THE DISPLACEMENTS OF ANCHORED DIAPHRAGM WALLS

Transcription

1 Studa Geotechnca et Mechanca, Vol. XXVII, No., 005 THE DISPLACEMENTS OF ANCHORED DIAPHRAGM WALLS ANNA SIEMIŃSKA-LEWANDOWSKA Warsaw Unversty of Technology, Insttute of Roads and Brdges, Warszawa, ul. Arm Ludowej 6, Poland. Abstract: Due to the nfluence of the engneerng works on buldngs n the vcnty of deep excavatons, two large Warsaw underground statons were constantly montored. The results of measurements of the dsplacements of daphragm walls are presented. Assessment of dsplacements was carred out on the bass of hgh-precson land surveyng of fxed ponts postoned on daphragm walls. The conclusons concernng maxmum horzontal dsplacement of daphragm walls as well as evaluaton of real value of sols parameters based on the results of measurements have been presented.. INTRODUCTION It was assumed that the cut-and-cover methods were to be used for constructon of all of the statons and a part of the route tunnels of the Warsaw underground. For ths reason the works were carred out n deep excavatons. Two underground statons: A 3 (Centrum) and A 4 (Śwętokrzyska) were bult n the center of the cty, n complex geotechncal condtons, n the area of compact settlement. The depths of excavatons for both statons were 7.5 m and 4.5 m, respectvely. In the course of the constructon of both statons, the dsplacements of deep excavaton walls and the adjacent areas were measured.. DESCRIPTION OF THE EXCAVATION OF STATION A3 There are the Quaternary sols n the area of the staton. Accordng to the report on geotechncal nvestgatons, the followng geotechncal layers were dstngushed: layer I uncontrolled flls, 3 m thck, n some places up to 4 m; layer II morane deposts reachng the depth of 8 m below ground level (bgl), consstng of medum and stff sandy clays and clayey sands of the Warta glacaton and deeper stff sandy clays of the Odra glacaton; layer III contnuous layer of sand deposts, 5 m thck, represented by fne and medum sands; layer IV cohesve sols, 5 m thck; layer V sand deposts (fne, medum and coarse sands as well as gravels and sandy gravels of 0 5 m thckness). Two levels of ground water table were observed. Due to the way of carryng out the works and consderng a temporary stablty of excavaton bottom, the water table

2 56 A. SIEMIŃSKA-LEWANDOWSKA was lowered durng the works. I ,00 = 34,5m - 00 st BENCHMARK LEVELS II 500 kn III IV IV V L = 5,0m kN L = 0,50m kN L = 0,50m 550kN L = 0,50m 600kN L = 5,0m nd 3rd 4th Fg..The cross-secton of the staton A3 The lnng of the staton A3 excavaton was made up of an anchored daphragm wall joned n ts upper part to a solder ple wall [3]. The daphragm wall s 0.80 m thck and m hgh. The stablty of the excavaton walls was ensured by four or fve levels of ground anchors. Schematc drawng of the structure as well as geotechncal condtons and locaton of the benchmarks s shown n fgure. 3. DESCRIPTION OF THE EXCAVATION OF STATION A4 In vcnty of the staton, there occur the Tertary Plocene deposts dsturbed by glacal tectoncs.they are manly cohesve deposts (clays, slty clays) ncludng layers of saturated slty sands and fne sands.these layers do not have a horzontal poston. The daphragm walls are located n the clays. There are two levels of ground water:

