Three dimensional computational studies of limit state on rock foundation of concrete- " , dams

~ .Dreidimensionale Untersuchungen des Grenzgleichgewichtzustandes vom Felsuntergrund einer

BetonstaumauerDe I'etat de contrainte du rocher de fondation du barrage en beton dans les conditions

'tridimensionneles '

YU. B.MGALOBELOV, 'Hydroproject' Association, Mosco~ USSRLD.SOLOVJEVA, SCientific and Research Institute of 'Hydroproject', Mosco~ USSR

ABSTRACT: Stressed-strained state of rock foundation and concrete dam in operation stage andin limit state as well as conditions of dam stability are analysed. Investigations are carri-ed out for concrete gravity dam (with height of 110 m) of Kapanda hydroelectric station ope-rating in three-dimensional conditions. Calculations of stressed-strained state are fulfilledby finite elements method in linear-elastic and non-linear definition. In operation stage theloads of basic combination were taken into account, limiting state was achieved at the ex-pense of increasing of hydrostatic load on upstream face. The results of dam stability calcu-lations by two schemas are compared with the results of experimental investigations on models.Recommendations concerning estimation of stabilities and load carrying capacity of rock foun-dation of concrete gravity dams operating in three-dimensional conditions are given.. ~RESUME: On etude l'etat de contrainte et deformation du rocher de fondation et du barrage enbeton pendant l'exploitation et a l'etat limite, ainsi que les conditions de la stabilite dubarrage. Les etudes sont realisees pour le barrage-po ids en beton de 110 m de hauteur del'amenagement de Capanda qui traveille das les conditions tridimentionelles. Les calculs del'etat de contrainte et deformation ont ete realises par la methode des elements finis pourle probleme lineaire-elastique et non lineaire. Pendant l'exploitation on tenait compte descharges principales, l'etat de contrainte etant obtenu par l'augmentation de la charge hyd-rostatique sur le parement amont. Les resultats des calculs de la stabilite du barrage selondeux schemas ont ete compares avec les resultats des experiments sur les modeles. Sont don-\nees les recommandations concernant l'estimation de la resistance et de la capacite portantedu rocher de fondation des barrages-poids en beton qui travaillent dans les conditions tridi-mentionnelles. s ; , -',

ZUSAMMENFASSUNG: Das Spannungsdehnungsverhalten des Felsuntergrundes·und der BetonstaumauerwAhrend des Betriebes und im Grenzgleichgewichtszustand sowie die Standsicherheit der Stau-Mauer werden analysiert. Die dreidimensionalen Untersuchungen sind fOr eine 100 m hohe Beton-gewichtsstaumauer (Projekt Kapanda) durchgefOhrt." Das Spannungsdehnungsverhalten ist mit derMethode derfiniten Elemente (FEM) als linear-elastische und nichtlineare Aufgabe berechnet.WAhrend der Betriebsphase'wurden verschiedene Kombinationen der Hauptbelastungen (LastfAlle)berdcksichtigt, der Grenzgleichgewichtszustand wurde durch die ErhOhung der Wasserdruckbelas-tung der Oberwasserseite erreicht. Die Ergebnisse der Standsicherheitsberechnungen der Stau-Mauer mach zwei unterschiedlichen AnsAtzen sind den Ergebnissen der experimentellen Modellun-tersuchungen gegendbergestellt worden. Die Empfehlungen zur EinschAtzung der Festigkeit sowieWiderstandsfAhigkeit des dreidemensional mitwirkenden Felsuntergrundes werden angeboten.

