south of Cairo (about 375 km),was subjected to flood in 1996, during which most of itshouses were destroyed. Therefore, its people tend toconstruct their houses on the hillside of the town awayfrom the danger of future floods. The soil of the hillside isa rocky soil, which is a very hard soil on which traditionalbuildings are built, so most of the buildings constructed onhillside in Dronka town were founded as stepped (thefoundation found to be on more than one level in mostcases) and raft foundations.

The response of a slope under seismic loading isdetermined by the temporal and spatial distribution ofthe seismic forces in the soil mass, which in turn depend onthe characteristics of the seismic input and on themechanical properties of the soil. In general, any founda-tion design should meet four essential requirements: (1)adequate geotechnical capacity of soil/rock surroundingthe foundation with a specified safety against ultimatefailure; (2) acceptable total or differential settlementsunder static and dynamic loads; (3) adequate overall

stability of slopes in the vicinity of a footing/mat; and (4)constructability with solutions for anticipated problems.The ground response analyses can be performed under

1D or 2D conditions, and the nonlinear soil behavior isusually described through the equivalent linear methodthat provides a reasonable estimate of soil response formoderate levels of shearing intensity and provided that nosignificant excess pore water pressure develop duringseismic shaking.

Analysis of slope stability: overviewNumerous methods have been developed for assessing thestability of soil slopes, most of which are based on theconcept of ideally plastic response when failure isimminent. Among them, the limit equilibrium methodsenjoy wide acceptance due to their reasonable agreementwith reality and their simplicity (Spencer, 1967). Complexsoil profiles, seepage, and a variety of loading conditionscan be easily dealt with (Yu et al., 1998). Limit equilibriumsolutions, however, are not rigorous. To be calledrigorous, a solution must satisfy the equilibrium equa-tions, the compatibility conditions, the constitutive rela-tions of all materials, and the boundary conditions.Limit equilibrium methods often violate the stress

boundary conditions; they do not enforce an appropriateplastic flow rule for the soil, while the developing stresses

Civil and Architectural buildings, Faculty of Industrial Education, SohagUniversity, Egypt

*Corresponding author, email [email protected]

2014 W. S. Maney & Son LtdReceived 23 January 2014; accepted 17 February 2014DOI 10.1179/1939787914Y.0000000053

International Journal ofGeotechnical Engineering 2014 VOL 0 NO 0 1

may not everywhere obey the requirement for non-incidence of soil strength. Moreover, the introduction ofassumptions necessary to remove static indeterminacyleads to kinematically inadmissible collapse mechanisms.

The finite element method (FEM) is an alternativeapproach employed with two different methodologies:(a)those that search for the critical slip surface using stressfields obtained from the stress and deformation finiteelement (FE) analysis; and (b) those that compute thefactor of safety through an iterative FE analysis, bythe strength reduction technique (Troncone, 2005). Inthe latter category of methods, FEs are utilized to modelthe development of shear zones and the progressive failureof soil. The advantages of the FE approach over theconventional slope stability methods can be summarizedas follows:

N No assumption needs to be made a priori about theshape and location of the slip surface. Failure occursnaturally within the soil when the applied shear stressesexceed the shear strength of the soil mass.

N The solution is kinematically admissible, and there areno arbitrary assumptions about the slice side forces.

N It can capture progressive failure phenomena, andprovides information about the displacement field untilthe ultimate state.

N It can readily (if not easily) handle irregular slopegeometries in two and three dimensions, complex soilstratigraphy, and calculation of low quantities (due tosteady seepage, or to transient flow).

Pitilakis (2009) and Anastasopoulos et al. (2007) discussedthe 2D wave propagation effects, and that it may perhapslead to topographic amplification, is taken into accountin their analysis. The authors have shown that such effectsmay lead to increased amplitude of ground shaking nearthe crest of the slope.

Figure 1 shows the techniques of building constructedin Dronka City (Area of study), which clears that theyare constructed on stepped isolated footings or raftfoundation.

Madhavi Latha and Aruna Kumari (2010) proved thatthe factor of safety for the slope was reduced by 46% withthe application of earthquake loads in pseudo-staticanalysis than static conditions and it is recommended to

flatten the slope from 50u to 43u to avoid wedging failuresat all pier locations.

