Numerical analysis of displacements of a diaphragm wall

Transcription

1 Numerical analysis of displacements of a diapragm wall M.Mitew Warsaw University of Tecnology, Warsaw, Poland ABSTRACT: In te paper, numerical analysis and parameter study ave been presented taking into account two calculation metods, based on different constitutive soil models. Numerical back analysis as been divided into two parts. Te first part considers te analysis performed using Geo4Seeting analysis and Rido software, employing te metod of dependent pressures, in wic magnitudes of pressures acting upon a structure depend on deformation of te structure. Due to its simplicity, te metod is widely used for te design purposes. For tis reason, it was cosen for wider discussion in te paper. Te second part includes numerical analysis performed using finite element metod software: Geo4FEM and Plaxis 7.2. In te last part of te paper te results of numerical analysis ave been compared to te results of insitu measurements, overall discussion as been performed and conclusions ave been presented. 1 INTRODUCTION Te paper presents te results and discussion under te wide scope of numerical back analysis of te displacements of a diapragm wall. Te case study considered witin tis paper is 3 level underground structure executed witin 80 cm tick and 14,5 m deep diapragm wall. Te crosssection including geotecnical conditions as well as te stages of construction, cosen for te calculation is sown in Figure 1. ± 0,00 1,10 "0" LEVEL OF THE STRUCTURE GROUND SURFACE 2,50 FILL (NN) DIAPHRAGM WALL EXECUTION STAGE 0 "0" SLAB Full Milan metod as been applied to provide te stability of te walls of te excavation (Fig.2). Te excavation was executed in te following stages: Stage 1 excavation to te dept of 4.40 m, Stage 2 casting of 1 slab, Stage 3 excavation to te dept of 7.10 m, Stage 4 casting of 2 slab, Stage 5 excavation to te final dept m, Stage 6 casting te ground slab; During te construction, continuous monitoring of diapragm wall displacements as been carried out using automatic inclinometer cain Geokon Vibrating Wire InPlace Inclinometer, designed for longterm monitoring of deformations of structures (SiemińskaLewandowska & Mitew 2002). CLAYAY SAND / SANDY CLAY (Pg + Gp) "1" SLAB STAGE 2 EXCAVATION 4,40 m STAGE 1 7,00 FINE SAND (Pd) 7,60 "2" SLAB STAGE 4 EXCAVATION 7,10 m STAGE 3 10,7 SANDY CLAY (Gp) FOUNDATION SLAB STAGE 6 FINAL EXCAVATION 11,09 m STAGE 5 CLAY (I) CLAY (I) 15,6 MEDIUM SAND (Ps) 15,9 0,8 m Figure 1. Te crosssection Figure 2. Te site (deep excavation) presented in te paper

2 Te results of insitu measurements ave been analysed, te displacements of te diapragm wall at eac construction stage ave been determined. Specified displacement s ave been used in te back analysis in order to compare it to te results of all numerical analysis. 2 THE METHOD OF DEPENDING PRESSURES 2.1 Calculation model For modelling of soil te subgrade reaction modulus metod (dependent pressures metod) uses oneparameter Winkler analogue subsoil model (Winkler 1867). Te soilwall contact is replaced by a system of independent elastic supports of stiffness k. Te wall is treated as an elastic beam of a unit widt and te of te orizontal, elastic soil reaction at examined point is directly proportional to orizontal wall displacement at te same point. p = z k y (1) and y = y( z) (2) In case of te discussed metod, te key question is te determination of k modulus, wic cannot be identified wit te coefficient defined by Winkler. Te metods of k parameter determination are presented below. 2.2 Analytic and empirical metods of determination of k modulus Since k parameter (subgrade reaction modulus) is not a pysical defining te soil, but a calculation parameter depending on te stiffness of te wall (EI), wall geometry (ratio of excavation dept to te dept of te wall below its bottom) and soil conditions. Tere is no possibility to define k using insitu metods. Te majority of k determination metods make use of displacement calculations of a rigid diapragm wall acting in condition of passive eart pressure. Many metods are known in literature (Siemińska Lewandowska 2001) for determination of te k modulus based on te classical teory of elasticity or on empirical investigation, particularly tose making use of te results of pressuremeter investigations. In tis paper tree of tem sall be discussed: Terzagi s metod, Cadeisson and Monnet as well as Menard and Bourdon metods, caracteristic by separate approac to te problem Te metod of Terzagi Terzagi s metod is based on te principles of classical teory of elasticity (Terzagi 1955). In case of noncoesive soils according to Terzagi s assumptions, te of k at given dept z depends on wall dimension perpendicular to displacement, weigt of soil and density index of te soil. p Aγ z z k = = = mh z = nh (3) y 1,35 B B B wall dimension perpendicular to its displacement, n H constant depending on te density index of te soil; te s of n H are sown in Table 1. Table 1. Values of n H [kn/m 3 ] for a wall of widt B=1m, cast in sand Density index Loose Medium Dense dense Dry and moist sand Wet sand Equation (3) can be applied for noncoesive soils. In case of coesive soils te of k H1 becomes te same as te of parameter k SI establised for a beam resting on orizontal surface of te same kind of soil. Based on expression (3), te of k for wall of a unit widt can be expressed by Equation (4): k = B B 1,5 B = kh1 = ks1 k S1 (4) B widt of wall, k SI constant depending on te liquidity index of te soil. Assuming B=1m, te s of k can be determined depending on te liquidity index (Tab. 2). Table 2. Te k [kn/m 3 ] for 1m wide wall, cast in coesive soil State of clay Medium Stiff Very stiff Dry and moist sand Te metod of Monnet Te goal of tis empirical metod is te evaluation of te magnitude of displacement necessary to mobilise te limit passive pressure. R. Cadeisson (1961) based on many years of investigations in constructing of diapragm walls, 60cm and 80cm tick, in varied geotecnical conditions, determined te of k depending on te sear strengt of soil (Coulomb Mor criterion) i.e. c and φ parameters, introducing into calculations te stiffness of te wall. Developed by Cadeisson and later simplified by Monnet (1994) te formula for determining te of subgrade reaction modulus k for given subsoil as te following form:

