Soil-foundation-superstructure interaction: effects on the soil

Transcription

1 Soil-foundation-superstructure interaction: effects on the soil A. Ghersi ^\ M.R. Massimino, M. Maugeri ^ Istituto di Scienza delle Costruzioni, Universita di Catania, vialea. Doria 6, CATANIA aghersi@isc.ing.unict.it Istituto di Strade Ferrovie Aeroporti, Universita di Catania, vialea. Doria 6, CATANIA mmaugeri@isfa.ing.unict.it Abstract In dynamic problems soil-structure systems have often been examined with two opposite approaches: on the one hand accurate soil dynamic analyses with a simplified superstructure have been proposed, on the other hand accurate superstructure dynamic analyses with a simplified soil have been used. Recently more sophisticated numerical methods, that consider global soil-structure systems, have been worked out. In the present paper a new finite element code, named SOFIA, was used to evaluate soil-foundation-frame interaction. The SOFIA code is an easy-to-use, very powerful tool, which allows both to analyse the effect of vertical loads and to simulate earthquakes through pseudo-static analyses. In particular, the aim of the paper is to evaluate the foundation settlements and the soil stress and strain level under vertical and seismic loads. The results point out the necessity of unitary soil-foundation-superstructure analyses for a reliable estimation of foundation differential settlements. 1. Introduction The dynamic soil-foundation-superstructure interaction phenomena have been very often studied by means of two separate analyses, taking into particular account either the superstructure or the soil behaviour. In the first case the soil influence has been considered including the soil impedances in the superstruc-

2 576 Earthquake Resistant Engineering Structures ture model; in the second case the superstructure has been simulated with a lumped-mass system on an accurate soil schematisation. Only in the last few decades more sophisticated methods have been proposed both for static (Majid & Gunnel [7]) and for dynamic interaction problems (Naesgaard et al [9]). They deal with unitary soil-structure systems and are based on numerical approaches, such as FEM, BEM, FDM and hybrid approaches. Even if the boundary element methods do not present the problem of the finite size of the soil mass interacting and thefinitedifference methods are particularly suitable for operating with the time parameter, the finite element methods are mostly used because they allow an easier consideration of several geometrical meshes and several strain-stress relationships. Besides, the FEM approach is the most used for structural problems. In the present paper a new FEM code, named SOFIA (Soil Frame Inter Action) is proposed in order to analyse the static and pseudo-static behaviour of soil-foundation-superstructure systems. One of the most important aspects of this code is the possibility of a unitary analysis of the above three interacting components. In particular, in the present study the SOFIA code was used to evaluate the behaviour of the asymmetric plane-frame considered in Ghersi et al. [5], pointing out the foundation settlements and the strain and stress effects on the subsoil. Above all, the global soil-frame interaction allows us to emphasise the importance of earthquake direction on foundation differential settlements especially for decidedly non-symmetric frames. 2. The SOFIA code: soil modelling The proposed FEM code, as mentioned in Ghersi et al. [5], can analyse planeframes with fixed-based columns, or with Winkler beds or resting on a soil FEM subdivided volume. In this last case the soil is subdivided by means of isoparametric quadratic plane elements. The latter can present straight or curved sides to model, for example, eventual soil cavities. For each soil-element nine Gauss integration points were considered, to reach a high calculation accuracy. Even if the code works in 2-D plane-strain condition, there is the possibility to take into account the 3-D effects by means of a simplified procedure, calibrating the stiffness of the elements by dividing the Young modulus of each soilelement by two coefficients. The first one, named kind, takes into account the foundation dimension in the direction orthogonal to the examined plane, according to the following expression: 0) being y(r.a.) the vertical deformation of a generic point in the soil at a y depth due to a rectangular uniform load area applied on the soil surface; Sy(SA.) the vertical deformation of the same point in the soil due to a strip load area (Z/Z?>100) with the same uniform load; % the Poisson coefficient of the soil, L

