Analysis of the effects of soil-structure interaction in reinforced concrete wall buildings on shallow foundation

Resumo This paper presents a study of the effects caused by soil-structure interaction in reinforced concrete wall building on shallow foundation. It was verified the influence of displacements of supports on the redistribution of internal forces in the structural walls and in the redistribution of loads on the foundation. The superstructure was represented by shell finite elements and the soil-structure interaction was evaluated by iterative methods that consider the stiffness of the building, the soil heterogeneity and the group effect of foundation elements. An alternative model that considers the soil-structure interaction is adopted and the concrete walls are simulated by bar elements. The results indicate that the soil-structure interaction produces significant changes of the stress flow, with larger influences on the lower walls, as well as a tendency of settlements standardization and load migration to supports with smaller settlements.


Introduction
A Concrete wall is a rationalized construction system that offers the advantages of high-scale production, in which the structure and the sealing are formed by a single system.In a concrete wall system, the window frames and electrical, sanitary and hydraulic installations can be incorporated.All the walls and slabs of the same cycle are concreted in a single step.Due to the high degree of industrialization, a concrete wall system is presented as a viable alternative.This constructive system is recommended for buildings that need to be executed quickly and that have a short delivery deadline and/or high repetition rate.
Behavior and structural analysis of reinforced concrete wall buildings has been topic of research in Brazil (Nunes [1] and Bragum [2]).The Brazilian National Standards Organization (NBR 16055:2012 [3]) regulates the quality, enforcement procedure and structural analysis of reinforced concrete wall buildings.Traditionally, in the behavior analysis of reinforced concrete wall buildings, fixed supports are considered.However, the settlement of the foundation causes the internal force redistribution in the structural elements.In short, the reinforced concrete wall system behavior is governed by superstructure, infrastructure and soil interaction.This mechanism is called soil-structure interaction (SSI) and has been the topic of many studies (Meyerhof [4], Chamecki [5], Goshy [6] and Gusmão [7]).Testoni [8 and 9] and Santos [10] discussed SSI in reinforced concrete wall buildings.Despite recent research and the design code, advances are still needed in knowledge regarding the reinforced concrete wall building behavior and their analysis models.In this paper, the procedures and results of an SSI analysis of a reinforced concrete wall building with 10 floors and a shallow foundation are presented.

