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SOIL-STRUCTURE INTERACTION IN THE SEISMIC

VULNERABILITY ANALYSIS OF RC BUILDINGS. APPLICATION TO

A CASE STUDY BUILDING LOCATED IN SOUTHWESTERN SPAIN

M.V. Requena-Garcia-Cruz1, A. Morales-Esteban1, P. Durand-Neyra1, E. Romero-

Sánchez1

1Department of Building Structures and Geotechnical Engineering, University of Seville, Spain. Av.

Reina Mercedes, 2, 41012, Seville, Spain

{mrequena1, ame, percy, eromero13}@us.es

Abstract

Most seismic vulnerability analyses do not consider the Soil-Structure Interaction (SSI).

However, it has been proved that SSI does not equally affect all types of structures and all

types of soils. The analysis of the state of the art reveals that SSI especially affects the per-

formance of mid/high-rise buildings under soft/inelastic soil conditions. This leads to overes-

timating the capacity of buildings and to obtaining unreliable results. This paper aims to

assess the soil influence in the seismic vulnerability analysis of a reinforced concrete (RC)

building. Three models of a real case study building have been determined (low-rise (real),

mid-rise and high-rise). A pre-code 1970s case study building, located in Huelva, has been

selected. This building shares typical constructive and structural characteristics with most RC

buildings constructed during that period. The 3D continuum model of the soil has been car-

ried out to simulate its nonlinear behaviour. The most probable soil profile has been defined,

observing a clayey soil. Therefore, the analyses have been performed under undrained condi-

tions. Nonlinear static analyses have been carried out to determine the seismic capacity of the

models through the finite element method (FEM). The damage has been assessed by means of

the local procedure, defined in the European seismic code, and the global fragility procedure.

The results have shown that the soil does not significantly influence the behaviour of low-rise

buildings. However, in the case of mid- and high-rise buildings, the maximum capacity can be

reduced by up to 10% and 30%, respectively.

Keywords: Soil Structure Interaction, Seismic analysis, Reinforced concrete, Buildings,

OpenSEEs.

COMPDYN 2021

8th ECCOMAS Thematic Conference on

Computational Methods in Structural Dynamics and Earthquake Engineering

M. Papadrakakis, M. Fragiadakis (eds.)

Streamed from Athens, Greece, 230 June 2021

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

1 INTRODUCTION

Most seismic vulnerability analyses of buildings are carried out without considering the

soil-structure interaction effects (SSI). Despite these notable effects, their consideration in

seismic analysis remains unclear. In fact, SSI was assumed to be beneficial in past research

[1]. This benefit emerges from the reduction of the internal forces and the drifts due to the

soil’s increasing flexibility. Hence, the vast majority of seismic vulnerability analyses consid-

er models with a fixed-based configuration to obtain more conservative results. However, re-

cent studies on the influence of SSI in the capacity assessment of buildings has proved that it

does not positively affect all types of structures and all types of soils [2]. They have conclud-

ed that structures are expected to experience different levels of damage when the soil’s influ-

ence is taken into account [3]. In fact, the Eurocode-8 Part-1 (EC8-1) [4] establishes that the

SSI effects must be born in mind when structures: i) present significant second order (p-Δ)

effects; ii) are slender; or, iii) are medium/high-rise buildings. Moreover, it was proved that

SSI might affect aspects related to the seismic performance of buildings such as the ductility

and the strength [5] or the energy dissipation [6]. Studies have even shown that the SSI can

greatly worsen the performance of buildings due to asymmetrical designs [7]. This suggests

that further research is needed.

The SSI effects can be taken into account by simulating the flexibility of the soil. To do so,

several approaches have been proposed over time. Among others, the most common ap-

proaches used in the behaviour assessment of buildings are the Nonlinear Beam on Winkler

method (NBWM) and the continuum modelling of soil (in 3D). The first approach is mainly

based on simulating the nonlinear behaviour of the soil by adding inelastic springs [8]. These

springs present different characteristics which are applied in certain directions. The NBWM

can simulate the SSI effects very easily and simply. In this way analyses do not become very

tedious [9]. However, this approach presents certain drawbacks: it does not consider the com-

plete behaviour of the soil, the frictional surface between the soil and the foundation and the

effects of deeper soil layers. Therefore, this method might not be applicable for all soil and

structural characteristics.