3 The dsplacements of anchored daphragm walls 57 the frst, free water table, s 4 m bgl, the second, artesan water table, below the bottom of the staton and t stablzes about 7 m hgher. The table of ground water was lowered by pumpng. Its level was mantaned about 0.50 m below the bottom of the excavaton FILLING CLAY 500 kn L = 0,0m 600 kn ,00 st nd 3rd BENCHMARK LEVELS DIAPHRAGM WALL STRUT L = 7,0m 4th Fg.. The cross-secton of the staton A4 In order to protect the excavaton, daphragm walls (0.80 m thck and 0.7 m deep) were desgned [4]. Two levels of ground anchors and one row of steel struts ensured the stablty of the walls. The cross-secton of the excavaton wall and geotechncal condtons are presented n fgure. 4. MEASUREMENTS At the staton A3 montorng of the daphragm wall was carred out on all levels of anchorng n 5 vertcal lnes spaced about 0 m along the excavaton. The measurng ponts dentfed by specal benchmarks were located on supports made of angle sectons and fxed near the anchors heads. Fgure 3 presents locaton of vertcal measurement lnes on a plan vew of the staton, and fgure shows locaton of the measurng ponts n a cross-secton of the excavaton. A tme schedule of the montorng

4 58 A. SIEMIŃSKA-LEWANDOWSKA matched the assumed sequence of works. 44,70m N ,00m ,80m Fg. 3. Sketch of vertcal lnes and measurng ponts of the staton A3 The method of measurements was desgned n such a way as to obtan a full pcture of the dsplacements of the excavaton walls n a perod of observaton (9 months). A great depth of excavaton (n the deepest 7.45 m zone) mplcated occurrence of the consderable values of horzontal dsplacements of the daphragm wall. Montorng and contnuous analyss of the results of the measurements allowed an nvestor and a contractor to control permanently the stablty of the walls as well as to supervse the stress and relablty tests of ground anchors n explotaton ensurng that ther capacty s n agreement wth that of the desgn. At the staton A4 the program of the montorng of the wall and the surface of the ground ncluded: Measurements of the horzontal dsplacements of daphragm walls n 9 (I IX) vertcal cross-sectons at the depths of.0 m, 3.8 m, 8.0 m and 3.5 m bgl (below ground level). The benchmarks, lke at the staton A3, were nstalled on angle sectons mounted n the wall. Measurements of the dsplacements of the surface of the ground benchmarks (P P6) nstalled on eastern and western sdes of excavaton n two cross-sectons nvestgated at the dstance of m, 7 m and 4 m from the excavaton wall.

5 The dsplacements of anchored daphragm walls 59 Measurements of heavng of the excavaton bottom on the bass of measurements carred out on the deep benchmarks (P d, P d ). IV Pd Pd IV 75,0m III III P6 P5 P4 P3 P P II II I,0m I Fg. 4. Sketch of vertcal lnes and measurng ponts of the staton A4 Fgure 4 presents a sketch of vertcal lnes on the plan of staton and locaton of the measurng ponts n the cross-secton of excavaton n fgure. The tme schedule of measurements matched the respectve stages of the excavaton makng. 5. RESULTS OF MEASUREMENTS At the staton A3 the maxmum values of horzontal dsplacements were measured on the frst measurng level and they were m at the depth of excavaton of 3.6 m and m at the depth of 7.5 m, whch consttuted 0.03% and 0.09% of ts heght. At the staton A4 the maxmum vertcal dsplacements of the anchored daphragm wall appeared on the frst measurng level reachng the value of m, whch was 0.64% of excavaton depth, that s 4.6 m (fgure 5). A total value of the vertcal dsplacements of excavaton bottom measured n the mddle of ts wdth and caused by relaxaton s m (fgure 6). In the geotechncal condtons of the Plocene clays, the maxmum value of the relaxaton of the ground surface was mm at the dstance of 4 m from the excavaton edge [3].

