SOIL-STRUCTURE INTERACTION IN THE SEISMIC VULNERABILITY ANALYSIS OF RC BUILDINGS. APPLICATION TO A CASE STUDY BUILDING LOCATED IN SOUTHWESTERN SPAIN

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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, 230 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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