An Experimental Study on the Effect of Foundation Depth, Size and Shape on Subgrade Reaction of Cohessionless Soil

Transcription

1 Engineering, 013, 5, Publihed Online October 013 ( An Experimental Study on the Effect of Foundation Depth, Size and Shape on Subgrade Reaction of Coheionle Soil Wael N. Abd Elamee Faculty of Engineering, Sinai Univerity, El Arih, Egypt Received June 9, 013; revied July 9, 013; accepted Augut 7, 013 Copyright 013 Wael N. Abd Elamee. Thi i an open acce article ditributed under the Creative Common Attribution Licene, which permit unretricted ue, ditribution, and reproduction in any medium, provided the original work i properly cited. ABSTRACT The modulu of ubgrade reaction k depend on everal factor uch a the ize and hape of the foundation a well a the embedment depth of the foundation. The preent tudy i an experimental analyi uing plate load tet to determine the effect of foundation depth, ize a well a the hape on the modulu of ubgrade reaction (k ) of coheionle oil. It wa carried out by uing nine rigid teel plate with different ize and hape (circular, quare and rectangular). The tet were carried out on coheionle oil with different relative denitie under different applied preure. The ettlement ha been meaured at the urface of the plate for different depth of footing. The ultimate bearing capacity [q u ] ha been determined from the tre-ettlement relationhip. The allowable bearing capacity (q a ) wa determined by dividing the ultimate bearing capacity (q u ) by F.S. = 3.0, after which the correponding ettlement (S a ) ha been obtained. However, k wa calculated baed on dividing the allowable bearing capacity (q a ) by the correponding ettlement (S a ). From the preent tudy it i concluded that the ubgrade reaction k of coheionle oil increae with increaing foundation depth a well a foundation ize. In addition, ubgrade reaction k of coheionle oil under rectangular footing i higher than that under quare and that under circular one with ame equivalent area. An empirical formula i preented to calculate the ubgrade reaction k of coheionle oil under quare foundation taking into conideration foundation depth. Fair agreement ha been obtained between value of k from the empirical formula at depth of footing = 0.00 B and Biot (1937) a well a Meyerhof and Baike (1965). Keyword: Subgrade Reaction; Plate Load Tet; Foundation Depth; Size; Shape 1. Introduction Soil bearing capacity and oil modulu of ubgrade reaction are ome variou meaure of trength-deformation propertie of oil. To perform the tructural analyi of footing one mut know the principle of evaluating the coefficient of ubgrade reaction k. One of the mot popular model in determining the modulu of ubgrade reaction i Winkler (1867) model [1]. In thi model the ubgrade oil i aumed to behave like infinite number of linear elatic pring that the tiffne of the pring i named a the modulu of ubgrade reaction. Thi modulu depend on ome parameter uch a oil type, ize, hape, depth and type of foundation. Iancu-B. T. and Ionut O. T. (009) preented a numerical imulation of plate loading tet in order to underline the ize effect on ettlement. The obtained reult are compared with Finite Element Method (FEM) uing the Mohr-Coulomb oil model. The obtained numerical re- ult revealed that the ubgrade reaction coefficient wa trictly dependent on the ize of the loaded area and the loading magnitude []. Elamny, M. K., Eledeek, M. B. and Abd Elamee, W. N. (010) preented field determination of the Young modulu E of footing on coheionle oil by uing plate load tet [3]. Dae. S. K. and Seong Y. P. (011) preented plate loading tet to evaluate the compaction quality of the railroad ubgrade in Korea. Two method to determine the deign modulu were ued. One i an unrepetitive plate loading tet (uplt) that obtain the ubgrade reaction modulu (K30) and the other i a repetitive plate loading tet (rplt) that obtain the train modulu (Ev) [4]. Aminaton M. et al. (01) preented Winkler model and the ub grade oil i aumed to behave like infinite number of linear elatic pring. The foundation ize effect on andy ub grade by uing of finite element oftware (Plaxi) i preented [5]. Copyright 013 SciRe.