Pandey et al. (2011) studied the behavior of buildings onhill slope through a 3D analysis of the building, usingwhich the static pushover analysis and response spectrumanalysis have been conducted on five buildings withvarying support conditions. These buildings have beenanalyzed for different soil conditions (hard, medium, andsoft soils) idealized by equivalent springs. In general it isfound that response, reduction factor decreases withincreasing time period, but is expected to be constantbeyond a certain value of the time period.

Kourkoulis et al. (2010) studied parametrically theeffects of foundation type (isolated footings versus a rigidraft) on the position of the sliding surface, on thefoundation total and differential displacements, and onthe distress of the foundation slab and superstructurecolumns. The authors showed that a frame structurefounded on a properly designed raft could survive thecombined effects of slope failure and ground shaking, evenif the latter is the result of a strong base excitationamplified by the soil layer and slope topography.

Failure mechanisms caused by shear strength reductionassume different characteristics depending on soil beha-vior, ductile or brittle, and soil type, granular or cohesive,as discussed by Rampello et al. (2008). These mechanismscan be analyzed in the static condition following theseismic event, using conventional limit equilibrium meth-ods, eventually accounting for the increase of pore waterpressure and the degradation of strength parametersinduced by earthquake loading.

On the contrary, when slope instability is produced byearthquake-induced inertial forces, a progressive develop-ment of slope displacements occurs for the duration ofground motion only. Accordingly, evaluation of sloperesponse to earthquake loading should be carried out, inprinciple, using analytical procedures that account fortime-dependent seismic action and that allow an evalua-tion of the induced displacement to be obtained. If apseudo-static approach is adopted in this case, theequivalent seismic coefficients used in limit equilibriumcalculations must be calibrated against specifying levels ofslope performance, in turn defined by specifying threshold

1 Techniques of building construction on hillside slope in Dronka City: a high slope angle with stepped foundation and b

small slope angle with stepped foundation

Farghaly Evaluation of seismic performance of buildings constructed on hillside slope of Dronka villageEgypt

International Journal of Geotechnical Engineering 2014 VOL 0 NO 02

values of earthquake-induced displacements. In fact, in thepseudo-static approach the safety factor provides anindirect estimate of the seismic performance of the slopeto earthquake loading, while under static conditions itrepresents a measure of the distance from a potentialfailure mechanism.

In situ soil slopes and embankments are often reinforcedwith nails to improve their static and seismic performance.Michalowski and You (2000) developed an approximatemethod based on the kinematic approach of limit analysisto estimate the permanent displacement of geosynthetic-reinforced soil slopes subjected to earthquake loading.Chavan et al. (2012), verified this approximate methodthrough FE analysis of nails, soil slopes considering thesoil and the nails as nonlinear and linear elastic materials,respectively. Radiation damping has been considered byusing LysmerKhulemeyer (LK) dampers at the soilboundaries of the FE model. Soil is assumed to be dry andcohesion-less, and analyzed under plane strain conditions.The permanent displacements from approximate methodand FE analysis have been compared. It is found that thedisplacements from FE analysis are considerable (morethan 10%) less than those from approximate method.

Krishnamoorthy (2007) obtained a procedure to eval-uate the factor of safety of the slope (1:1) subjected toseismic load using a Monte Carlo technique. The proposedmethod can be used to obtain simply the factor of safety ofthe slope and deformation of the slope. The stresses in thesoil due to static (self-weight) and dynamic loads areobtained using FEM. The critical slip surface and factor ofsafety is obtained using a Monte Carlo technique. Theapplicability of the analysis is demonstrated by analyzinga 1 : 1 slope when it is subjected to the dynamic loadfrom the El Centro earthquake and harmonic ground

acceleration. It is concluded from the study that themethod of determining the factor of safety is simple. Theproposed method can be used to obtain the factor of safetyof the slope and deformation of the slope.

Mavrouli et al. (2009) presented an analytical methodol-ogy to evaluate rock slope stability under seismic conditionsby considering the geo-mechanical and topographic proper-ties of a slope. The objective is to locate potential rock fallsource areas and evaluate their susceptibility in terms ofprobability of failure. For this purpose, the slope face of astudy area is discretized into cells having homogenousaspect, slope angle, rock properties, and joint set orienta-tions. A pseudo-static limit equilibrium analysis is per-formed for each cell, whereby the destabilizing effect of anearthquake is represented by a horizontal force. The value ofthis force is calculated by linear interpolation between thepeak horizontal ground acceleration PGA at the base andthe topof the slope. The groundacceleration at the topof theslope is increased by 50% to account for topographicamplification. The uncertainty associated with the joint dipis taken into account using the Monte Carlo method. Theproposed methodology was applied to a study site withmoderate seismicity in Sola de SantaColoma, located in thePrincipality of Andorra. The results of the analysis areconsistentwith the spatial distribution of historical rock fallsthat have occurred since 1997.Moreover, the results indicatethat for the studied area, (1) the most important factorcontrolling the rock fall susceptibilityof the slope is thewaterpressure in joints and (2) earthquake shaking with PGA of0?16gwill cause a significant increase in rock fall activityonlyif water levels in the joints are greater than 50% of the jointheight.