Numerical modeling of superstructure
The numerical analysis of structural walls can be carried out using discrete or continuous techniques.The discrete procedure enables more flexibility because it is able to solve problems with varied geometry and loads.Liu et al. [11] shows three general methods for the wall structural analysis following a discrete technique, as shown in Figure 1.In this paper, two types of superstructure discretization were used.In the first one, called the SHELL model, discretization by shell elements was adopted, as shown in Figure 1d.This model provides accurate results that were not obtained using the beam elements, e.g. the internal force flow in the walls and consequent migration of the load for the supports.However, laborious computational modeling and result analysis can make it unfeasible for the daily use of structural design.Therefore, using a simplified model is preferred.A second type of superstructure discretization, called MIXED model, to analyse a simplified model was considered.This model adopted equivalent beam-column elements (Figure 1a) above the second floor.Taking into account the effects caused by SSI, the shell elements on the two lower floors were kept.The finite element method (FEM) was used adopting the SAP2000 software to carry out the numerical analysis of the study building.The material was considered as linear elastic behavior.
To discretize the wall in the SHELL model, four-node quadrilateral shell finite elements (Shell-thin) were used with dimensions of 0.4mx0.4mand 0.12 thickness, as shown in Figure 2. Braguim [2] made comparisons between meshes with 0.2mx0.2mand 0.4mx0.4mdimensions and concluded that the differences in the results are practically non-existent.In this paper, a prior analysis was carried out to evaluate the influence of the mesh discretization on the results of the study building.The 0.4mx0.4mmesh element presents similar results to more refined mesh and a lower computational cost.The floor slab was considered as a rigid planar diaphragm.In the MIXED model, the walls are discretized by frame elements.This discretization was based on Yagui [12 and 13], where the walls are replaced by the plane frame formed by horizontal rigid beams and a flexible column.This frames are join by a rigid floor Analysis of the effects of soil-structure interaction in reinforced concrete wall buildings on shallow foundation slab (rigid planar diaphragm), forming a three-dimensional system.The columns must have the same geometric features as their respective walls and should be located in the geometric center of the walls.The walls are connected by a rigid horizontal beam and are applied on the floor level.Corrêa [14] recommends that the adopted value of beam rigidity is sufficiently large, as long as it does not disturb the numerical instability.In this paper, the Young's modulus value was multiplied by 100, as applied in Testoni [8]. Figure 3 shows a schematic drawing of the equivalent beam-column element discretization.The connection between two rigid beams are considered joints, where the only vertical shear stress is only taken into account.In this model, door and window openings are considered as flexible beams of infinite axial rigidity as shown in Figure 4.According to NBR 16055:2012 [3], the wall of the structural system can be represented by a linear element as long as the shear deformation is considered.Nascimento Neto [15] suggests a refinement of the model proposed by Yagui [12 and 13] to consider shear deformation in a simplified way.A shape factor of c = 1.2 was used to reduce the section area of the walls and determine the equivalent shear area (A s = A ⁄ c ).In the three-dimensional frame model proposed by Yagui [12 and 13] it is not possible to analyse the migration tendency of the load for the supports.Considering this behavior on the structural model, the walls of the first and second floor had to be discretized by shell elements, based on Nunes [1] and Testoni [8 and 9].In this model, the first and second floors were discretized by a 0.2mx0.2mmesh to ensure that all the columns were connected to a node of the shell element.

Methodology for SSI analysis
Aoki [6] proposed an iterative procedure based on Chamecki [5] for the SSI analysis.This methodology analysed the separate superstructure of the foundation, searching for a final balance configuration through the displacement compatibility of the superstructure/foundation. Initially, the support loads considering the rigid base hypothesis are calculated.These loads are used to calculate the shallow foundations.The shallow foundation are considered rigid elements and a linear pressure diagram is allowed at the base/ soil contact.The Mindlin [17] equations calculate the strain and stress in the soil points caused by a normal force.These equations consider the soil as an elastic isotropic and semi-infinite solid.Figure 5 presents the variables involved in this problem.The displacements of the shallow foundations are calculated by Eq. ( 1). ( Where P is the normal force, c is the depth of applying the normal force, ν is the PoSSIon's ratio, B (x,y,z) is the point where the displacements are determined, z is the depth of the B (x,y,z) point and E is the Young's modulus.R 1 and R 2 are calculated by the geometric properties.In order to determine the displacements, the base of the loaded footing in subareas was discretized in which the occurrence of a  concentrated load can be considered.In order to consider the group effect, the settlements are added due to the loads of all the footings in the building, according to Figure 6.The total settlement δ of footing k is calculated in the geometric centre of its base by Eq. ( 2).The rotations in the footings were determined directly by the settlements obtained at their ends, according to Figure 7.The stratification of the soil mass is considered using Steinbrenner's technique [18]. (2) After determining the vertical settlements and the footing rotations, the spring coefficients are determined by dividing the reactions of each support by the corresponding displacements.The calculated spring coefficients are imposed on the superstructure supports.Then the superstructure is recalculated and the new support reactions are determined.The whole procedure is repeated until the values of the reactions converge or the settlements are obtained between two consecutive iterations within a desired tolerance.More details about the methodology adopted can be found in Santos [10].In this paper, the convergence criterion presented in Eq. ( 3) was applied, with tolerance ξ = 10 -3 . ( Where P k is the axial force of footing k in the current iteration, P k * is the axial force of footing k in the previous iteration and ξ is the tolerance.A computational routine was developed in MATLAB v7.10.0. to automate this procedure.