2 786 W. N. ABD ELSAMEE. Determination of Subgrade Reaction k.1. Determination of Subgrade Reaction k Uing the Elatic Parameter E, The coefficient of ubgrade reaction k i the ratio between the preure q at any given point and the ettlement produced by load application at that point. Biot (1937), Terzaghi (1955), Veic (1961), Meyerhof and Baike (1965), Selvadurai (1984) and Bowle (1998) have invetigated the factor affect the determination of k. Biot (1937) olved the problem for an infinite beam with a concentrated load reting on a 3D elatic oil continuum. Biot found a correlation of the continuum elatic theory and Winkler model [6]. Veic (1961) tried to develop a value for k, by matching the maximum diplacement of the beam. He obtained an equation for k to be ued in the Winkler model [7,8]. However, different formulii to calculate the modulu of ubgrade reaction k by ome different author are preented in Table 1... Determination of Subgrade Reaction k in-situ Uing Plate Loading Tet (P.L.T) The plate-load tet provide a direct meaure of compreibility and occaionally of the bearing capacity of oil which are not eaily ampled. The modulu of ubgrade reaction can be determined by uing the plate-load tet a follow:..1. Terzaghi Method (1955) A major problem i to etimate the numerical value of k. One of the early contribution wa that of Terzaghi (1955) [9]. He uggeted value of k for (1 1) ft rigid lab placed on a oil medium. k f for full-ized footing could be obtained from plate-load tet uing the following equation: 1) For quare footing on coheionle oil with dimenion = B B. k f k p B B (1) ) For rectangular footing on coheionle oil with dimenion = B L. k fr k f B 1 L ) For long foundation [trip footing] with a width = B The modulu of ubgrade reaction i approximately equal to 0.67 k f where: () Table 1. Some different formulii to calculate the modulu of ubgrade reaction, k. No. Invetigator year Suggeted formula 1 Winkler (1867) q k Biot (1937) 3 Terzaghi (1955) 4 Veic (1961) 5 Meyerhof and Baike (1965) 6 Selvadurai (1984) 7 Bowle (1998) E B E k B1 1 EI k f B B B 1 kp 0.65E k B 1 k 1 E k B E k B 1 B E EB EI mi I 1 1 F k = the coefficient of ubgrade reaction. q = the preure per unit of area. = the ettlement produced by load application. B 1 = ide dimenion of quare bae ued in the plate load tet. B = width of footing. k p = the value of ubgrade reaction for (1 ft wide) bearing plate. k f = value of modulu of ubgrade reaction for the full-ize foundation. E = modulu of elaticity. υ = poion ratio. E I = flexural rigidity of footing, M = take 1, and 4 for edge, ide and center of footing, repectively. I S and I F = influence factor depend on the hape of footing. Copyright 013 SciRe.

3 W. N. ABD ELSAMEE 787 k p = plate-load tet value of modulu of ubgrade reaction kn/m 3, uing quare plate (1 1) ft or circular plate with diameter = m; k f = deired value of modulu of ubgrade reaction for full-ized quare footing B B, kn/m 3 ; k fr = deired value of modulu of ubgrade reaction for rectangular full-ized footing B L, kn/m 3 ; B = footing width, meter or leat dimenion of rectangular or trip.... Different Cod American Code (ASTM D1194) (1994) and Britih tandard Code (BS5930) (1997): American Code (ASTM D1194) (1994) and Britih tandard Code (BS5930) (1997) etimated the numerical value of k from plate load tet reult [10]...3. Peck, Hanon and Thobrnburn (1997) Peck, Hanon and Thobrnburn (1997) etimated the numerical value of k by uing plate load tet a follow: 1) Settlement on and occur almot entirely during contruction. ) Maximum differential ettlement between footing on and i le than 0 mm. 3) k i calculated from the traight line portion of the load-ettlement curve...4. Ping-Sien Lin, Li-Wen Yang and C. Hein Juang (1998) Ping-Sien Lin, Li-Wen Yang and C. Hein Juang (1998) made a erie of plate-load tet to invetigate the load ettlement characteritic of a gravelly cobble depoit and etimate the value of modulu of ubgrade reaction k a follow: qa k (3) where: k = modulu of ubgrade reaction, kn/m 3 ; q a = allowable bearing capacity, kn/m ; a = allowable ettlement againt q = q a, meter qu qa (4) f.. where: q u = Ultimate bearing capacity, kn/m ; f.. = Factor of afety = 3 [11]...5. Egyptian Code (001) Egyptian Code (001) made a erie of plate-load tet to invetigate the load ettlement characteritic and etimate the value of modulu of ubgrade reaction k a a follow: q k (5) where: k = Modulu of ubgrade reaction, (kn/m 3 ); q = Stre at ettlement =1.3 mm after ten time loaded, (kn/m ); = Settlement againt q (meter) [1]...6. Reza Z. M. and Maoud J. (008) Reza Z. M. and Maoud J. (008) preented a direct method to etimate the modulu of ubgrade reaction by the plate load tet done with cm diameter circular plate or equivalent rectangular plate [13]. However, Table preent ome different method uing plate load tet with different ize and hape to determinate the value of modulu of ubgrade reaction, k. 3. Preent Experimental Study Plate load tet have been carried out in field and the ettlement of andy oil wa meaured under different tre level. In the preent tudy each ample ha been placed in an open box and compacted in layer with different relative denitie. Settlement ha been meaured under different tree and at different relative denitie a well a different depth of foundation Field Sample Graded and (GS) at different relative denitie wa ued in field. Each ample ha been compacted in layer and the relative denity for each layer ha been determined by uing and cone. 3.. Loading The load ha been applied by uing teel frame fixed in the ground a hown in Figure 1. The applied load ha been meaured by uing preure gauge connected to a jack Ued Plate Nine teel rigid plate were ued in the tet which are divided into three group. The firt group ha rigid three circular hape plate. The econd group i three rigid quare plate firt one having dimenion (1 * 1) ft and the other two quare plate having equivalent area for 455 mm and 610 diameter. The lat group i a rigid three rectangular plate having the ame equivalent area a the firt group. The plate have concentric marking on one face and plated againt corroion. The plate have a finihed thickne of 3 mm and are according to ASTM Copyright 013 SciRe.