The continuum modelling of soils can exhaustively capture the soil constitutive behaviour,

obtaining more realistic results [2]. Moreover, this type of analyses has been gaining im-

portance over the past decade due to the availability of new methods and the increase of com-

putational capacity [10]. Some related studies showed that the foundation characteristics and

the soil modulus (shear and bulk) are the parameters that most affect the seismic response of

buildings [2]. Others proved that the SSI are significant when both the structure and the soil

are simulated as inelastic [6]. These parameters cannot be considered in SSI assessment via

the NBWM.

Owing to the lack of studies and guidance, this paper aims to analyse the soil’s influence in

the seismic vulnerability analysis of a reinforced concrete (RC) building. To do so, different

models of a real case study building have been simulated (low-rise (real), mid-rise and high-

rise). The EC8-1 statement and past research have been proved. The 3D continuum modelling

of the soil has been carried out to simulate its nonlinear behaviour. Furthermore, the charac-

terisation of the most probable soil profile at the location has been done by considering differ-

ent geotechnical studies. As a clayey soil has been observed, the analyses have been carried

out under undrained conditions. Nonlinear static analyses have been performed to determine

the seismic capacity of models by using the finite element method (FEM). The damage has

been assessed by means of the local procedure established in Eurocode-8 Part-3 (EC8-3) [11]

and the fragility procedure.

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

The case study building is a 1970s primary school building located in Huelva (southwest-

ern Spain), which is an earthquake-prone area. This building shares typical constructive and

structural characteristics with most RC buildings of the area. What is more, these buildings

were constructed prior to the applications of seismic codes.

The key contributions of this paper are: i) the analysis of the soil influence in the seismic

vulnerability analysis of RC buildings considering different geometrical characteristics; ii) the

characterisation for the 3D continuum modelling of the most probable soil profile in Huelva;

iii) 3D FEM models in OpenSees to realistically reproduce the entire system’s behaviour

(soil+foundation+structure); iv) the analysis of the seismic damage by means of both local

and global procedures.

2CASESTUDY

2.1 Building configuration

The case study building selected is a primary school building located in Huelva. It has been

defined as an index-building of the typology of RC buildings [12]. This typology represents

27% (75 buildings) of the total (279) of the primary school buildings constructed in the prov-

ince. As they were built during the 1970s, they share constructive and structural characteris-

tics with a major part of the area’s RC buildings: insufficient longitudinal and transversal

rebar ratio, wide beams, short columns, very slender RC columns sections and low-quality

structural materials. Moreover, these buildings have not been designed according to seismic

criteria since they were constructed prior to restrictive seismic codes.

The case study building is a two-story RC frame building (Figure 1). Although it is regular

in height, it presents short columns on the ground floor. This is a typical constructive configu-

ration that can be commonly found in most RC buildings of the 1970s. Short columns are

created due to the elevation of the ground floor from the soil surface to avoid humidity and

water problems. This ground-floor construction often leads to isolated footings (superficial or

deep). In this case, the building was constructed with isolated footings of a depth of 0.80 m.

The structural characteristics of the building are listed in Table 1.

Figure 1: Case study building’s configuration.

Characteristic

Columns

Load beams

Tie beams

Dimensions (cm)

30x40

60x30

30x30

Cross-section (cm2)

1,200

1,800

900

Longitudinal rebar (cm2)

1.572

Top: 0.786

Top: 0.786

Bottom: 3.495

Bottom: 0.786

Transversal rebar (cm2)

0.196

0.196

0.196

Spacing of stirrups (cm)

15

20

25

Table 1. Case-study’s structural elements geometrical characteristics.

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

2.2 Soil characterisation

A characterisation of the soil under the building has been carried out to properly model its

constitutive behaviour. The information has been compiled from 8 nearby geotechnical stud-

ies. These studies include information related to laboratory tests done with samples as well as

in-situ geotechnical prospections. Based on the available information, an interpretation of the

soil layering at the site has been performed. In this study, the most probable soil profile has

been considered. To do so, the probability of each stratum according to its depth has been as-

sessed. This determination has considered 17 boreholes. As shown in Figure 2a, four different

geotechnical strata have been identified: tilled, grey clay, brown silt and clay loam. The labor-

atory tests have revealed a predominance of clay. Therefore, only the parameters to perform

undrained analyses have been calculated.

(a) (b) (c)

Figure 2: Soil characterization. (a) Soil profile (b) Nspt and Vs(c) according to depth.

