A RAPID TECHNIQUE to DETERMINE ALLOWABLE BEARING PRESSURE

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1 A RAPID TECHNIQUE t DETERMINE ALLOWABLE BEARING PRESSURE Semih S. Tezcan -1, Zuhal Ozdemir -1, Ali Keceli -2, and Aykut Erkal -1 Adress: 1- Bgazici University, Bebek, Istanbul, Türkiye 2- Istanbul University, Beyazit, Istanbul, Türkiye. supernline. cm Key wrds: Bearing capacity, shear wave velcity, shallw fundatins, allwable bearing pressure, seismic technique. ABSTRACT Based n a variety f case histries f site investigatins, including extensive bre hle data, labratry testing and gephysical prspecting, an empirical frmulatin is prpsed fr the rapid determinatin f allwable bearing capacity f shallw fundatins. The prpsed expressin crrbrates cnsistently with the results f the classical thery and is prven t be rapid, reliable and safe. It cnsists f nly tw sil parameters, namely, the insitu measured shear wave velcity, and the unit weight. The unit weight may be als determined with sufficient accuracy, by means f anther empirical expressin, using the P-wave velcity. It is indicated that nce the shear and P- wave velcities are measured insitu by an apprpriate gephysical survey, the allwable bearing capacity may be determined rapidly and reliably thrugh a single step peratin. Such an innvative apprach, using the seismic wave velcities nly, is cnsiderably cst and time-saving, in practice. INTRODUCTION Prfessr Schulze (1943) [1], a prminent histrical figure in sil mechanics and fundatin engineering in Germany, stated that Fr the determinatin f allwable bearing pressure, the gephysical methds, utilising seismic wave velcity measuring techniques with abslutely n disturbance f natural site cnditins, may yield relatively mre realistic results than thse f the getechnical methds, which are based primarily n bre hle data and labratry testing f s-called undisturbed sil samples. Since that time, varius significant cntributins have been made t slving getechnical prblems by means f gephysical prspecting. The P-wave velcities, fr instance, have been used t determine the uncnfined cmpressive strengths and mdulus f elasticity f sil samples by Cates (1970)[2]. Hardin and Black (1968) [3], and als Hardin and Drnevich (1976) [4], based n extensive experimental data, established indispensable relatins between the shear wave velcity, vid rati, and shear rigidity f sils. Similarly, Ohkuba and Terasaki (1976) [5] supplied varius expressins relating the seismic wave velcities t weight density, permeability, water cntent, uncnfined cmpressive strength and mdulus f elasticity. The use f gephysical methds in fundatin engineering has been extensively studied als by Imai and Yshimura (1976) [6], Tatham (1982)[7], Willkens, et.al. (1984)[8], Phillips, et. al. (1989)[9], Keceli (1990) [10], Jngmans (1992) [11], Sully and Campanella (1995)[12], and Pyrak-Nlte, et.al. (1996) [13]. Campanella and Stewart 234

2 (1992) [14] determined varius sil parameters by digital signal prcessing, while Butcher and Pwell (1995) [15] supplied practical gephysical techniques t assess varius sil parameters related t grund stiffness. A series f guidelines have been als prepared in this respect by the Technical Cmmittee TC 16 f IRTP, ISSMGE (1999) [16], and als by Sieffert (2000) [17]. Turker (2004) [18], based n extensive case studies, supplied an explicit expressin fr the allwable bearing pressure, using shear wave velcity. Massarsch (2004) [19] determined defrmatin prperties f fine-grained sils frm seismic tests. In this presentatin, typical empirical expressins have been prpsed fr the rapid determinatin f the allwable bearing pressures in sils, sft and hard rcks. This is actually an extensin f an earlier publicatin by the writers [20], presenting a theretical backgrund fr the frmulatin and als intrducing a number f refinements, including the crrectin factrs fr the fundatin size. The insitu measured shear wave velcity, as a single field index, represents the real sil cnditins, much mre effectively and reliably than the insitu r labratry tested shear strength parameters. In additin t gephysical refractin seismic survey, there are several ther techniques f measuring the shear wave velcity at site as discussed by Stke and Wds (1972) [21], Tezcan et. al. (1975) [22], and Butcher, et.al.(2005) [23]. Insitu measured shear wave velcity reflects the true phtgraph f the sil, cntaining the cntributins f vid rati, effective cnfining stress, stress histry, shear and cmpressive strengths, gelgic age etc. As will be seen later in this study, the shear wave velcity enables the practicing engineer t determine the allwable bearing capacity in a mst cnvenient, ecnmic, reliable and straight frward manner. THEORETICAL BASIS FOR THE EMPIRICAL EXPRESSION The mst general frmat fr the allwable bearing pressure, q a, under a shallw fundatin with depth H frm the surface, may be assumed t be cmpatible with the weight f the sil clumn abve the fundatin base and therefre may be expressed as q a γ H / n (1) where, γ unit weight (kn/m 3 ), n factr f safety. The fundatin depth, H, may be replaced by the prduct f V s shear wave velcity and the time parameter, T, as; H V s T (2) which is substituted in Eq.1 t yield q a γ V s T / n (3) A typical hard rck frmatin, fr which the essential parameters are available, will be used t calibrate the abve expressin. Namely, q a kn/m 2, γ 35 kn/m 3, 235