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. 1 INTRODUCTIONKapanda hydroelectric station is built in An-gola at Kwanza river by Odebrecht (Brazilianbuilding co.) by the Hydroproject project(the Soviet'Union). Hydroelectric stationconsists of concrete dam, 'intake, buildingof'hydroelectrical power plant and openspreading device." Gravi ty dam is buH t of .Roller Compacted Concrete (ReC) with total

- length of 1203 m and maximal height of 110 m.Bed of Kwanza river is situated in relative-ly narrow canyon with height of 60 m at ra-tio of site width to height· about 2.5. In .bed part the dam is designed as unified. blockwith length by crest of 217 m (Fig,J1),'this provides to increase dam stability andto avoid the cutting in rock foundation.: Theexperience of operation of concrete gravitydams in three-dimensional conditions showsthat in bank zones of foundation under up-stream face there are appeared decompactionarea and connecting with them higher filtra-tion. In connection with this the investiga-tion of stress-strained state of dam andfoundation taking into-account their joint

operation and bearing capacity of dam - foun-dation~system is of great importance in theproject.

According to the existing in the USSR buil-ding codes and regulations (SNiP), the bear-ing capacity of concrete dam rock foundationshould be based on calculations of foundationlocal strength and dam stability.Examinationof foundation local strength should be rea-

-lized by calculated planes:,a) coinciding with cracks in foundation;b) contact of dam with foundation,c) not-coinciding with cracks and. contact.The following conditions [3, 4] are the

criterion providing local strength by theplanes mentioning in p. a) and b).

(1.1)

Q' -6,.h'fa1T+CIIII'\111 = ~ 'n ..:l 1l' ~ .: (1. 2)

, •.." 'tIl •

where ~" and ,;.- normal and tangential "stresses on plane, ell' - factor~of strength,tt'fn.J and Cn.1- normative value of shear

Fig. 1. Dam of Kapanda hydroelectric stationat Kwanza-river (Angola): a) view of upstream;b) section by C-C; I - fissure of bank unload-ing; 2 - argillite interlayer; 3 - zone boun-daries in foundation with different deforma-tion and strength characteristics; 4 - joint;5 - grout curtain; 6 - drainage; - 7 - calcu-late plane of symmetry. .

! r ,

strength parameters~.normative value of ten-sile strength in per~endicular direction tocalculated plane.

Criterion of local strength of planes men-tioned in p. c) are the following conditions(for linear eve lope of Mohr ultimate cir-cles) [3, 4]:

(1. 3)

(1. 4)

where 0; and 6" - principal stresses( eft'~ c:r.ap ~ , plus - tension, minus - com-pression) ;, , - thesame as in formulaes (1.1) and (1.2) but forrock foundation.

Criterion of dam ,stability is the condi-tion [1]:

, !

(1. 5)

where Rand F - calculated values of genera-lized forces of limit resistance and genera-lized shearing forces respectively: In - reli-ability factor being equal to 1.25 for damsof first class; lk - factor of load combina-tions being equal'to 1.0 for basic combinationo~ loads; I, - factor of operation condi-t1.ons.

The investigated gravity dam is operating-in three-dimensional conditions but, unfortu-nately, there are no recommendations in thebuilding codes and regulations (SNiP) aboutthe value 1, 'which is necessary to take intoaccount in this case; the values Y&s 0.95for gravity dams operating in two-dlmensionalconditions and ¥, sO. 75 for arch dams at ba-sic cOmbination of loads are given. Let usconsider that normative stability factor forinvestigated dam should be

(1. 6)

,Investigations of stress-strain state of

dam and foundation in assumption of linear-elastic operation show tha; local strengthconditions (1.3) and-(1.4) in foundation un-der upstream face of dam are not satisfiedand, as a-rule, the conditions (1.1) and A

(1.2) ,at contact of dam"with foundation arenot satified. Unfulfilment of conditions of

I • -local strength is not in the least of evi-'dence of insufficient bearing capacity ofbed; this points to illegality of hypothesisabout linear-elastic operation of foundation.This is confirmed by natural observation da-ta concerning the decompaction processes inrock foundation under upstream face of con-crete dam which. practically has no influenceon dam bearing capacity and cause inconveni-ence in their operation.

According to this it is evident that it is~essary to provide non-linear problem solu-tion' about stress distribution for valuableinvestigation of local strength of founda-tion and stability of dam.2 INITIAL DATAIn dam foundation are bedded mainly low-cracked sandstones, ferrum-containing, weak-ened with cracks of V and VI degree, with sub-

,horizontal. beddings, argillite interlayersand fissures of bank unloading (Fig. la). Asa ,result of calculated scheme of engineering-geological structure there are four preserva-tion zones of rock massive marked out: wea-thering zone Sa , unloading zones 8.. and 8,and zone A.of preservated rocks. Under foun-dation preparation the zone 8, is removed.