3 k K = 20EI γ (1 K p dr / K p ) t( c / c0 ) + Apc 0 dr0 γ specific gravity of soil, K P passive pressure coefficient, K 0 pressure coefficient at rest, dr 0 caracteristic displacement (0.015m), c effective coesion, A P coefficient allowing for soil coesion, c 0 30 kpa. Substituting te s of parameters K P, K 0, γ, c into above expression and assuming wall tickness 80 cm (E=2x10 7 kpa) te cart sown in Figure 3 was obtained, serving to evaluate k on te basis of parameters c and φ Te metod of Menard and Bourdon Menard and Bourdon (1964) made te first approac towards empirical determination of te of subgrade reaction modulus taking advantage of pressuremeter investigation results. Te metod developed by tem was complemented in later years by Balay (1984), Gigan (1984) and Scmitt (1995). On te base of pressuremeter tests results in te surroundings of retaining walls, Menard and Bourdon determined te relationsip between k and te pressuremeter modulus by te following expression. 1 αa α k = ( 9a) E 2 (6) M E M pressuremeter modulus of soil, α reological soil coefficient, assumed: 1/3 in noncoesive soils, 1/2 in silts, 2/3 in coesive soils, a [m] eigt, witin wic soil is acting in passive pressure, defined by Menard as 2/3 amount of te penetration of te wall below te final bottom of te excavation Figure 3. Te cart of Cadeisson for te evaluation of k basing on c and φ s Degrees (5) C t/m2 (coesion) 3 APPLICATION OF THE METHOD OF DEPENDENT PRESSURES IN DIAPHRAGM WALL ANALYSIS Tree calculation sequences were made for a cosen caracteristic crosssection, leaving basic geotecnical parameters (defined after te geological report) witout cange, but varying subgrade reaction modulus k, defined according to te metods discussed in paragrap 2. Parameters of individual geological layers are compiled in Table 3 togeter wit te suitable moduli k defined on te basis of Terzagi s, CadeissonMonnet and MenardBourdon equations. Te results of eac sequence of calculations are compiled in Table 4. Table 3. Geotecnical parameters of individual soil layers k [kn/m 3 ] I D / γ c u φ u I L kn/m 3 Caidesson MenardkPa [ ] Terzagi Monnet Bourdon Table 4. Comparison of results of analysis (Geo4Seeting analysis, Rido) Terzagi Cadeisson Monnet Menard Bourdon FEM ANALYSIS OF THE CASE Numerical analysis of te structural model using Finite Element Metod (FEM) includes apart from te diapragm wall under examination also te interacting soil and objects in wall environment. Te coice of te soil constitutive model is te basic element of FEM analysis. Substantial number of models can be mentioned (Gryczmański 1995), from wic te most often applied in geotecnics are elasticideal plastic models wit associate law of flow and isotropic plasticity surface (e.g. Coulomb Mor, Tresca, Huber Mieses Hencky, Drucker Prager) and elasticplastic models wit isotropic strain ardening of volumetric kind (e.g. CamClay, Modified CamClay). Depending on te soil model adopted, different parameters are needed during analysis. In engineering practice te most popular is te elasticideal plastic model wit CoulombMor plasticity surface, because of its simplicity and small number of model parameters (φ, c, E, ν), wic can

