Verka Prolović Chair of Civil Engineering Geotechnics, Faculty of Civil Engineering and Architecture, Niš, R. Serbia

Transcription

1 3 r d International Conferene on New Developments in Soil Mehanis and Geotehnial Engineering, 8-30 June 01, Near East University, Niosia, North Cyprus Values of of partial fators for for EC EC 7 7 slope slope stability stability analysis: analysis: solved solved mystery? Jovan Papić Chair of Geotehnis, Faulty of Civil Engineering, Skopje, R. Maedonia Ljupčo Dimitrievski Chair of Geotehnis, Faulty of Civil Engineering, Skopje, R. Maedonia Verka Prolović Chair of Civil Engineering Geotehnis, Faulty of Civil Engineering and Arhiteture, Niš, R. Serbia KEYWORDS: Euroode 7, partial fators, slopes, DA 3, global safety fator ABSTRACT: Although the era of Euroodes has started, some ountries are still in the proess of introduing them. This is speially related to the geotehnial EC 7 whih is designed in a way to be easily aepted by different ountries. Aording to it, eah ountry has to hoose adequate design approah for eah geotehnial design and to selet appropriate partial fators due to whih appliation there are three different DAs. The ECs were expeted to minimize the design differenes between the ountries, espeially present in the field of geotehnis, and they prinipally fulfilled the task, but there have also remained further tasks e.g. to redue the DAs and NDPs. Beside foundations and retaining walls, slopes are one of the most ommon geotehnial strutures. But, there are some opposite opinions about the seletion of DA and partial fators. This paper tries to make an attempt to demystify them and to reommend a way for seletion of partial fators. Namely, through mathematial relations, implementing Bishop s method for slope stability, it has been given support to DA 3 and it was shown that the values of partial fators, whih are going to be inluded in the further National Annex, should be equal to the former global safety fator. This explanation an be useful for other ountries interested in EC 7 whih still haven t made their seletion and an also help on the way of minimizing the number of design approahes. 1 INTRODUCTION Slopes are strutures that are often found in onstrution and mining, so it is lear why one of the priorities for seleting the appropriate design approah (DA) and partial fator (PF) in drafting the National Annex to Euroode 7 is set on them. Until now, slopes have been designed and analyzed in aordane with proven methods based on the global fator of safety (FS). One of the most popular methods to alulate their limit equilibrium stability is ertainly the Bishop s method, where the iterative alulation is arried out by the following equation: n i1 b ( W u b) tan' m n i1 W sin (1) 193

2 3 r d International Conferene on New Developments in Soil Mehanis and Geotehnial Engineering, 8-30 June 01, Near East University, Niosia, North Cyprus where m 1 os 1 tan tan' () Other methods usually vary in regards of treatment of inter-slie fores (Maksimović 008), but alulations and analyses have shown that they do not affet the amount of the partial fators. FEW ARGUMENTS ON THE SIDE OF SELECTED DESIGN APPROACH For eah geotehnial struture, the ountries should selet one/two/three of the offered DA whih would be appropriate for their urrent pratie and to make deision on the value of partial fators due to whih appliation there is priniple differene among the approahes (Frank et al. 004). The presene of global fator in the equation for alulation of slope stability may mislead to adopt DA as appropriate. But, besides the global fator, the denominator of the m α member also inludes the tangent of the angle of internal frition, whih is to be divided exatly by the fator of safety, i.e. tan '/ (3) This an be reognized as a redution of the speified shearing resistane parameter (SRP). As it is already known, suh redution is performed in DA 1 C and DA 3; but having in mind that DA 1 demands two alulations, the suitable DA appliable to a urrent pratie not only in the Balkan region, but even wider, should be loated in DA 3. From this point of view, it offers some more important advantages, when ompared to others. Namely, sine the soil s shearing resistane in a plane depends on the normal load ating on that plane, its strength is a funtion of load, and thus requires attention when setting the partial fators, beause the inrease of the load with PF leads to inrease in the strength. All of the loads are inreased in the DA 1 C 1, as well in the DA. This is only one reason why during the seletion of the appropriate approah for analyzing slope stability it is advisable to adopt DA 3: there the onstant loadings due to weight of soil do not inrease, what is also important in performing stressstrain alulation in the finite elements method (FEM) software, while multiplying only the variable loads. Moreover, when analyzing the stability using the DA 3, all loads - either strutural or geotehnial - are treated as if originating from the ground, and thus are not subjet to hange of values, beause the partial fator is 1.0. Performing alulations with harateristi values might seem as enouraging DA * as a probable to use in slope stability analysis. Still, this advantage is not appliable in ase of slope stability simply beause it is diffiult to determine where the resistane subjeted to redution appears in slopes. Besides that, a part of the soil has a favourable effet on stability, while its upper part auses a disturbane, thus the Single Soure Priniple in the appliation of DA for slope stability analysis does not apply. For these obvious reasons, many ountries that implement Euroode 7, i.e. the vast majority of those who do not aept double alulation in DA 1, have reommended the approah 3 for slope stability analysis (only one or two ountries prefer DA (Bond 011), even though in an unprinipled manner). Coneptually, almost idential is the DA 1 C, whih is also the most ompetent in DA 1 sine milder slopes are obtained, and it allows /φ' redution: this is an option to determine the safety fator for software based on FEM. This insight is enouraging for the future in terms of harmonization when the DA 3, most ertainly, will be reommended for alulation of slope stability aording to Euroode 7 (Shuppener 010). This approah will in R. Maedonia also be reommended for a numerial modelling by FEM for slopes and it will serve for a ase in whih slopes and foundations are simultaneously treated sine DA 3 is also reommended for designing spread foundations (Papić et al. 011). Thus, their onsisteny is enabled, respeting that ground and struture are parts of the same problem, in diret ontat and interation (Simpson 008). 194