Among other in-situ tests, standard penetration tests (SPT) were executed to determine the

Nspt. In Figure 2b, the Nspt for each soil stratum has been plotted. According to [13], the shal-

low layers can be classified as low-dense soils (Nspt≈11-30) while the deepest layers are dense

(Nspt≈31-50) .

The shear wave velocity (Vs) and the Poisson ration (ν) are required to numerically model

the soil in 3D. In [14], several correlations were defined to obtain Vs. However, in this work,

only the Imai equation (Eq.(1)) has been used since it is widely accepted. In Figure 2c, the Vs

values for each soil layer have been defined according to Nspt and depth. Since there are sever-

al values of Vsfor each depth, the most probable value has been used to determine the param-

eters presented below.

Vs=91Nspt0.317 (1)

The soil behaviour is defined according to three parameters: shear (G), elastic (E) and bulk

(B) modulus and the unit weight (γ). The moduli have been calculated according to certain

widely known geotechnical correlations (Eq.(2)(3)(4)). G,Eand Bhave been plotted in Figu-

re 3 for each soil stratum. The soil constitutive behaviour has been plotted considering the

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

medium values of each modulus. As can be observed, the shallow layers are weaker than the

deepest ones, which relates to Nspt. The soil stiffness increases at around 5 m depth. The clay

loam’s modulus rises slightly with depth. In order to take the variability of the modulus into

account, four soil layers have been defined following the procedure established in Section 4.2.

G=γVs2(2)

E=2G(1+ν) (3)

B=E/3(1-2ν) (4)

(a) (b) (c)

Figure 3: G(a), E(b) and B(c) values obtained from correlations according to geotechnical prospections.

3 NONLINEAR STATIC ANALYSES

3.1 Models defined

The state of the art has revealed that SSI must be considered in the seismic analyses of

mid- and high-rise buildings. Therefore, in order to better understand their influence, different

configurations of the case study building have been determined by varying its height. As

shown in Figure 4, three models have been defined: low-rise (real) (M1), mid-rise (M2) and

high-rise (M3). The total mass and height of each model have been listed in Table 2. Fixed-

base and solid models have been identified with “F” and “S”, respectively. The nodes at the

base of the F-models have been fixed in the 6 degrees of freedom (DOF): X, Y, Z, Rx, Ryand

Rz. The modelling of the soil is presented in Section 4.2. It has also been checked that the

foundations’dimensions are valid for the soil with each model’s configuration.

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

Figure 4: Models’ configuration.

Model

Nº of floors

Total mass (ton)

Total height (m)

M1

2

1,058

7.30

M2

4

1,952

13.90

M3

6

2,846

20.50

Table 2. Number of floors, total mass and height of the models analysed.

3.2 Analysis procedure

Nonlinear static analyses have been carried out to determine the capacity of the models by

using the FEM OpenSees software [15]. Since the models are very large, the analyses have

been done using the parallel option available in OpenSees by defying partitions. The outputs

have been handled in PYTHON [16]. A load-control and displacement-control integrator have

been used to perform the gravity and the pushover analyses, respectively. Only the modal load

pattern results have been considered since this has been the most restrictive. Modal analyses

have been carried out to define the load pattern. The -genBandArpack solver has been used

due to the numerous constraints. As models have worked in Mode 1 and 2, torsional effects

can be neglected.

3.3 Damage determination

The N2-method has been used to determine the single-degree-of-freedom (SDOF) ideal-

ised bilinear curves and the target displacement. Its extended version has also been used,

which takes the infills’ effects into account. A 0.1g PGA for Huelva has been used according

to the Spanish updated seismic action values [17]. The response spectrum has been construct-

ed using the EC8-1 procedure.

Two approaches have been considered to determine the damage: the local and the global.

The first one has borne in mind the demand/capacity ratio (DCR) established in EC8-3 and

the local damage of RC structural elements. Three damage states have been determined: dam-

age limitation (DL), significant damage (SD) and near collapse (NC). The NC is calculated

considering the ultimate chord rotation (θum). The SD is determined as 3/4 of θum.The DL is

worked out by means of the yielding chord rotation (θy). The formulae of each parameter are

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

established in the EC8-3. Each damage state has been calculated when the demand chord of

one column reaches the capacity values of θum,θum and θy.