3 and V s m/sec. Assuming a safety factr f n 1.4 fr hard rcks, the time parameter is btained as T 0.10 sec, frm Eq.3, as fllws: q a 35 (4000) T / kn/m 2 (4) Therefre, the allwable bearing pressure, acquires the general frm f q a 0.1 γ V s / n (5) Fr varius sil (rck) types, the factrs f safety, as well as the allwable bearing pressures, are given in Table 1. Table-1. Factrs f safety, n, fr sils and rcks (1) Sil type V s range (m/sec) n q a (kn/m 2 ) Hard rcks 750 V s n 1.4 q a γ V s Sft weak rcks 750 V s n V s q a 0.1 γ V s / n Sils 750 V s n 4.0 q a γ V s α (1) Linear interplatin is made fr sft weak rcks with 750 V s m/sec. EFFECT OF FOUNDATION WIDTH It is determined by Terzaghi and Peck (1967) [24] that the width f fting has a reducing influence n the value f allwable bearing pressure. Therefre, a crrectin factr α is intrduced int the frmula, fr sils type frmatins nly, as shwn in the third line f Table 1. The prpsed values f this crrectin factr, fr different fundatin width B, as deduced frm Fig f Ref. [24], are as fllws: α fr (0.00 B 1.20 m) α B fr ( 1.2 B 3.00 m) (6) α B fr ( 3.0 B 12.0 m) COEFFICIENT OF SUBGRADE REACTION 236

4 The shear wave velcity may als be used t determine k s cefficient f subgrade reactin, d ttal settlement and E mdulus f elasticity as fllws: k s 40 q f (kn/m 3 ) (7) d q f / k s (m) (8) E H k s (kn/m 2 ) (9) q f n q a 0.1 γ V s (kn/m 2 ) (10) in which, q bearing pressure at failure, H the layer thickness fr which the mdulus f f elasticity is required. The empirical expressin in Eq.7 is given by Bwles (1982) [25]. Substituting Eq.10 int Eq.7, we btain k s 4 γ V s ( kn/m 3 ) (11) It is seen frm Eq.8 and Eq.11 that, the maximum settlement is permanently set t d m, as shuld be the case fr all shallw single r strip ftings. ESTIMATION OF UNIT WEIGHT There is a direct relatinship between the average unit weight γ, and the P-wave velcity f a sil layer. Based n extensive case histries f labratry testing by the writers [20], a cnvenient empirical relatinship is prpsed as fllws: γ p γ V p (12) where, γ the unit weight in kn/m 3 based n P-wave velcity, V P-wave velcity in p p m/sec, and γ the reference unit weight (kn/m 3 ) values given as fllws: γ 16 γ 17 γ 18 γ 20 fr lse sandy, silty and clayey sils, fr dense sand and gravel, fr mudstne, limestne, claystne, cnglmerate, etc., fr cracked sandstne, tuff, graywacke, schist, etc., 237