6 60 A. SIEMIŃSKA-LEWANDOWSKA Cross-secton II Horzontal dsplacements of walls

7 The dsplacements of anchored daphragm walls 6 measurement 0 measurement measurement measurement measurement 3 measurement 4 Fg. 5. Horzontal dsplacements of daphragm wall at the staton A4

8 6 A. SIEMIŃSKA-LEWANDOWSKA benchmarks P P6, vertcal dsplacements of surcharge benchmarks Pd, Pd, vertcal dsplacements of bottom excavaton cross-secton II, vertcal dsplacements of walls The objectve of theoretcal consderatons presented below was to calbrate an elastc perfectly plastc sol model wth Coulomb Mohr s yeld crteron by means of back analyss based on the test measurements of the dsplacements of anchored daphragm wall. The model parameters for a gven sol are never constant but rather depend on the tenson or the deformaton hstory, whose mutual dependence s random by nature. They can be optmally estmated by an attempt to match the results of theoretcal predctons wth those of expermental test usng varous crtera. A specfc form of the crteron depends on the calbraton procedure and the defnton of ts state varables. As reported by GRYCZMAŃSKI [] n local calbraton, the best soluton seems to assume the expected sum J of square of varance of the values of sol load response measured n laboratory based on those calculated from the calbrated constmeasurement 9 measurement 0 measurement measurement measurement Fg. 6. Vertcal dsplacements of bottom of excavaton 6. BACK ANALYSIS

9 The dsplacements of anchored daphragm walls 63 tutve model equatons. Ths crteron was gven by Gryczmańsk n the form of equaton: J s N = { C = + C θ ν [ ˆ ε [ ˆ ε ϑ ν ε ( p, q, θ ; A,..., A ε ( p, q, θ ; A,..., A ϑ n n )] + C s [ ˆ ε )] } = mn, s ε ( p, q, θ ; A,..., A n] () where: N the number of measurements, Cν, Cs, Cϑ, C ν the weght coeffcents, ˆ εν, ˆ ε ˆ s, εϑ the measurement results for p = p, q = q, θ = θ, A,..., A n the set of estmated model parameters. In the case of consttutve models that relate current effectve tenson states to the deformaton, the regresson functons ε ν, εs, εϑ are gven n analytcal form. The values of ε ν, ε s, ε θ are obtaned by gradual solvng the calbrated model equaton gven by a specfc tenson path. Condton () s therefore modfed by GRYCZMAŃSKI [] to the form: J ε N = [ C = ν ( ˆ ε ε ) + C ( ˆ ε ε ) + C ( ˆ ε ε ) = mn. () ν ν s s In such a crteron, the values of ε ν, ε s, ε θ are obtaned numercally at the measurng ponts. At each step of the optmzaton, the values of model parameters are determned and ntroduced to the numercal analyss (consttutve equatons). Then ε ν, ε s, ε θ are calculated and J ε s determned n order to mnmze ts value. In practce, ths procedure n geotechncal engneerng employs smplex method. Because of the specfcty of the test results and the mportance of the representatve measurements of the horzontal and vertcal daphragm wall dsplacements n each phase of excavaton deepenng, the method of smplfed back analyss has been used. The realty s descrbed by the values of horzontal dsplacement of the wall n a chosen measurng secton as a response not to a load path but rather to one of the tenson states n the sol and the constructon structure. Equaton () s smplfed to the form: N s θ Jε = [ y yˆ ( E, ν, φ, c)] = mn, (3) = where: y the measurng results of horzontal dsplacements of anchored daphragm wall n the pont, ŷ theoretcal horzontal wall dsplacements n the pont obtaned from the calbrated model. ϑ ϑ

10 64 A. SIEMIŃSKA-LEWANDOWSKA ŷ s a functon of the above-mentoned model parameters (E, ν, φ, c), provded that Coulomb Mohr s yeld crteron s used. Such an approach to a global calbraton of the sol model assumed and the rules of the back analyss s due to the shortcomngs and errors of an avalable measurng database that has been created from expermental analyss of anchored daphragm wall. Ths allows a holstc descrpton of the realty for all load paths descrbed Fg. 7. FEM mesh of the excavaton A4 The calculatons have been performed usng fnte element method, applyng a computer program that takes nto account an elastc plastc analyss of b-phases medum, assumng plane stran. The elastc perfectly plastc model for ground sol wth Coulomb Mohr s yeld crteron s used for sol deprved of sotropc or knematc renforcement. The assumpton of unassocated rule of flow s accepted. The sotropc lnear elastc medum model for the renforced concrete structure (daphragm wall, bottom plate) of ground anchors and struts s used. Axal symmetry over excavaton center s assumed. The mesh has been created from soparametrc sx- and ffteennode trangle elements of the nterface type. The sol, the daphragm wall and the