3 Earthquake Resistant Engineering Structures 577 and B the foundation dimensions in the horizontal directions respectively orthogonal and parallel to the examined plane. The vertical deformations were determined basing on well known formulations provided by the theory of Elasticity A more appropriate value of /w was estimated as the average of the values ktaaside (y) and ktn&centre (y), calculated considering the deformations along the vertical across the middle point of the foundation side and the deformations along the vertical across the foundation centre respectively. The second coefficient, named /ta</, is related to the presence of other eventual frames near the one examined. Following the same steps to determine expression (1), the /I* / was evaluated by a numerical procedure: where %/,-/ is the vertical settlement of the i-soil element due to the j-uniform load area; r is the number of the uniform load area next to the examined one; w,,o is the vertical settlement of the i-soil element due to the given uniform load area. Rotations, horizontal and vertical displacements are restrained along the lower horizontal soil boundary, while only rotations and horizontal displacements are restrained along the vertical soil boundaries. The soil mesh can present a gradual increasing of the soil-element number near the frame, where the biggest strain and stress changes are expected. The subsoil can be completely homogeneous, or with different horizontal homogeneous layers or,finally,can present a variation of the Young modulus with the depth according to the Janbu [6] law. While for the structural elements only a linear-elastic stress-strain relationship is actually considered; the soil-elements can have a linear and a non-linear stress-strain relationship. In this last case the Duncan and Chang ([2]) hyperbolic constitutive law is used. The frame, subdivided into the typical monodimensional beam and column elements, can be put on the top of the soil mesh or at a certain depth from the soil surface, to simulate the foundation embedment. The code simulates a soil excavation and the different phases of the related load increments due to the construction process. In this way it is possible to analyse a frame that changes its configuration, its rigidity and its load condition at different times, such as in the monitoring of full-scale buildings during their construction process. As regards the load condition, the SOFIA code presently allows the consideration of vertical spread or concentrated loads and horizontal forces applied to each elevation. In this way it is possible to evaluate the earthquake effects on the unitary soil-foundation-superstructure system by means of a pseudo-static analysis, according to Italian seismic code [1] and Eurocode 8 [4]. The code, however, was made with a greatflexibilityto easily increase, for example, the number of element typologies and of strain-stress relationships. Finally, for static condition it was widely tested through different comparisons with other codes, theoretical and experimental literature data and through full-scale building monitoring (Massimino, [8]).

4 578 Earthquake Resistant Engineering Structures 3. FEM analysis of a plane-frame resting on sand deposits In the present paper the SOFIA code was used to simulate the behaviour of the soil-foundation-superstructure systems shown in Fig. 1. The same system was also studied in Ghersi et al. [5] pointing out the soil-structure effects on the superstructure behaviour. The system consists of a 5-floor reinforced concrete plane-frame with a beam foundation resting on a sand deposit. The soil was subdivided by means of isoparametric quadratic elements with smaller dimensions approaching the soil-frame interface, where a big stress and strain variation is expected. The soil-mass extends 33 m in the vertical direction and m in the horizontal direction, so that the boundary does not influence the frame behaviour. For all the structure-elements and the soil-elements the elastic-linear constitutive law was considered. In particular, for the structural elements a Young modulus of N/mnf and a Poisson coefficient of 0.28 werefixed;while for the sand subsoil the geotechnical parameters reported in Table 1 were used. The subsoil was also considered homogeneous across the whole interacting mass. The geometrical properties of the frame are reported in Ghersi et al. [5]. The 3-D effect was also taken into account by means of the k^a values shown in Fig. 2. In particular, in Fig. 2 both the side and centre ktnd (y) curves are reported. It is easy to see that there is not a significant difference between the two curves especially as the depth increases. Firstly, an excavation of 3 m was simulated. Secondly, putting the frame at the bottom of the excavation, the soil-foundation-frame system was analysed under the dead and live loads evaluated according to the Italian code. /I 161n 1 *T"T^I V 1II II m Isoparametric quadratic ^^ element "* m Figure 1. The examined soil-foundation-frame system

5 Earthquake Resistant Engineering Structures Figure 2. The k^d coefficient versus thej/ depth Finally, the seismic action was simulated through the application of horizontal forces at the different frame elevations (Table 2), following the pseudo-static approach. In particular, the three different values of the seismic intensity coefficient proposed by Italian seismic code [1] were used. The two possible horizontal force directions were also analysed, considering the decidedly asymmetric configuration of the plane-frame. Table 1. Geotechnical parameters of the sand subsoil f [kn/m*} 19 c* [KN/m*] 0 9" ns KE Vs OCR n / / / / elevation I II III TV V VI Table 2. Pseudo-static horizontal forces c = force fknl c= c =