5 γ 24 fr hard rcks. The unit weights calculated by Eq.12, are in excellent agreement with thse determined in the labratry. In the absence f any bre hle sampling and labratry testing f sil samples, the abve empirical expressin prvides a reliable first apprximatin fr the unit weights f varius sils, nce the in-situ measured P-wave velcities are available. In fact, the speedy evaluatin f unit weights, prir t any sil sampling, enables the practicing engineer t calculate the allwable bearing capacity q, readily frm Eq. 5. As a an example, cnsider a sft clayey sil layer f H15 m beneath a shallw fundatin with insitu measured seismic wave velcities as V s 200 m/sec, and V p 700 m/sec, the varius sil parameters, which are als verified by cnventinal getechnical methds are calculated as fllws: Eq.12 Eq.11 Eq. 9 Eq.10 γ k s E q f γ V p 4 γ V s H k s 0.1 γ V s (700) 4(17.4) (13 920) 0.1(17.4) kn/m 3 kn/m 3 kn/m 2 kn/m 2 n 4 (since, V s < 750 m/sec, see Table 1) Eq.10 q a q f / n 348 / 4 87 kn/m 2 Eq. 8 d q f / k s 348 / m CASE STUDIES The allwable bearing pressures have been determined, at mre than 120 cnstructin sites in and arund the Kcaeli Prvince in Turkiye, using bth the cnventinal methd recmmended by Terzaghi and Peck (1967)[24], and the seismic methd as prpsed herein. The results f bth methds are illustrated in a cmparative fashin in Fig.1. The stability and cnsistency f the results by the seismic methd prpsed herein are clearly visible. CONCLUSIONS 1. The shear wave velcity is a single and mst pwerfull sil parameter representing a family f getechnical sil cnditins, ranging frm cmpressive strength t vid rati, frm shear rigidity t chesin etc, 2. Extensive bre hle and labratry testing wuld n lnger be needed if the shear and P-wave velcities are measured, as accurately as pssible, right under the fundatin level. Then, the allwable bearing pressure, the cefficient f subgrade 238

6 reactin, as well as the apprximate value f the unit weight are rapidly determined, using relatively simple empirical expressins. 3. The results btained frm seismic methd are mre stable, cnsistent and reliable when cmpared with thse f the cnventinal methd, as already demnstrated by mre than 120 case studies (Fig.1). ACKNOWLEDGEMENT The writers gratefully acknwledge the technical supprt and encuragement, as well as the cnstant and ample supply f field data fr the case studies by Mr. Mustafa Cevher, Chief Gephysical Engineer, Municipality f the Greater City f Kcaeli, Turkiye. 450 q allwable bearing pressure, kpa a by Cnventinal Methd by Seismic Methd (Tezcan, et. al) Vv s s shear wave velcity, m/sec m/sn Figure-1. Cmparisn f Cnventinal and Seismic methds (Frm a data base cntaining 123 case studies in and arund the Kcaeli Prvince, ) REFERENCES Schulze, W.E., (1943) Grundbau, Deutsche Frschungsgesellschaft für Bdenmechanik, 7 th ed., B.G. Taubner Publishers, Leipzig, Germany. Als available: Technical University f Istanbul, Issue 48, N DK624-15, Uçler Printing Huse, Istanbul, Turkiye. Cates, D.F., (1970) Rck Mechanics Principles: Mines Branch Mngraphs, N Hardin, B. O., and Black, W.L., (1968) Vibratin mdulus f nrmally cnslidated clays, Jurnal f the Sil Mechanics and Fundatin Divisin, ASCE, Vl.94, N. SM2, pp