3 Value of partial fators for EC 7 slope stability analysis: solved mystery? Papić, Dimitrievski, & Prolović 3 DETERMINATION OF VALUE OF PARTIAL FACTORS Following this speifi terms and onditions regarding the seletion of a design approah, it should be ontinued with determination of PF to redue the SRPs of the soil. The basi and main ondition whih is to be fulfilled for determination of the PF for the SRPs is to provide the same extent of stability so far presribed, i.e., to ahieve the same slope inlination. If 0 kpa and u 0 kpa, then the Bishop s expression (1) an be redued to W tan' m W sin and introduing () in (4), will get tan' sin os sin tan' From this expression an be derived that tan' sin os sin tan' (6) 1 sin sin os tan' (7) tan' tan (8) where the allowable safety fator is not onstant, but is a funtion of the load ase in whih the stability is onsidered. If (5) is applied in terms of ultimate limit state, with FS = 1.0, then the design value of the angle of frition should be entered instead of tan ': tan' tand (9) so the expression (5) would be as follows tand (10) sin os sin tan with further derivation tan d sin os sin tan d d and, similar to the fore mentioned transposing of tan d ' to the left side and adjusting the trigonometri expression tand tan (1) i.e. with respeting (9) tan' tan (13) Equalizing the expressions (8) and (13) with the same member tan ' on the left side, would gain and finally tan tan (14). (15) (4) (5) (11) 195

4 3 r d International Conferene on New Developments in Soil Mehanis and Geotehnial Engineering, 8-30 June 01, Near East University, Niosia, North Cyprus Aording to this derivation and additional indiations, it an be stated that the PF used to redue the angle of frition (i.e. its tangent in ultimate limit state onditions) while maintaining the same level of seurity that was previously provided with a global fator of safety, does not depend on geometrial, material, or loading properties, but only on load ase in whih the stability of the treated slope is onsidered: permanent, transient or inidental state, et! Similar approah an also determine the PF for ohesion, onsidering the soil with frition and ohesion and with no pore pressure, so in the ase of global fator: so b W tan' m (16) W sin tan' m b m (17) sin W sin Arranging the equation by gains tan' W sin m sin (18) b Expression (18) may be used in limit state ondition (FS=1.0) when PF are inluded, with d d where from, (19) tan d W sin (0) m, d sin b 1.0 tan d W sin (1) m, d sin b Similarly as previously, equating the expressions (18) and (1) with on the left side implies that 1.0 tan d W sin tan' W sin m, d sin b m sin () b and, onsidering, tan tan' 1 tan' 1 sin os (3) tan' tan tan' sin os 196