Values of deformation and strength charac-teristics of rock foundation are given inTable 1.

The following loads were taken into accountat calculations (Fig. lb):

- hydrostatic load on upstream and down-stream faces of dam;

- dead weight of dam concrete ( fa = 2.45t/m3) •

- w~ter uplift on'dam bottom (with ordina-tes. Hw - under upstream face, H", ••. q41(, HJ+~fH-on line of curtain grouting and drainage, ~-under downstream face);

- filtration pressure on the surface of cur-tain grouting (with ordinates: O.CH- on the le-vel of dam bottom and 0 - on the level of cur-tain lowest part.

Rock foundation was assumed as weightlessin order to exclude the influence on damstressed state of foundation displacement un-der dead weight.3 INVESTIGATION METHODStress-strain state of dam-foundation systemwas determined by finite elements method bySTADIO programm [5]. Finite-elemental net in-volved 2924 elements and 3328 nodes. At thelow foundation boundary being below of dambottom by 145 m the absence of displacementsby three directions is preset; at,the sidesurface being removed from intersectional ••joint 4 by 180 m (Fig la), at ,the surfaces onside of upper and low bief being removed fromupstream and downstream faces by 120 and 300 mcorrespondingly - symmetry conditions are pre-set (i.e•.absence of displacements in horizon-tal direction). In order to save computer cal-culation time and taking into account thatdam contour is closed to symmetric about sitecenter line - t.he,left-coast part of dam andfoundation was considered., .

Deformation and strength properties of dif-ferent foundation zones, fissures of bank ~n-loading l.and horizontal argillite interlayer2 (Fig. la) are reproduced in the calcula-tion. .

Inclusion of non-linear deformations infoundation was realized by iteration methodof variable rigidity. Linear-elastic calcula-tion of stress-strain state for continuousfoundation and continuous contact of dam-

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Table 1

Foundation zone Deformation Poisson's Tensile Shear strength parametersmodulus E' , ratio, II strength,

Co», MPa_.MPa R~I tt'l!Ba. " 14000 0.18 0 0.80 0.20, 20000 0.16 ,0 0.85 0.306,

Fissufe of375000 0.16 0 0.95 0.40

bank 1000 0.20 0 0.55 0.05unloading

0.45Argillite inter- 100 0.20 0 , 0.05layer

0 0.80 0.20Dam-foundation - -contact

~ d

Fig. 2. Isolines of principle streSses ~. in section 1-1 (a) and strength factors 9", in sec-tion 2-2(b). Linear-elastic calculation

.J .•

foundation was realized at the first iterat-ion; normal ..1:5'" and tangential 'tIl stresses ondam-foundation contact, by fissures of bankunloading and argellite interlayer and ,strength factors 6" by them were determined;principle stresses 'C;, ds , c~ in founda-tion and strength factors &m were also de-fined. Elements with the most tension stres-ses ($f or 6" were choiced and E.,O weremade in those elements; calculation ofstress-strain state was repeated as long asthe strength conditions (1.3) and (1.1) wereperformed in all elements. Then the elementswith 9 '" ~ 1 and 9" < 1 werlf choiced for whichthe new values g - and Y were calculatedby formulae [3] and after this the calcula-tion of stress-strain state was repeatedagain; the calculations were repeated as longas the strength conditions (1.1)-(1.4) wereperformed in all elements. The obtained solu-tion was analysed from the viewpoint of di-mensions and state in foundation of decompac-tion areas (elements with E =0) and plasticdeformations areas (elements with E', l'and 8m"1) and distributions eft, 0'" and 6",in the rest part of foundation determiningbearing capacity of system dam-foundation.