4 be determined on te basis of laboratory investigation, or insitu. Finite element plain strain analysis as been carried out using GEO4FEM and PLAXIS version 7.2 software. Due to te fact, tat sopisticated soil parameters were not available simple Coulomb Mor constitutive soil model was cosen for modelling te soil body. Te diapragm walls, as well as supporting slabs were modelled as beam elements (2D elements). Contact elements ave been applied for modelling te interaction between te soil and te structure. Four calculation sequences ave been performed varying te stiffness (modulus of elasticity E) of soil layers. In te Table 5, calculation sequences are called respectively: FEM 1 stiffness determined according to Polis Code, FEM 2 stiffness determined basing on literature recommendation, FEM 3 stiffness determined basing on geotecnical report recommendation, FEM 4 stiffness determined basing on pressuremeter investigation results. In eac case described above staged construction analysis ave been carried out in order to obtain results (displacements) in all construction pases. FEM model mes (Fig. 4), generated automatically, consisted of or 15 nodes elements, 1741 nodes and 2319 stress points. Te teoretical displacements resulting from all calculation cycles ave been compared to te results of insitu displacements measurements. Detailed results are presented in Table 5. Table 5. Comparison of results of analysis (Geo4FEM, Plaxis v7.2) FEM 1 FEM 2 FEM 3 FEM Figure 4. Numerical model 5 SUMMARY In total seven calculation sequences ave been performed using two types of software: based on te metod of depending pressures and te oter using Finite Element Metod (FEM). Results of static analysis of te case are compared in Table 6. Table 6. Comparison of results of all analysis (Geo4Seeting analysis, Rido, Geo 4FEM, Plaxis v7.2) Dependent pressures metod Finite Element Metod Terzagi Cadeisson Monnet Menard Bourdon FEM 1 FEM 2 FEM 3 FEM Te results obtained in static analysis using te dependent pressures metod prove te significant influence of te of subgrade reaction modulus k on determined teoretical displacements (as well as on internal forces). K modulus, determined using various metods for individual geotecnical layers is varying witin te range: kn/m 3 layer 2 clayey sand/ sandy clay, kn/m 3 layer 3 fine sand, kn/m 3 layer 4 sandy clay, kn/m 3 layer 5 clay, kn/m 3 layer 6 medium sand. So large scattering of s results in visible differences in obtained results. It can be observed, tat te displacements determined using teoretical metods of specifying k modulus (Terzagi, Monnet) are similar, despite great differences in module s for individual layers. Results obtained on te basis of empirical metods (Menard) differ muc from tose based on teoretical metods, but are nearer to real s (from te point of view of safety). imum teoretical displacements of te wall estimated in all FEM analysis, in general, are very close to te of maximum real displacement measured during construction. Te approximate compatibility of te results of measurements and calculations as been observed in te top part of te wall in all calculation series and in all construction stages. All calculation sequences sowed a significant diapragm wall displacement towards te excavation in te span above te foundation slab in last two construction pases, wic as not been observed insitu. Tat may be due to a great, not realistic, relaxation of te bottom of te excavation estimated in te FEM calculations. Relatively best results ave been obtained wen te soil parameters

5 were based on te results of pressuremeter investigations. Furter analysis of te case will be performed. Taking into account te difficulties in assessing te parameters of te soils as well as te great discrepancy of obtained results, it sould be stressed tat regardless of te metod of static analysis, close observation of te real diapragm wall displacements is a necessary item in construction process. REFERENCES Balay, J Recommandations pour le coix des paramètres de calcul des écrans de soutènement par la métode aux modules de réaction. Note d'information tecnique. Paris : LCPC Cadeisson, R Parois continues moulées dans le sol, Proceedings of te 5t European Conference on Soil Mecanics and Foundation Engineering. Paris : Dunod, Vol. 2, p , Gigan, J.P Expérimentation d un rideau en palplances ancré par tirants actifs. Bulletin de liason des Laboratoires des Ponts et Caussées No 129, p Gryczmański, M Wprowadzenie do opisu sprężystoplastycznyc modeli gruntów. Wyd. KILiW PAN, IPPT PAN Studia z zakresu inżynierii, No. 40. p.156 Ménard, L. & Bourdon, G. & Houy, A Étude expérimental de l encastrement d un rideau en fonction des caractéristiques pressiométriques du sol de fondation. Soil. Sols No. 9 Monnet, A Module de réaction, coefficient de décompression, au sujet des paramètres utilisés dans la métode de calcul élastoplastique. Revue Française de Géotecnique 66. p Scmitt, P Métode empirique d'évaluation du coefficient de réaction du sol vis à vis des ouvrages de soutènement souples. Revue Française de Géotecnique 71. p. 310 SiemińskaLewandowska, A Przemieszczenia kotwionyc ścian szczelinowyc, Wyd. Oficyna Wydawnicza Politecniki Warszawskiej, Prace naukowe, Budownictwo z. 139 SiemińskaLewandowska, A. & Mitew, M Diapragm wall monitoring report. Geokonstrukcja Sp. z o.o. Warsaw Terzagi, K Evaluation of coefficients of subgrade reactions. Géotecnique. Vol. 4 Winkler, E Die Lere von der Elastizitat und Festigkeit. Dominicus. Prague