5 Value of partial fators for EC 7 slope stability analysis: solved mystery? Papić, Dimitrievski, & Prolović tan tan' 1 tan' 1 sin os (4) tan tan' 1 tan' 1 sin os whih already demonstrated, implies that! (5) The same would be onluded even if soil with no frition was treated. Thus, it is onfirmed that in the alulation of slope stability the amount of PF by whih are redued SRPs is equal both for the tangent of the angle of frition and ohesion, and is equal to the former global fator of safety. Beside, adopting the same value of PF for both SRPs has advantage for obtaining safety fator in FEM analysis sine it opens possibility of implementation of /φ' redution during whih both SRPs are equally dereased. However, the intensity of the global safety fator depends on the onditions in whih the stability of slopes is onsidered: permanent, transient, or inidental, sudden disharge, bak analysis et, whih may also vary depending on the struture (dam, road, open mine, et.). EC 7 and its Annexes did not offer suh lassifiation of PF values, sine they are proposed as onstant (Euroode 7 004) and independent of the ase onsidered, whih is one of its shortomings. However, EC 0 and EC 1 open the possibility of varying PF, depending on the onsequenes lasses, lasses of reliability, and load ase: permanent or transient, that exatly suits former Yugoslavian and now Maedonian, Serbian et. urrent pratie! Pat of the above mentioned is stated in partiular Annexes: UK, Germany, Austria, Sweden, Finland and so on (Orr 011). At the same time, the proposed values maintain the existing safety level, i.e. same slope inlination, whih is also important during any repairs or upgrades; it avoids future threats to servieability of slope and allows engineers to easier adjust to new alulations in aordane with the EC7. The presented proedure enables analysis to be used not only in the appliation of the Mohr Coulomb law, but also in nonlinear failure envelope of hyperboli type (Maksimović 008) where the angle is not onstant, i.e. is related to stresses. Its realisti desription of the shear resistane in wide stress domain is of great help in optimization of slopes, beause of rational usage of soil shear resistane, espeially in the zone of lower stresses whih often is the ritial ase for designing slopes. Namely, we may reall that the design SRP is the harateristi one divided by PF: tan' d ' (6) in whih ase FS thus obtaining the already known equation d (7) FS then the latter equation an be diretly used to desribe the nonlinear failure envelope, for example through "user-defined model" option, when it is suffiient to "orret" laboratory obtained values for the shearing stress by division with FS, i.e. γ, and redued that way to enter them into the software. This way, the slope that previously has had a global safety fator of 1.40, in the limit state, i.e. after the division of shearing stress by 1.40, will have a fator of In both ases the speified values of fator shall refer to the same sliding surfae. 197

6 3 r d International Conferene on New Developments in Soil Mehanis and Geotehnial Engineering, 8-30 June 01, Near East University, Niosia, North Cyprus 4 CONCLUSIONS In the analysis of slope stability, one might onlude that Design Approah 3 fits the demands for keeping the existing safety degree and slope inlination as well it offers other opportunities as desribed above, among whih is also the easier appliation of FEM analyses and transfer of engineer s pratial work from global to partial safety fators. Beause of these reasons, it was adopted in various European ountries and is expeted to be adopted in others looking forward to introduing Euroodes. Thus the number of design approahes, at least for slope stability analysis, ould be redued in further EC 7 revisions. Through presented relations, it was shown that the partial fators for shearing resistane parameters are not onstant, but their value is equal to the former global safety fator whih depends stritly upon load ase: permanent, transient, inidental et. This proedure and same fators value are also favourable from the aspet of enabling the analysis of slope stability in the desription of shearing resistane with nonlinear failure envelope, as well as when applying FEM where /φ' redution is used to determine the safety fator. All of these findings were onfirmed by numerial analyses whih are not presented in this paper (Papić et al. 01). But, sine that these load ase values are different among the ountries, to enable elimination of possible appearane of many partial fators, it is probable to suggest inreasing the number of laboratory tests through whih SRPs are determined and suh to derease the value of partial fators without redution of their onfidene or endangering safety. REFERENCES Bond, A. (011). Past, present and future of Euroode 7. 3rd ISSMGE Webinar, 011 Euroode 7. (004). Geotehnial design - Part 1: General rules. Frank, R., Bauduin, C., Drisoll, R., Kavvadas, M., Krebs Ovesen, N., Orr, T., Shuppener, B. (004). Designer s guide to EN Thomas Telford, London, 16p Maksimović, M. (008). Soil mehanis. 4 th Edition, AGM knjiga, Belgrade, 643p Orr, T. (011). Experienes with the Implementation of Euroode 7 in Europe. Workshop: Safety Conepts and Calibration of Partial Fators in European and North Amerian Codes of Pratie, Delft Papić, J.Br., Dimitrievski, Lj., Prolović, V. (011). Is anybody (else) afraid of Euroode 7?. 4 th sientifi and pratial meeting Geotehnial aspets of ivil engineering, Zlatibor, R. Serbia, pp.9-16 Papić, J.Br., Dimitrievski, Lj., Prolović, V. (01). Verifiation of seleted design approah and partial fators for slope stability analysis aording to EC 7. nd International sientifi meeting GTZ 01 State and trends of ivil engineering, Tuzla, Bosnia and Herzegovina (aepted paper) Shuppener, B. (010). Update on Euroode 7, its implementation and maintenane, nd International Workshop on Evaluation of Euroode 7, Pavia Simpson, B. (008). Approahes to ULS design The merits of Design Approah 1 in Euroode 7. International seminar on Euroode 7 and geotehnial aspets of Euroode 8, Struga, R. Maedonia, pp