The second approach is based on the fragility curves assessment. These curves provide the

probability of reaching or exceeding a certain damage state (ds), given a certain spectral dis-

placement (Sd). They are determined by the well-known lognormal cumulative distribution

(Eq.(5)), where: βds is the dispersion at dsand Sd,ds is the median value of the spectral dis-

placement at which a building reaches the dsthreshold.

P[ds|Sd]=Φ[(1/βds)ln(Sd/S(d,ds))] (5)

Both βds and Sd,ds are statistical parameters that take into account different uncertainties.

They should therefore be determined according to the models analysed. However, in this case

they have not been studied since further research should be carried out considering many

models and including the SSI effects. However, an exhaustive work carried out in [18] has

been used to define these parameters. The authors performed the fragility assessment of typi-

cal Spanish RC buildings and determined the fragility parameters for low-, mid- and high-rise

RC buildings. The values of βds for each building class are listed in Table 5. The values of

Sd,ds have been determined for each of the models analysed and following the provisions es-

tablished in [18], listed in Table 4. This procedure considers the parameters that characterise

the idealised SDOF system curves: Dyand Du, yielding and ultimate displacement.

Damage state/Class

Slight (β1)

Moderate (β2)

Severe (β3)

Complete (β4)

Low-rise

0.28

0.37

0.82

0.83

Mid-rise

0.28

0.36

0.50

0.61

High-rise

0.28

0.29

0.34

0.45

Table 3. βds for each RC building class.

Slight (Sd1)

Moderate (Sd2)

Severe (Sd3)

Complete (Sd4)

0.7Dy

Dy

Dy+0.25(Du-Dy)

Du

Table 4. Sd,ds determination for each damage state threshold.

4 NUMERICAL MODELLING

The different models considered in this study have been modelled with the STKO software

[19], a Graphical User Interface (GUI) for OpenSees.

4.1 Superstructure

The nonlinear behaviour of the RC elements has been simulated though the distributed

plasticity approach. This can automatically compute deformations and curvatures, reducing

the modelling time. The RC beams and columns have been discretised into different fibres

with the fibre section aggregator. In order to take p-delta (p-Δ) effects into account, force-

beams elements have been applied to the RC frames. “Concrete01” has been considered to

simulate concrete. The concrete’s core has been defined by increasing its strength and strain

according to [20]. “Steel02” has been used to model steel. In this case, the smooth rebars have

been considered by decreasing the steel elastic modulus as in [21]. The effects of infills have

been taken into account by means of the two-diagonal truss approach defined in [22]. Due to

the rigidity of the concrete slabs, rigid diaphragm interactions have been applied to the nodes

of each floor. Masses have been applied to each structural member considering the gravita-

tional loads and the self-weights. Gravitational loads have also been applied to each structural

element bearing in mind: dead (self- weight and the weight of constructive elements) and live

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

loads. The characteristics of the structural materials considered in this study are listed in Table

5.

Concrete

Steel

Infills

ƒc(MPa)

28

ƒy(MPa)

370

Gw(GPa)

1240

ƒcu (MPa)

4

Es(GPa)

310

α

0.05

ɛc(%)

0.002

τcr (MPa)

280

ɛcu (%)

0.04

Ew(GPa)

4092

Table 5. Values of the structural materials’ parameters.

Where: concrete compressive (ƒc) and crushing strength (ƒcu); concrete strain at maximum (ɛc) and ultimate

strength (ɛcu); steel yielding strength (ƒy); steel modulus of elasticity (Es); infills shear modulus (Gw); post-

capping degrading branch coefficient (α); shear cracking stress (τcr); masonry elasticity modulus (Ew).

4.2 Continuum modelling of the soil

The underlying soil of the building has been modelled with a mesh of 125x40x21 m (X, Y

and Z directions). The mesh has been defined according to the Vsand to the frequency (ω) of

the models. “SSPbrick” brick elements have been applied to the solid elements to capture the

soil small deformation (Figure 5). The mesh is characterised by 51,954 nodes and 120,040

brick elements. The lateral boundaries have been fixed in the corresponding direction and the

base in all directions.

According to the different test results (Section 2.2), the soil beneath the building is clayey.

Therefore, the analyses have been performed under undrained conditions since this is the most

restrictive. Hence, the soil constitutive behaviour has been simulated by means of the “Pres-

sureIndependMultiYield” (PIMY) material. This has been implemented in OpenSees to model

elasto-plastic undrained clay-type soils, which are independent from pressure. The soil’s fail-

ure criterion is based on Von Mises’multi-surface plasticity theory (Figure 5) determined in

[23]. “EqDOF” has been applied to the interaction between the soil’s and the foundation’s

surfaces. Four soil layers have been defined according to the characterisation performed in

Section 2.2, which can be observed in Figure 4.