Building description
The evaluated building is the same one adopted in Braguim´s study [2] and is an adaptation of the Condomínio das Árbores building, built in the city of São Bernado do Campo, Brazil designed by the company OSMB Engenheiros Associados Ltda.The adapted building has ten floors, wall thicknesses of 0.12m, slab thicknesses of 0.10m and ceiling of 2.80m.The adaptations aimed to simplify the computational modelling and basically consisted of considering all floors equal to the type and modifying all measurements for multiples of 0.4m.The layout and names of the walls are shown in Figure 8.The abbreviations PH and PV were used for the horizontal and vertical walls, respectively.The wall lengths are shown in Table 1.Reinforced concrete was considered as isotropic material with the  Analysis of the effects of soil-structure interaction in reinforced concrete wall buildings on shallow foundation following mechanical properties: compression strength of 25MPa, secant modulus of elasticity of 24GPa, PoSSIon coefficient of 0.2 and specific weight of 25kN/m³.In the analysis, only vertical loads were considered: dead load (sum of the weight of the structure with the slab coating loads) and live loads (overhead of residential building slabs according to NBR 6120: 1980 [20]).The stairs were simplified by considering a slab with a thickness of 0.12m.The load distribution of the slabs on the walls was done adopting the yield line theory, using the values presented in Table 2.A ground beam was considered under the building with cross sec-tion dimensions of 0.2mx0.5m.In the computational model, the ground beam was discretized by beam elements.A total of 47 shallow foundation were used at 1.5m depth, according to Figure 9.The foundation design was defined after considering the   normal loading results of the model with fixed supports, assuming the symmetry of the foundations.Table 3 shows the characteristics of the shallow foundations adopted in the design.
To characterize the soil type, the boreholes used in Santos' paper were adopted [10].This profile has three SPT (Standard Penetration Test) boreholes, identified by S1, S2 and S3, located according to the Figure 9. Table 4 presents a summary of the Young's modulus values for each soil layer considered in the borehole.The PoSSIon coefficient was adopted at 0.30 for all layers.The Young's modulus values were estimated based on the soil parameters, as described in Santos [10].

Results and discussion
In the first series of comparisons, the effects produced in the building after considering the soil-structure interaction are presented.To do this, comparisons are made between the SHELL model with the rigid supports (SHELL RIG) and the SHELL model with the movable supports (SHELL SSI), using the methodology described in item 3. The results of the normal stress in the walls, the loads applied to the foundations and the settlements of the shallow foundations are presented.The desired convergence in the sixth iteration was obtained using the SHELL SSI model.
In the second series of comparisons, the results of the proposed simplified model (MIXED model) are presented.The results obtained in the MIXED model are compared with the reference model (SHELL model).In the simplified model analysis, the soil-structure interaction is addressed in two ways.In the first one, called the MIXED SSI model, the soil-structure interaction is considered using the methodology presented in item 3.In the second approach, called the MIXED SIMP model, the spring coefficients are determined by the estimated settling method, which basically consists of dividing the reactions of each support by its settlement, obtained by Mindlin's equation [17].In practice, the spring coefficient of the MIXED SIMP model is determined in the first iteration, while the spring coefficient for the MIXED SSI model is obtained after convergence of the algorithm, according to the criterion presented in Eq. ( 3).The MIXED SSI model produced the desired convergence in the seventh iteration.
According to NBR 8681 [21], the weighting coefficient γ f can be considered as the product of two others, γ f1 and γ f3 .The partial coefficient γ f1 considers the variability of actions and coefficient γ f3 considers the possible errors of evaluation of the effects of the actions, either by constructive problems or by deficiency of the calculation methods.Therefore, considering the weighting coefficient γ f =1,4 for the normal considerations, the γ f1 and γ f3 coefficients can unfold in the product of two equal values, i.e., γ f1 = γ f3 = 1.18.Thus, the variation of 18% would be considered covered by γ f3 = 1.18.
In this paper, the differences below 5% are considered as an excellent approximation.Values between 5 and 18% are considered good or satisfactory approximation.Differences above 18% are considered bad or unacceptable.