11 The dsplacements of anchored daphragm walls 65 renforced concrete constructon have been modelled usng D soparametrc massve elements. The anchors and the struts have been modelled by D soparametrc lnear elements assumng ther proper stffness. Contact elements (nterfaces) of zero thckness are provded to model a contact of the constructon structure wth the sol. Ths allows us to model stckng and slppng phenomena n accordance wth Coulomb Mohr s yeld crteron. The parameters chosen for the contact elements are n agreement wth the parameters of the adjacent sols. Table Horzontal dsplacements of daphragm wall at staton A4 Zn damaged benchmark; zd dsassembled benchmark; * measurements of addtonal benchmark; sgn + means dsplacements towards the excavaton Pont No Data II/W Zd Zd Zn Zd Zd The realty ( y n formula (3)) s here represented by horzontal wall dsplacements n the pont. The measurng data from secton II (shown n fgure 5) were taken as the bass for the back analyss. The results of measurements n secton II n the consecutve phases of excavaton deepenng and constructon buldng are gven n table. The data from the th dsplacement measurement of ponts 0, 0, 03 have been taken as the bass for the back analyss, whch corresponds to the strut dsassembly phase after completon of the bottom plate. A full pcture of the excavaton wall dsplacements has been responsble for ths choce. Dscrete presentaton of the terrtory n ths phase s shown n fgure 7. The theoretcal ( ŷ n formula (3)) horzontal wall dsplacements of ponts 0, 0, 03 n phase X, determned from the calbrated model, have been calculated for the varable values of the sol parameters. The back analyss has been performed by step-by-step method. Formula (3) s wrtten n the followng equvalent form: J ε N = y yˆ ( E, ν, φ, c) = ε = mn. (4) = The values for the sol parameters are taken from the documentaton of BP Metroprojekt [4]. For the surface layer, constant parameters that do not change n the subsequent phases of calculatons are assumed. For classfed layer II tght clay sol

12 66 A. SIEMIŃSKA-LEWANDOWSKA Plocene clay (Pl), the values for φ and c are assumed to be n the range between the generalzed values (φ u, c u ) determned wthout outflow of water and the effectve values (φ, c ). For the back analyss an assumpton has been made that determnaton of the mnmum value of J ε wll be made for the ncreasng values of elastcty modulus E 0 of clay (from 4 MPa) and a combnaton of φ wth c. The value of E 0 = 4 MPa has been determned from the geotechncal documentaton [5]. The value of the coeffcent K 0 has been determned from the Jaky formula. It has been assumed that t s constant for the entre wall heght. The summary of the parameters assumed for the calculatons s gven n table. Sol type The values of sol parameters assumed for the calculatons of the excavaton wall at staton A4 Table Γ Ф u Ф C u C E 0 kn/m 3 kpa kpa Mpa NN I In the calculatons, the followng combnatons of φ wth c have been taken: φ = 3, c = 37 kpa; φ = 6, c = 37 kpa; φ = 9, c = 37 kpa; φ = 3, c = 0 kpa; φ = 6, c = 0 kpa; φ = 9, c = 0 kpa. For each combnaton of φ wth c, the calculaton of ŷ n ponts 0, 0, 03 has been performed n X phase of constructon wth the clay elastcty modulus E 0 takng the followng values: 4, 50, 65, 75, 80, 85, 90, 95, 00, 05, 0,5, 0, 5, 30, 40,50,60,70,80, 00,0, 40, 60, 80 MPa. In order to determne the mnmum values of sum of modul of the dfference between the actual and the theoretcal wall dsplacements n the three ponts under consderaton, for the above descrbed combnatons of E 0, φ and c, more than 000 calculatons have been performed []. The evaluaton of the results has been done n two steps: ndependently for each sngle measurng pont ( y yˆ ) and globally for the three ponts smultaneously 3 y y ˆ. = In the case of the back analyss performed ndependently for each sngle measurng pont, dentcal values y and ŷ have been obtaned for 9 combnatons of φ, c and E.