Figure 2 illustrates the models used for the analysis ofdifferent cases for constructing both isolated and raft

2 Finite element (FE) mesh. In the area of the slope the discretizaton is denser (0?560?5 m quadrilateral elements): a slopewith angle w with the direction of earthquake; b building on slope founded on isolated footing; c stepped buildings on

slope founded on isolated footing; d stepped buildings on slopes founded on raft foundation


International Journal of Geotechnical Engineering 2014 VOL 0 NO 0 3

foundation cases. The angles of slopes w are 60u45u25udepending on the slope location in the nature (dimensionof the models were in m). The FE analyses can besuccessfully utilized to model the generation of slidingfailure surfaces in the slope, reproducing similar failuresurfaces with those derived from limit-equilibrium andlimit-analysis methods, and leading to similar yieldaccelerations. However, the capability to treat realisticallythe dynamic response to ground shaking is an exclusiveattribute of the numerical (FE) methodology, not of thepseudo-static limit equilibrium/analysis methods. Anadditional capability of the numerical (FE) methodologyis that any structure-foundation system can be placed onthe slope. For the purpose of the present study, adiscretization of 0?560?5 m has been adopted as inKourkoulis et al. (2010).

The FEM is one of many stressdeformation methods.It is widely accepted for its accuracy in modeling differentgeological geotechnical phenomena as it implementsphysical laws. During the last decade, major improve-ments in efficiency and configuration have made it easierand cheaper to use and therefore it has become a morecommon tool in science and engineering.

Selection of adequate accelerographsThe recorded accelerographs of Nothridge (1989) and ElCentro (1940) earthquakes are shown in Fig. 3. Since thereare no accelerograph available (neither recorded, norpredicted based on the seismic risk analyses) in the area,the above accelerographs selected for seismic analyses ofthe model. According to the Egyptian code of practice forseismic resistant design of buildings (ECOL201, 2008), the

city of Dronka is classified as the area by relatively lowseismic risk, and the design acceleration of the area isrecommended to 0.25g. Thus the above mentionedaccelerographs have been scaled and corrected for thisamount. Egypt in the last years was classified as highseismic regions so, the research will analysis the buildingsconstructed on hillside slope subjected to earthquakeacceleration 0.25, 0.5, and 1g to cover all possibilities ofearthquake force can affect the area. Time history analysisis carried out using SAP200 (2010) program consideringthe factor of acceleration 0.25, 0.5, and 1g and nonlinearanalysis with 4000 step at 40 sec for both time history usedearthquakes (El-cento and Northridge Earthquakes). Thetime history corresponding to 5% damping is consideredwhich is reasonable for concrete structure.

Model descriptionThe 2D building model consists of frame elements as beamand column. The column dimension is 50650 cm and thebeam section is 25650 cm all over the height of thebuilding. The foundation is chosen to be either raft orisolated foundation in the analyses. A four-story buildingwas modeled with a 3 m height (each story) and a 15 mlength, as shown in Fig. 2.

No matter what type and size of RC structure is underinvestigation, the FEM is the most accurate and reliablenumerical technique for assessing the demands onstructure components in both 2D and 3D domains.

Frame members primarily serve to carry the majority ofgravity loads in a building, but also serve as part of lateralresisting systems. EulerBernoulli beam theory and,Timoshenko beam theory (Hjelmstad, 2005) if considering

3 Acceleration time histories of the earthquakes in NS direction: a El Centro and b Northridge

Table 1 Description of used symbols in different curves

Symbols Description

I 60u Building on 60u slope angle founded on isolated footingR 60u Building on 60u slope angle founded on raft footingI 45u Building on 45u slope angle founded on isolated footingR 45u Building on 45u slope angle founded on raft footingI 25u Building on a 25u slope angle founded on isolated footingR 25u Building on a 25o slope angle founded on isolated footingFixed ISO Building with fixed, stepped isolated footingFixed Raft Building with fixed raft footing



shear effects of deep beam, are widely used and have beenimplemented in most computer-based frame analysispackages. A beam element was loaded with constantdistributed loads equal to 2?50 ton m21 at all floor levels,in addition to own weight of elements. Table 1 shows thedifferent types of models and their abbreviations.