First series of comparisons
Initially, the effects caused by considering the soil-structure interaction in the normal stresses of the building´s walls were evaluated.The normal stresses (at the foundation level) of the building´s walls are presented and compared in Table 5.
Consideration of the soil-structure interaction generated a redistribution of the stresses of the building walls, with a mean absolute deviation of 34%.This redistribution of stresses is accounted for by the high rigidity of the superstructure, which limits differential settlements and sets a trend towards settlement uniformisation.Therefore, symmetrical walls with the same geometric characteristics present different normal stresses due to soil heterogeneity.Among all the walls of the building, 64% presented differences greater than 18% and out of these, approximately half had an increase of normal requests.There are marked increases in stresses, for example on PH04, PH43, PH44 and PH50 walls which increased by more than 100% and which would exceed the normalized resistance limits.
Figure 10 shows the normal force diagrams on some of the building´s walls.We decided to analyse PH01, PH02, PH03, PH13, PH15, PV06, PV09, PV13 and PV16 walls because they had different characteristics (length, door and window openings, etc.) and

Figure 9
Foundation plan It can be observed that the greatest differences between the normal stress values in the building´s walls occur, as expected, on the lower floors.However, in some of the building´s walls, the influence of the soil-structure interaction affected the upper floors, for example in the PH03, PV13 and PV16 walls.
The loads applied in the building´s foundation obtained from the shell model with the fixed supports were compared with the loads obtained from the shell model on the flexible supports, presented in Table 6. Figure 11 shows a graph of the dispersion of values of the vertical load applied in the foundations.In this graph, the peripheral foundations are highlighted by vertical lines.In general, load redistribution occurred in the building´s foundations with a mean absolute deviation of 27%.Approximately 64% of the foundations showed differences of more than 18%, highlighting the increase of 126% in the F47 footing.There was also a tendency to reduce the bending moment in both directions, where the majority of the values were cancelled.
The mechanism that governs the load redistribution in the supports is the tendency to standardize the settlements.In the analysed building, the foundations located in the region of the S2 borehole show the behaviour of yielding to the neighborhood, since this region presented the highest settlements.There is also a trend of load transfer to the peripheral foundations.
Table 7 shows the vertical displacement of the supports of the building and Table 8 presents some information about the behaviour of the

Figure 11
Scatter plot of the vertical load of the building foundations Analysis of the effects of soil-structure interaction in reinforced concrete wall buildings on shallow foundation settlements after considering the soil-structure interaction.Figures 12  and 13 present the isosettlement curves for the SHELL RIG and SHELL SSI models, respectively.To make the isosettlement curves, the centroid coordinates of each footing were considered in the (x, y) plane and the settlement was adopted as the z coordinate.The linear triangulation interpolation method was used to determine the multiple settlement values of 0.5mm, and thus generate the same value curves.
Observing the isosettlement curves of the SHELL RIG model, it can be observed that the largest settlements are in the region of the S2 borehole, where the soil is more deformable.However, when analysing the soil-structure interaction, a reduction of the settlements in this region can be observed, accounted for by the rigidity of the superstructure that limits differential settlements and redistributes the loads to the neighbouring foundations.
The results show a reduction of 44% in the maximum differential settlement and 30% in the maximum settlement.The reduction in the coefficient of variation emphasizes the tendency of settlement uniformisation caused by the consideration of the soilstructure interaction.The average settlement presented a low reduction, of the order of 10%.When analysing the isosettlement curves, a clear trend of settlement uniformisation can be clearly observed.