Figure 5: “PressureIndependMultiYield” soil material’s failure criterion.

5 RESULTS AND ANALYSIS

The results obtained from the analyses appear in this section. In Figure 6, the deformed

shape of each model after the application of the gravity loads is shown. As can be observed,

the settlement of the structure is higher when the height increases. The displacement in the Z

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

direction of the control node (in the rooftop) increases 220% and 323% when adding 2 floors

(M2) and 4 floors (M3), respectively. Therefore, this increase is not linear.

Figure 6: Deformed shape of models analysed after the application of gravity loads.

In Figure 7, the SDOF capacity curves for each of the models have been plotted. Also, the

damage states (Section 3.3) and the target displacements (demand) have been determined. In

order to compare the results, the multi-degree-of-freedom (MDOF) curves have been normal-

ised by dividing the base shear (Vb) by the weight (W) and the displacement (d) by the total

height (Ht).

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

Figure 7: SDOF normalised capacity curves for each of the models assessed.

It can be observed that the higher the structures’ height, the higher the soil effects. In the

case of the low-rise model (M1), the SSI just decreases the initial stiffness of the systems. In

the X direction, the difference between the demand and the NC displacement is higher for the

S models. In the Y direction, for the F model, the demand is located between the LD and the

SD. However, when considering the SSI, the demand is after the SD; therefore, it will not

comply with the EC8 requirements like in the X direction. Mid-rise buildings are more affect-

ed by the SSI than low-rise buildings due to the considerable modification of the initial stiff-

ness. The maximum capacity has been reduced by around 10%. In the Y direction, the

demand displacement is considerably higher for the S model. High-rise models are the most

affected by the SSI, the maximum capacity being reduced by up to 30%. In terms of damage,

the models behave worse due to the failure of columns located in the irregularity of the

ground floor.

In Figure 8, the fragility curves for each of the models analysed are plotted considering the

demand displacement. It can be noted that the fragility curves for the models with SSI are

worse than the F-model’s curves. Therefore, the probability of reaching higher damage in-

creases in models that bear the soil influence in mind. This probability also increases with the

height. As can be seen, the S-model’s fragility curves are worse than the F-model’s curves

when the height increases. This results in the high-rise models being the most affected. More-

over, the fragility curves of high-rise buildings are worse than the rest due to the statistical

parameters’values.

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

Figure 8: fragility curves considering fixed-based and solid models and low-, mid- and high-rise models.

6 CONCLUSIONS

This paper aims to analyse the SSI in the seismic vulnerability analysis of RC buildings.

The state of the art has revealed that SSI must be considered in the seismic analyses of mid-

and high-rise buildings. Therefore, different configurations of a case study RC building have

been defined by varying the height: low- (real), mid- and high-rise. The characterisation of the

location’s soil profile has been carried out. This characterisation has revealed that the soil is

clayey.

Nonlinear static analyses have been performed to assess the models’ capacity. The seismic

damage has been determined by means of the European seismic code (local damage of ele-

ments) and the fragility procedures (global damage). 3D nonlinear models considering the soil

as a continuum have been modelled using the FEM to simulate the soil nonlinear behaviour.

The results have shown that the soil does not significantly influence the behaviour of low-

rise buildings. However, in the case of mid- and high-rise buildings, the maximum capacity

can be reduced by up to 10% and 30%, respectively. Moreover, according to the local damage

assessment, structural elements might collapse due to considering the soil, even for low-rise

buildings.

In the light of the fragility assessment results, it can be concluded that the probability of

reaching higher seismic damage increases when considering the SSI. Moreover, this probabil-

ity increases with the height.

This work has considered the most probable soil profile that can be found in the area.

However, further research should be carried out in order to consider several soil profiles since

softer layers could worsen the building’s seismic capacity. This research has considered statis-

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M.V. Requena-Garcia-Cruz, A. Morales-Esteban, P. Durand-Neyra, E. Romero-Sánchez

tical parameters from other works in the fragility assessment. Yet, further research should be

assessed to properly determine these values according to the models’characteristics and the

type of soil. This research has not considered the element contact between the soil and the

foundation’s surfaces, which can capture the soil behaviour better, leading to more accurate

results.

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