Results and analysis

The evaluation of the performance of buildings con-structed on hillside slopes at Dronka city was carried outin two main parts. The first part is the performance of thebuilding with a different foundation system under seismicloads on the hillside slope and presents their strainingactions resulting from two earthquake (El Centro andNorthridge earthquakes) analysis in steps i.e. 0?25, 0?5,and 1g in increasing order of the PGA. The second partevaluated the performance of hillside slopes (slope angles60u, 45u, and 25u) under static and seismic loads with andwithout constructed buildings, to evaluate the static anddynamic stability of the hillside slope.Figure 4 represents the straining actions of the analyzed

model, using the El Centro earthquake time history,taking into consideration the various types of slope angles,ground accelerations, and foundation systems (isolated orraft foundation system). Figure 4a shows variations ofnormal force in base columns, for a building founded at a60 slope with raft foundation the normal force recordedthe highest value with respect to the other cases. Thegreater the slope angle the greater normal forces.Figure 4b illustrates base shear force on a raft foundationat 60u slope angle given the maximum value at all in thethree selected ground acceleration, but a raft foundationon a 25u slope angle gives the highest value in base shearfor 0?50g acceleration.Figure 4c shows bending moment for base column. A

maximum bending moment occurs in raft foundation ona slope angle of 60u at 1g acceleration, but at 0?50gacceleration, the maximum value was found in raftfoundation on a 45u slope angle. Figure 4d representsthe top floor displacement; the maximum value ofdisplacement for the tested model was founded in raftfoundation on slope angle 60u. This behavior was repeatedin all used accelerations.Figure 4e shows the values of top floor acceleration of

the building model. The maximum top floor accelerationwas registered in the case of raft foundation on a 25u slopeangle, which was nearly 2?4 times the applied accelerationon the model for 1g acceleration, 2?7 times the appliedacceleration on the 0?50g model, and equal to two timesthe applied acceleration on the 0?25g model. From thefigure it can be proved that the slope has no effect on thevalues of bending moment of the base column except for R25 (raft foundation on hillside slope 25u), which nearlyincreased by 1?75 times than all cases. The bendingmoments in fixed base cases registered a lower value withrespect to the rest of the cases.Figure 5 shows the straining actions of the analyzed

models, using Northridge time history earthquake model,taking in consideration the various types of slope angles,ground accelerations, and foundation systems (stepped

isolated or raft foundation system). Figure 5a shows thevariation of normal force in base columns. Buildingsfounded on 60u slope with raft foundation give the highestvalue of the normal force with respect to the other cases(nearly more than the other cases by 2?5 times), the largeslope effect on the oblique of the building results in thehigh value of normal force. Figure 5b illustrates that thebase shear force at the raft foundation system on 60u slopeangle give the maximum value with respect to the otherslopes and a foundation system. This phenomenonrepeated for the three selected ground acceleration.Figure 5c shows that the base bending moment for base

column maximum bending moment occur in raft founda-tion case on slope angle 60u and raft on slope 25u in 1gacceleration, but in 0?50 and 0?25g acceleration the valueswere nearly constant. Figure 4d represents the top floordisplacement the maximum value of displacement of thetested models, displacement of model in 60u slope wassmaller than in 25u by 1?15 times, this behavior wasrepeated in all used accelerations.Figure 5e shows the values of top floor acceleration of

models, the maximum top floor acceleration was regis-tered in the case of raft foundation on a 25u slope angle,nearly 1?6 times the applied acceleration on the model for1, 0?50, and 0?25g cases of the applied acceleration.The results founded from El-Cento earthquake excita-

tion were in the same trend with Northridge earthquakeexaltation.Figure 6 displays the stress distribution in x and z

directions of 2D slopes (angles 60u45u25u) under staticcondition. Figure 6c shows the stress distribution in x andz directions, all stress are negative (compression stress)with the allowable stress for the rocky soil of the hillside.In Fig. 6b, stress in the hillside with slope 45u is moderatecompression stress, but in Fig. 5a there is also compres-sion stress but with low value because of the higher valueof slope angle 60u.To evaluate the effect of different kind of foundation