Second series of comparisons
The results of the simplified models are compared and evaluated.
In Table 9, the normal (foundation level) stresses of the building walls were compared.Figure 14 shows the diagrams of normal force along the walls studied.
By analysing the results of the normal force on the building´s walls, it can be observed that the simplified models were able to adequately represent the load distribution between the walls.However, there is a perturbation on the second floor.This perturbation is accounted for by the concentration of force at the top of the wall (transition from the column element to the shell element).This characteristic does not interfere in the results, as in all cases the diagram, outside the perturbation region, presented good results, compared to the more refined model.The MIXED SSI model presented a mean absolute deviation of 9%, where 45% of the walls had excellent results, 44% had good results and only 12% presented results with differences above 18%.The quality of the MIXED SIMP model is somewhat lower, but represents the redistribution of loads between the walls.This model presented a mean absolute deviation of 15%, in which 22% of the results were optimal, 53% good and 25% bad.
Tables 10 and 11 present the comparisons of the loadings on the foundations for the MIXED SSI and MIXED SIMP models, respectively.The simplified models presented a good approximation of the vertical reactions in the footings, with a mean absolute deviation of 4% and 9% for the MIXED SSI and MIXED SIMP models, respectively.The MIXED SSI model did not present any results outside the acceptable range, with 85% of the results in the optimal range and 15% in the good ones.The MIXED SIMP model presented 38% of the results in the optimal range, 53% in the good and only 9% in the bad one.For the moments applied there is a high divergence between the results.

Figure 12
Isosettlement curve of the SHELL RIG model  Table 12 shows the estimated settlements for the building foundations.Table 13 presents some additional information.
The MIXED SSI model presented excellent results, with a difference of 1% in the mean settlement and a difference of 5% for the maximum settlement and maximum differential settlement.In this model, none of the absolute settlements exceeded the 18% difference limit.The MIXED SIMP model presented a mean difference of 2%, 3% for the maximum and the 15% for the maximum differential.In this model only three foundations presented differences higher than the limit of 18%.

Conclusions
Consideration of the soil-structure interaction caused a general Analysis of the effects of soil-structure interaction in reinforced concrete wall buildings on shallow foundation

Figure 14
Normal force diagram of the walls of the simplified models Analysis of the effects of soil-structure interaction in reinforced concrete wall buildings on shallow foundation   trend towards the standardization of settlements.The maximum differential settlement and the maximum absolute settlement showed a marked reduction.The mean settlement, however, was not very influenced.
The soil-structure interaction provided a redistribution of the loads in the foundations and a significant reduction of the applied moments.As a general rule, there was a load transfer from foundations with higher settlements to the neighbouring foundations of lower settlements.There were important changes in the normal stresses of the walls.The greatest influence of the soil-structure interaction occurred on the first floors, where there were differences greater than 18%, adopted as an acceptable limit in this work.The simplified models adequately represented the stress flow on the walls and the load distribution on the foundations.The MIXED SSI model presented the best results.

Figure 1 Figure 2
Figure 1 Modeling wall methods (Source: adapted from Liu et al, 2010)

Figure 3 Figure 4
Figure 3 Discretization of the wall in frame elements (Source: Nascimento Neto, 1999)

Figure 13
Figure 13Isosettlement curve of the SHELL SSI model

Table 1
Length of walls

Table 2
Slab loads

Table 3
Characteristics of the footings

Table 4
Young's modulus values

Analysis of the effects of soil-structure interaction in reinforced concrete wall buildings on shallow foundation are
subject to different levels of loading.The percentage values in the graph indicate the differences in normal forces between the SHELL RIG and SHELL SSI models.

Table 5
Normal wall force -kN Figure 10Normal force diagram of the buildings walls Analysis

of the effects of soil-structure interaction in reinforced concrete wall buildings on shallow foundationTable 6
Loading of the foundations -kN and kN.m

Table 7
Settlement of the building supports -mm

Table 8
Supplementary information on settlements

Table 9
Normal wall strength in the simplified models -kN

Table 10
Loading on the foundations of the mixed model SSI -kN and kN.m

Table 11
Loading on the foundations mixed model SIMP-kN and kN.m

Table 12
Settlement for simplified models -mm