7 Hardin, B.O., and Drnevich, V.P., (1972) Shear mdulus and damping in sils. Jurnal f the Sil Mechanics and Fundatin Divisin ASCE, Vl. 98, N. SM7, pp Ohkub, T., and Terasaki, A., (1976) Physical prperty and seismic wave velcity f Rcks. OYO Crpratin, Japan. Imai, T., and Yshimura, M., (1976) The relatin f mechanical prperties f sils t P and S- Wave velcities fr sil grund in Japan. Urana Research Institue, OYO Crpratin. Tatham, R.H., (1982) V p / V s and lithlgy. Gephysics, 47: Willkens, R., Simmns G. & Carus, L., (1984) The Ratin V p / V s as a discriminant f cmpsitin fr siliceus limestnes. Gephysics, 49(11) Phillips, D. E., Han, D. H. & Zback, M. D., (1989) Empirical relatinships amng seismic velcity, effective pressure, prsity, and clay cntent in sandstne. Gephysics, 54:(1) Keçeli, A. D., (1990) Determinatin f bearing capacity f sils by means f seismic methds ( in Turkish), Gephysical Jurnal, Ankara, Turkiye, 4, Jngmans, D., (1992) The applicatin f seismic methds fr dynamic characterizatin f sils. Bulletin f Internatinal Assciatin f Engineering Gelgy. 46: Sully, J. P. & Campanella, R.G., (1995) Evaluatin f in situ anistrpy frm crsshle and dwnhle shear wave velcities measurements. Getechnique, 45(2): Pyrak-Nlte, L. J., Ry, S. & Mullenbach, B., l., (1996) Interface waves prpagated alng a fracture. Jurnal f Applied Gephysics, (35): Campanella, R.G. and Stewart, W.P. (1992) Seismic cne analysis using digital signal prcessing fr dynamic site characterizatin, Canadian Getechnical Jurnal, Vl.29, N.3, June 1992, pp Butcher, A.P. and Pwell, J.J., (1995) Practical cnsideratins fr field gephysical techniques t used assess grund stiffness. Prc. Int. Cnf. n Advances in Site Investigatin Practice, ICE Lndn, March Thmas Telfrd, pp IRTP, 1999:ISSMGE Technical Cmmittee TC16 Grund Prperty Characterizatin frm In-situ Testing, (1999) Internatinal Reference Test Prcedure (IRTP) fr the Cne Penetratin Test (CPT) and the Cne Penetratin Test with pre pressure (CPTU). Prc. XIIth ECSMGE Amsterdam. Balkema. pp Sieffert, J. G., and Bay-Gress, Ch, (2000) Cmparisn f the Eurpean bearing capacity calculatin methds fr shallw fundatins. Getechnical Engineering, Institutin f Civil Engineers, Vl. 143, pp , England. Turker, E., (2004) Cmputatin f grund bearing capacity frm shear wave velcity, Cntinuum Mdels and Discrete Systems, Eds. D. Bergman, et. al., Netherlands, pp Massarsch, K. R. (2004) Defrmatin prperties f fine-grained sils frm seismic tests. Keynte lecture, Internatinal Cnference n Site Characterizatin, ISC 2, Sept. 2004, Prt, Tezcan, S. S., Ozdemir, Z., and Keceli, A., (2006) Allwable bearing capacity f shallw fundatins based n shear wave velcity, Jurnal f Getechnical and Gelgical Engineering, 24: pp , DOI / s , Netherlands, Springer, 240

8 Stke, K. H., and Wds, R.D., (1972) Insitu shear wave velcity by crss-hle methd, Jurnal f the Sil Mechanics and Fundatin Divisn, ASCE, Vl. 98, N.SM5, pp Tezcan, S. S., Erden, S. M., and Durgunğlu, H. T., (1975) Insitu measurement f shear wave velcity at Bğaziçi University Campus, Prceedings f the Internatinal Cnference n Sil Mechanics and Fundatin Engineering, Vl. 2, April 1975, pp , Istanbul Technical University, Istanbul, Turkey. Butcher, A.P., Campanella, R.G., Kaynia, A.M., and Massarsch, K. R., (2005) Seismic cne dwnhle prcedure t measure shear wave velcity. A guideline prepared by ISSMGE TC10, Prceedings f the Internatinal Sympsium n Gephysical Testing in Getechnical Engineering, May, 2006, Osaka, Japan. Terzaghi, K., and Peck, R.B., (1967) Sil Mechanics in Engineering Practice. 2 nd ed., Jhn Wiley&Sns, Lndn. Bwles, J.E., (1982) Fundatin Analysis and Design, 3 rd Cmpany, New Yrk. ed., McGraw-Hill Bk 241

Seismic technique to determine the allowable bearing pressure in soils and rocks

Earthquake Resistant Engineering Structures VII 53 Seismic technique to determine the allowable bearing pressure in soils and rocks S. S. Tezcan 1, Z. Ozdemir 1 & A. Keceli 1 Bogazici University, Istanbul,