system on hillside slopes under El Centro earthquake with0?25, 0?5, and 1g pick ground acceleration (PGA)excitation, three actual slopes were tested (60u45u25u).Only hillside slopes under 1g PGA are shown in Fig. 7. Ahillside slope of 25u subjected to El Centro earthquakewith PGA 1g with raft foundation, showed stress in x-direction no tension between foundation and soil under-neath the model and so in z-direction, generally no tensionstress come out in the whole of the slope. The surface offailure appears under raft foundation more straight, butfor steeped foundation the surface looks like a quartercircle (critical circle of slip). Compression stress in hillsideslope underneath steeped foundation is bigger than raftfoundation. For a hillside slope of 45u, the straining actionon the slope is moderate with respect to slope angle 25uwithout tension stress between raft foundation in z-direction and the hillside soil will cause the collapse ofthe building model, but there is a tension stress betweenthe raft foundation building model and the hillside soil inx-direction, which means collapse of the building model,there is a tension stress in the hillside slope in a crest parts,and the steeped foundation shows a minimum effect of theslope. This appears as a small value of compression stress



in both directions and no tension stress appears under-neath the steeped foundation of the model. For hillsideslope angle 60u deformation of hillside slope with raftfoundation, a small part of the hillside will take off, atension stress appears underneath the foundation in bothdirections, stepped foundation model appear more stable

than raft foundation model because of there is no tensionbetween foundation and soil.

If the PGA is equal to 0?5g for the hillside slope 25u,there is no tension between both types of foundation andthe soil underneath, both stresses are compression in bothdirections, which have large values. In hillside slope 45u

4 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake

excitation: a base column normal force; b base column shear force c base column bending moment; d displacement of

top oor; e acceleration of top oor



stress underneath a raft foundation model approximate tozero in both directions this means the model is aboutrotation to be destroyed, but the steeped foundation wasmore stable, because of there is a small value ofcompression stress underneath foundation. If the hillsideangle is equal to 60u, tension stress between the raftfoundation and soil appears such that the model will be

subject to collapse under earthquake excitation. However,for stepped foundation, stress between foundation and soilnearly equal to zero (about rotation), the stability isunclear in this case.

Figure 8 illustrates the straining actions of the hillsideslope under Northridge earthquake excitation with differ-ent kinds of foundation systems and slopes. For PGA 1g

5 Straining actions of 2D model with different types of foundation and slope angles with Northridge earthquake: a base col-

umn normal force; b base column shear force; c base column bending moment; d displacement of top oor;

e acceleration of top oor



6 Stress distribution on 2D slope with different slope angles under static load: a slope 60u; b slope 45u; c slope 25u



7 Straining actions of 2D building with different types of foundation system and slope angle with El Centro earthquake excitation

with PGA equal to 1g: a straining action on slope 60u (i) raft foundation (ii) stepped foundation; b straining action on slope 45u (i)stepped foundation (ii) raft foundation; c straining action on slope 25u (i) stepped foundation (ii) raft foundation



7 Continued



8Straining actions of 2D building with different types of foundation system and slope angle with Northridge earthquake excitation with

PGA equal to 1g: (i) raft foundation (ii) stepped foundation; a straining action on slope 45u (i) stepped foundation (ii) raft foundation; bstraining action on slope 25u (i) raft foundation (ii) stepped foundation



and slope 60u there is a tension stress between foundationand soil on the slope. This indicates a failure of the modelfor both kinds of foundation (raft and stepped), deforma-tion for stepped foundation is bigger than a raft

foundation model, and the straining action seems to belower than the corresponding values of El Centro earth-quake exaltation. For slope 45u and 1g PGA, there is notension stress between foundation and soil on the hillside

8 Continued



slope, but the compression stress in the slope is small withrespect to 60u slope, the corresponding values in 25u slopeare greater than 45u and no tension stress appears.The results obtained from Northridge earthquake is

similar in trend with these founded from El Centroearthquake excitation.

Table 1 concluded the results of model stress foundedon the slopes with the view of stability under differentearthquake excitation. The stability of a series of buildingconstructions on a slope under earthquake excitation wasstudied and also concluded in Table 2. It seem that seriesbuildings can be more critical than one building and it isshown that the construction of series buildings on a slopefrom 6045 angle can be destroyed under moderateearthquake, even so, the series buildings withstand underthe same earthquake magnitudes if it is founded on a flatland foundation.