Values of normal forces Pi and tangentialforces Fu and F•••; (where t and 1i '- vec-tors of drop and spread of contact planes,Fig. 7a) were determined by values of nor-mal 15"" and tangential 'rIOt and't." stresseson the contact of dam with foundation,values of normal and tangential forces wereused in calculations of dam stability. Ac-cording to building codes and regulations(SNiP) [1,2] at calculation of stability thegeneralized force of limit resistance' andshear force F -in (1.6) were defined by the'formulae:

r-----I PUl I .

I I J'1.--' II

, IIi

- ,

, '.R -r (r.J."''ftr + CilAi),

Co-t '7 ~ #

F.J.F.._&4 ,\. l' ~ .where Ai - area of i-st contact section.

It is seen from the analysis of formula(3.1) that in stability calculation the for-ces F't( are ignored. Taking into accountthis fact as well as the fact that thrustedforces H, (Fig. 7b) are the main indicationof dam space operation the force R was alsocalculated by formula

(3.1)

(3.2)

R1zf (C-jl-nt/iJ + HiI~fi 1 ~el,rA,). (3.3)t-f '7, "1,

where C." P;G.'Ji -+- J:'~j$"'1;, H1cli Si"'i-~je"J,<3.4)By determination R is the resistance

force in the limit state but in the formulae(3.1) and (3.3) R corresponds to operationstage. Therefore it was hypothesized that atthe limit state force R is determined byformula '

~ •.f(pi 1-~'fi1+CjlAi), (3.5)i-I 1.<' I I

where P~.'~/C.~fl (Fig.7b).It is necessa~ to note that according to

building codes and regulations (SNiP) [1,2]in-calculations of stability there are usedthe calculated values of shear strength para-meters 4.ffr and Cr connected with norma-tive values (Table 1), ratios:

where

fJlID ~.pJ_.'Tx=-y;-I,. - factor rock.

(3.6)

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4 INVESTIGATIONS OF STRESS-STRAIN STATE4.1. Linear-elastic calculation "IT

Calculation results in assumption of linear-elastic foundation operation of continuousdam-foundation contact are given at the Fig.2and 3~' , ,\

Principle tension stresses OJ I,,achieved to0.8 MPa (Fig. 2a) cover foundation'area underupstream face by all perimeter of dam bottomand extend in downstream, crossing grout cur-tain, and upstream practically up to the endof calculated field. It is necessary to out-line that the principle tensile stresses indam are absent, qualitative jump in stresses'on both sides of dam-foundation contact oc-curs at the expense of water uplift forcesapplied to dam bottom. It is 'also necessaryto remember that natural stresses in founda-tion were not taken into account under calcu-lations and in'connection with this the ex-pansion zone of tensile stresses ~ deep in-to the foundation is really sufficiently low-er.

Distribution and values of normal'stresson dam-foundation contact (taking into

account that surface is a little bit belowthan dam bottom) shows that at steep part thetensile stresses of up to 0.6'MPa are seenwhile zone of their distribution crossesgrout curtain (Fig. 3). Small tensile contactstresses are seen at side part of dam at in-tersectional joint •• ~Jr ' -

From the viewpoint of present tensilestrength the obtained tensile principle and

t ••

Fig. 3. Epure of contact stresses '6n (MPa).Linear-elastic calculation

, ',

pi

••. I"': ".. .,,

,........

0', r,r;J'.!:. ~J! t

,r:,.; i

-0 "f~~.t..i~ rltIW L'"

contact stresses have no meaning7 thus, linear-elastic solution of the problem is generallyapproximate fo~ the dam-foundation system andis not equal in tensile stresses field.

Distribution of strength factors eM underdam downstream face (Fig. 2b). shows that com-pression strength of foundation is satisfied,while in site bank unloading fissure of thestability is limited ( 8M -1).4.2. Non-linear calculation ••The problem of distribution of stresses indam-foundation system was non-lineary solvedwith iterations by variable rigidity method.In the foundation it was formed the decompac-tion area 1 covering along prolongation ofdam upstream face over all perimeter of damsupport (Fig. 4), in bed part this area isspread at depth of up to 8 m, in side part _at depth of up to 20 m behind the fissure ofbank unloading. Plastic shear deformations(by planes not coinciding with fissure direc-tion) were formed in the filler of fissurepart of bank unloading. Plastic deformationswere also formed in the foundation under damon prolongation of bank unloading fissure

i(Fig. 4). It is necessary to note that plas-tic areas 2 were formed not directly behinddecompaction area but at some apart from it,in direction to down stream.