6 580 Earthquake Resistant Engineering Structures 4.Results of static and pseudo-static simulation To analyse the effects of an earthquake in respect of the static condition, firstly the soil-frame system, described in the previous section, was submitted to its typical dead and live loads (Fig. 3). In this case the frame shows a vertical rotation due to the eccentricity of the total vertical load. This rotation decreases considering the seismic horizontal forces applied to the frame elevations with the left-right direction, as shown in Fig. 4 for the higher value of the seismic coefficient C = 0.10, while the static rotation becomes larger changing the horizontal force direction (Fig. 5). In particular, in Fig. 5 it is possible to see an increasing rotation of frame and foundation with the increase of the seismic intensity. In all the Figs. 3, 4 and 5 the movements are shown with a scale of 1:250. Figs. 6 and 7 show also respectively the vertical and horizontal stress increments on the soil due to the horizontal forces directed from right to left and with a seismic coefficient equal to 0.07, that in Italian seismic code characterises the medium intensity seismic zones, such as the Catania area. The above mentioned figures represent only some of the many graphical outputs of the SOFIA code regarding the effects on the soil due to the soilfoundation-superstructure interaction. As regards the soil stress and strain levels it is also possible to plot the initial in-situ vertical and horizontal stresses, the increments of shear stresses, the increments of the maximum and minimum principal stresses, the directions of these last two stresses and the vertical and horizontal movements. The evaluation of the stress and strain level due to the soilstructure interaction regards not only the soil-structure effects on the soil, as shown in the present paper, but also the soil-structure effects on the superstructure, as reported in Ghersi et al. [5]. In Fig. 8 the foundation settlements are plotted, showing a maximum differential settlement of about 5 mm. The differential settlement, particularly for worse soil characteristics, should be evaluated and compared with the values allowed by Eurocode 7 [3]. 5. Conclusion In the present paper a global soil-foundation-superstructure interaction analysis in static and pseudo-static conditions was presented. It was carried out by means of a new finite element code, named SOFIA. In particular, the behaviour of a decidedly non-symmetric plane-frame resting on a sand subsoil was evaluated. After the excavation simulation, the soil-frame system was submitted to the dead and live frame loads. Finally an earthquake was simulated, according to the pseudo-static analysis mentioned in Italian seismic code [1] and in Eurocode 8 [4]. In the earthquake simulation both the possible directions of the seismic horizontal forces were considered. The seismic horizontal force direction reduces or increases the maximum differential static settlement in a significant way. Besides, the SOFIA code supplies

7 Earthquake Resistant Engineering Structures 581 important information on the stresses and strains induced by the soil-structure interaction not only on the soil but also on the superstructure. Figure 3. Soil-frame deformation under static condition displacement scale 1:250 Figure 4. Soil-frame deformation under pseudo-static condition (C = 0.10) with left-right direction of the horizontal forces - displacement scale 1:250

8 582 Earthquake Resistant Engineering Structures Figure 5. Soil-frame deformation under pseudo-static condition with right-left direction of the horizontal forces - displacement scale 1:250

9 Earthquake Resistant Engineering Structures 583 Figure 6. Vertical stress increments on sand soil in pseudo-static condition with horizontal seismic forces directed from right to left and C = 0.07 Figure 7. Horizontal stress increments on sand soil in pseudo-static condition with horizontal seismic forces directed from right to left and C 0.07

10 584 Earthquake Resistant Engineering Structures 1.5 left-right earthquake (C = 0.04) left-right earthquake (C = 0.07) left-right earthquake (C = 0.1) static condition right-left earthquake (C = 0.04) right-left earthquake (C = 0.07) right-left earthquake (C = 0.1) Figure 8. Foundation settlements in static and pseudo-static condition References 1. DM , Norme tecniche relative alle costntzioni sismiche ~ Suppl allag. U. dellarepubblicaitalianan. 29, , Roma, Duncan, JM and Chang, C Y, Non-linear analysis of stress and strain in soils, JSMFDM,ASCE, 96, pp , Eurocode 7, Geotechnical design, General Rules - Part 7, European Committee for Standardisation, Eurocode 8, Design provisions for earthquake resistance of structures ~ Part 5: Foundation, retaining structures and geotechnical aspects, European Committee for Standardisation, Ghersi, A., Massimino, MR & Maugeri, M., Soil-foundationsuperstructure interaction: effects on the superstructure, Proc. 2"** Int. Symp. on Earthquake Resistant Engineering Structures, ERES 99, Catania, Italy, June Janbu, N., Soil compressibility as determined by oedometer and triaxial tests, Proc. ECSME, Wiesbaden, 1, pp , Majid, KL and Cunnel, M.D., A theoretical and experimental investigation into soil-structure interaction, Geotechnique, 26(2), pp , Massimino, MR., Analisi non-lineare delvinterazione terreno-fondazione-sovrastruttura mediante tin nuovo codice FEM, PhD thesis, Naesgaard, E, Byrne, P.M. and Ven Huizen G, Behaviour of light structures founded on soil "Crust" over liquified ground, Geotechnical Earthquake Engineering and Soil Dynamics III, ASCE, Geot. Special Publication n 75, 1, pp , 1998.