ConclusionA 2D building model founded on a hillside slope wasevaluated to check the performance of buildings andslopes under various earthquake time history excitationsand magnitudes in a real case study in Dronka village inUpper Egypt. Two earthquake time histories were used, ElCentro and Northridge earthquakes, with 0?25, 0?5, and1g PGA magnitude. The models used were prepared toagree with the reality of the nature of the case study, theslopes used were 60u, 45u, 25u, and the foundation systemswere stepped isolated or raft foundations. The nonlinearparameters of the rocky type soil were provided to theSAP2000 program as a curve of soil under cyclic loading.On applying the two selected earthquake time historieswith different PGA on a free hillside slope with only onebuilding, and then with a series of buildings, the highlightpoints can be drawn as:

N Static analysis of the hillside with different angles ofslopes was found to be stable.

N The study gives an overview of the stability of hillsideslopes under earthquake excitations especially forconstruction requirements.

N The stability of slopes (without constructed buildingsand with slope angles ranging from 60u to 25u) is

acceptable in the high PGA for the study rocky soil; notensile stress was found in the hillside slope.

N Compression stress in a hillside slope angle 60udecreased by 1?5 times than hillside slope angle 45uand decreased by 1?4 times than hillside slope 25u underseismic excitations.

N The interplay between dynamic (inertial) effectsarising from the ground vibration and the quasi-static(kinematic) effects arising from the downward move-ment of a shallow sliding soil wedge was studied. It wasthus determined that a rigid raft foundation, placed ona high angle slope that is in a precarious equilibriumand fails during very strong shaking, cannot protect thesuperstructure from both falling (being dragged) withthe sliding soil mass and from suffering large damaginginternal forces.

N This is in qualitative agreement with several casehistories of structures that have survived the combinedeffects of strong seismic shaking and soil downwardsliding. The penalty to pay, however, is: (a) appreciablerotation and lateral displacement of the whole system,which may impair the serviceability of the structure,and (b) generation of large bending moments and shearforces in the foundation slab in contrast to what mostengineers would have intuitively predicted; placing astructure with isolated footings on a seismicallyunstable slope would be a prudent decision.

N It is recommended to flatten the slope from 60u to 45u toavoid wedge failures at all isolated stepped foundationlocations (normal force decreased by 50% for a slopeangle 60u than slope angle 45u and base shear decreasedby 40% in a slope angle 60u than slope angle 45u).

N The difference in straining action between steps and raftfixed base under dynamic loads is not significant (baseshear in raft foundation increased by 2% than steppedisolated footing, bending moment by 3%, top displace-ment by 5%, and top floor acceleration by 7%).

N Stepped isolated foundation represents the best solutionfor both dynamic performance of superstructure con-structed on hillside slope and the stability of the slope(columns normal force for isolated footing decreased by1?33 times than raft foundation, and decreased by 1?45times in base shear) (In 2D, the effect of the tie beamsused to connect stepped footing has been ignored).

Table 2 Conclusion of model stable with different earthquake PGA

Earthquakeacceleration/g

Hillsideslopeangle

Static stabilityof slope only

Dynamic stabilitywith constructedone building

Dynamic stabilitywith constructedseries building

Tensionstress

Compressionstress

Tension stressunder building

Compression stressunder building

Tension stressunder building

Compression stressunder building

1 60u No Stable Unstable Unstable 45u No Stable Unstable Unstable 25u No Stable No Stable Unstable

0.50 60u No Stable Unstable Unstable 45u No Stable Unstable Unstable 25u No Stable No Stable Stable

0.25 60u No Stable Unstable Unstable 45u No Stable No Stable Unstable 25u No Stable No Stable Stable



N In the series building model constructed on a hillsideslope, especially at 60u angle, normal force increased bynearly 1?5 times than the one building model, shearforce by 1?75 times, bending moment by 1?40 times,displacement by 1?25 times, and top floor accelerationdecreased by 0?20 times.

This conclusion drawn from a 2D analysis remains validfor the 3D cases, since more attenuation would beobserved if the radiation damping into the third dimensionwas taken into consideration. These very local conditionsare not adequately captured by the analysis. However,verification is required to check the results in 2D and 3D.

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