The obtained stress distribution is charac-terized with absence of principle tensilestresses I5j > in foundation, normal stresses"'11' on dam-foundation contact were suffici-ently changed: tensile strength in upstreamface area were disappeared, compressing stres.

~ ses at downstream face were some increased -(Fig. 5)."Displacement of crest (by symmetryaxis) in horizontal direction was increasedof up to 7.5 mm against 6.4 mm in linear-elas-tic solution~ Strength factors under down- •stream face were some decreased but strengthcondi tions (1.4) are realized. J" "' •••

Thus, according to nonlinear solution (itis'supposed that this solution corresponds'considerably more.to real solution than' to Ilinear-elastc) "in foundation under upstreamface it was formed the decompaction: area, byfissure part of bank unloading and in founda-tion under bottom the plastic deformationarea was formed (namely', areas with' 6",-1) ,butthese'areas' are minor in comparison with foun-dation massive'but in the other bed areas thestability conditions are realized with reserveindicting about'high bearing capacity of foun-dation. • - II ,I "-.,,

f ,

t .,.,r;

f .:. ~

to- I (' • r ~ .I. ~ r 1Fig. 4. Picture oi' decompactio~tarea formation (1) in foundation under upstream face of damand plastic areas' (2). Nonlinear calculation, 3 - fissure of-bank unloading, 4 _ argellitinterlayer. .• $'1 • ;> J. _ '\~

782

Sign change of contact stresses and disap-pearance of principle tensile stresses infoundation after formation of decompactionarea confirm, the necessity of slot making infoundation under upstream face of Schlegeisarch dam (Austria) in order to liquidate ten-sile stresses in foundation [6]. Successfullydam operation after slot making confirms theefficiency pf,adopted solution [6].4.3. Nonlinear calculation at two-times

overload .In,order to investigate the stress-strain stat,and mainly to determine the force of limit re-sistance R in stability calculations the nonlinear calculation was realized under increas-ed by two-times hydrostatic load on upstreamface, all other loads were not changed._Theresults of ~his problem solution are shown atFig. 6. Decompaction area 1 was spreaded invertical direction in depth of foundation (inbed part - at depth of up to 15 m, in sidepart - at depth of, up to 30 m) and in horizon-tal direction (5 at Fig. 6) of up to 8-10 m.Plastic deformation area 2 covered the fillerof practically whole fissure of bank unloadingand spreaded in foundation in direction ofdownstream under boundary of downstream face.Displacement of crest in horizontal directionis increased of up to 22.05 mm, i.e. almostby ,three times in.comparison with the earliersolution. Conditions of foundation strengthunder downstream face are practically satis-fied, principle tensile stresses ef underupstream face and contact stresses ~" areclosed to zero (it was impossible to obtain

..

. ,

Fig. 5.'Epure of contact stresses 6'nNonlinear calculations.

(MPa).

the solution with zero stresses; this indi-cates about some error of the solution).

5 ANALYSIS OF DAM STABILITYCalculations of stability were carried out bythree schemes (Fig. 7). Values of forces(ths. tons) by five sections of calculatedsurface of shear (dam-foundation contact) forlinear-elastic and non-linear solution aswell as for two-times overload are given inTable 2•.

In order to investigate the influence ofthree-dimensional character of dam operationon its stability (besides calculations bythree schemes) it was carried out the stabili-ty calculation by scheme 11' for the whole damin supposition of its shear over equivalent

,flat surface (i.e. by scheme of flat shear);H, sO was introduced in fo~ula (3.2). Theresults of stability calculation are shown inTable 3.