13 The dsplacements of anchored daphragm walls f = 7, c = 0 f = 7, c = 0 f = 7, c = 0 f = 7, c = 0 f = 7, c = Fg. 8. The results of calculatons done based on back analyss Evaluatng the results of the back analyss of the three pont dsplacements t can be stated that such a combnaton of φ, c and E for whch ε = 0 has not been obtaned. The mnmum value of 3 y yˆ = has been obtaned for the above-descrbed sx combnatons of φ wth c and the elastcty modulus value rangng from 5 MPa to 60 MPa. For the further analyss of the

14 68 A. SIEMIŃSKA-LEWANDOWSKA results we assume that for a model parameter estmaton such a combnaton of φ, c and E s relable at whch ε 0.0. The combnaton of φ = 3 wth c = 0 kpa has been dsregarded snce t does not fulfl the crtera assumed. The analyss results of the remanng fve combnatons are presented n fgure 8. It can be stated that the value of the elastcty modulus, determned from the results of the back analyss, for whch the crteron ε 0.0 s fulflled, ranges from 85 to 0 MPa. For the value of elastcty modulus determned from the geotechncal documentaton (E = 4 Mpa), the value of ε 0,056,0, 38 and t does not fall below the assumed value of 0.0. Ths means that the theoretcal horzontal wall dsplacements for ths value of the modulus sgnfcantly dffer from the actual. 7. CONCLUSIONS The maxmum actual horzontal dsplacements of an anchored daphragm wall appear on the top of the wall, n the deepest excavaton secton and ther value does not exceed 0.% of H W (the greatest depth of excavaton). The shape of the dsplacements has a cantlever-lke character, whch means that they decrease wth depth. Ths concluson was based on the analyss of the measurement results of horzontal dsplacements of anchored daphragm walls. The measurements were carred out n 34 vertcal lnes for four measurement levels durng 9 months. These walls were properly desgned and the anchors ensured ther stablty achevng the capacty requred. The elastc-perfectly plastc sol model wth Coulomb Mohr s yeld crteron assumed n the back analyss of the daphragm wall of staton A4 allows an approprate evaluaton of the anchored constructon dsplacements. The strongest agreement between theoretcal and actual results of the wall dsplacements (ε 0.0) has been obtaned for the Plocene clay elastcty modulus E 0 85, 0 MPa []. REFERENCES [] GRYCZMAŃSKI M., On calbraton of consttutve models (n Polsh), Zeszyty Naukowe Poltechnk Śląskej, Budownctwo, 995, Nr 80, pp [] SIEMIŃSKA-LEWANDOWSKA A., Dsplacements of anchored daphragm walls (n Polsh), Ofcyna Wydawncza Poltechnk Warszawskej, Prace Naukowe, Budownctwo, 00, Vol. 39. [3] SIEMIŃSKA-LEWANDOWSKA A., GRZEGORZEWICZ K., Analyss of dsplacements of anchored daphragm walls of the Centrum and Śwętokrzyska statons (n Polsh), Proc. Conference on Underground Constructons, AGH, Kraków, 000, pp [4] B.P. METROPROJEKT, I lna metra w Warszawe. Projekt technczny korpusu stacj A3. [5] B.P. METROPROJEKT, I lna metra w Warszawe. Projekt technczny stacj A4, Konstrukcja metody budowy korpusu.