According to experimental investigations ongeomechanical model being carried out byPh.D. Antonov S.S. (The Union Scientific andResearch Hydrotechnical Institute, Leningrad),the'stability factor is estimated as 2.05-2.10.

The following conclusions are based on theresults of analysis of calculated and modeldam, stability investigations:

- scheme of calculation I is not acceptablebecause stability factor is lower QY this c

scheme than by scheme II' (i.e. space charac-ter reduces dam stability in comparison withflat scheme) and it is physically not real,

-,the best agreement with results of model'investigations is obtained by scheme IIIwhile stability factor'by this scheme doesnot practically depend on the. method of prob-lem solution by stress determination 1 if thisconclusion will be confirmed in future itwill be of great importance because for stabi-lity calculation the solution of linear-elas-tic problem will be enough and in this casethe calculations will be sufficiently simpli-fied," ,

- value of total thrust ZH" only slightlydepends on account of nonlinear deformationsin foundation and does not depend on increas-ing of horizontal load •

.'f

,.J

, t t:»:Fig. 6.'Picture of decompaction area formation (2) in foundation. Nonlinear calculation atoverload 2.0:3 and 4 (Fig. 4), 5 - decompaction area with horizontal direction. l

783

J '

Fig.,7. Schemes to calculation of dam stabi-lity.

Table 2

Sectior: , Schemes of stability calculationof surface 01 I II IIIshift

p,'ft ~.., F'.,l . cr, Hi. ~.. ••... ,

Linear-elastic solution1 , 136 3 75 136 3 1362 193 39 113 195 26 -2063 123 24 64 -. 123 24 1234 43 61 .78 ; 71 25 2445 74 19 52 76 13 83-

rrotal .. - 382 601 91 -Nonlinear solution . ~ ~

1 136 3 79 136 3 1362 202 20 114 198 46 2173 134 23 76 134 23 1344 44 46 60 58 28 1955 74 16 53 75 15 81

'I'otal - - 382 -601 115 -Two-times overload

1 136 7 152 136 7 f 1362 198 35 232 197 28 2083 133 42 131 133 42 1334 52 53 141 68 28 2385 65 19 108 67 8 72

rt'otal - - 764 601 115 -

6 CONCLUSIONIn order to investigate stability of con-crete dam rock foundation, especially opera-ting in three-dimensional conditions, it isnecessary to have the solution of problemconcerning the determination of stress-strain state in nonlinear development. Li-

" , Table 3Scheme Formula Linear- Nonli- Two-timesof sta- for deter- elastic near overloadbility mination calcula calcu-calcula- of ~ tion lationtionI (3.1) 1.63 1.68 1.70II (3.2) 1.89 1.94 1.99II' '.(3.2) at 1.70

H, •• 0III (3.5) 2.10 2.13 2.15.

near-elastic solution gives not only dis-torted information about stress-strainstate of dam-foundation system but does notpractically provide to satisfy to stabilityconditions. -, Stability calculations of concrete damsin space conditions. is recommended to carryout by scheme 'III with preliminary determina-tion of forces of dam-foundation interaction.

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REFERENCES ' , .[1] Building codes and regulations (SNiP)

_2.02.02-85. Foundations of hydraulic en--,gineering constructions. M., Stroiizdat,

1986. _[2] Building codes and regulations (SNiP)

2.06.06-85. Concrete and reinforced con-crete dams.

[3] Mgalobelov Yu.B. Strength and stabilityof concrete dam rock foundations. M.,Energy, 1979.

[4] Reference book for designer of concretestructures of hydraulic power stations.Ed. Mgalobelov Yu.B. and Sergeev I.P.M., Energyatomizdat, 1985.

[5] Belostozky A.M. Modelling of interaction-of structure with foundation and liquidmedium at three-dimensional dynamic cal-culation by finite elements method. Sci~entific publications of Gidroproject,issue 123. M., 1987, p. '108-118.

[6] Stauble H. The Behaviour of the Sch1egeiSArch Dam and the Measures Taken to Im-prove It. Proe. of the Inter.Conf. onSafety Dams, Coimbra, 23-28 April, 1984,p. 115-121. ' ,

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