4 788 W. N. ABD ELSAMEE D1194 and D1196 pecification a hown in Table 3 and Figure Depth of Foundation The ettlement ha been meaured at urface and at different depth. The depth of foundation i conidered a function of width of the plate B. Circular, quare and rectangular teel boxe have been placed around the rigid teel plate to be ued in cae of filling oil around a urcharge for different foundation depth (0.5 B, 0.50 B, 0.75 B and 1.00 B) Tet Procedure The tet procedure i a follow: 1) The oil ha been placed in a quare open box. ) The box wa filled with different oil layer compacted to different denitie which ha been determined by and cone tet. The field compaction ha been done Table. Some different method uing plate load tet to calculate k. No. Invetigator Year Ued plate hape Ued plate dimenion (ize) 1 Terzaghi (1955) Square [305 * 305] mm = (1 * 1) ft ASTM Committee D1194 on Soil and Rock and i the direct reponibility of Subcommittee D18.08 on Special and Contruction Control Tet. (1994) Circular Diameter from (305 to 76 mm), 3 Britih tandard code (BS5930) (1997) Circular or quare of equivalent area Diameter from 300 mm to 1000 mm 4 Peck, Hanon, Thornburn (1997) Square [305 * 305] mm 5 Ping-Sien Lin, Li-Wen Yang, and C. Hein Juang (1998) Circular Diameter from 0.75, 0.90, and 1.05 m 6 Egyptian Code (001) 7 Reza Z. M. and Maoud J. (008) Circular or quare of equivalent area Circular or rectangular of equivalent area Diameter from m and quare equivalent area 0.3 * * Diameter from cm. Table 3. The ued plate in the experimental tudy. Circular plate (diameter) B (mm) Square plate (B B) (mm) Rectangular plate (B L) (mm) Equivalent area mm Thickne (mm) Weight (kg) 305 mm - 38 * 307 mm mm 3 mm 14.5 kg mm mm 3 mm 18.5 kg 455 mm 403. mm 360 * mm mm 3 mm 33 kg 610 mm mm 458 * 638 mm mm 3 mm 56 kg Figure 1. Loading frame. Figure. The nine rigid plate. Copyright 013 SciRe.

5 W. N. ABD ELSAMEE 789 uing the following: a) Each compacted layer ha (7.5) cm thick ne. b) A (4.5) kg weight hammer wa ued and releaed from (30) cm height. 3) The urface of the teted oil wa prepared for plate tet uing fine and at the urface. 4) The teel plate were placed on the prepared urface. 5) A hydraulic jack wa placed on the teel plate. 6) Four dial gauge ha been placed on the plate urface. 7) The ettlement ha been meaured by uing dial gauge of enitivity 0.01 mm placed on the edge of the teel plate. Figure 3 how meauring ettlement at urface. 8) Steel boxe have been placed around the rigid teel plate to be ued in cae of filling oil around a urcharge for different foundation depth (0.5) B, (0.50) B and (1.00) B a hown in Figure 4 and 5. 9) The load wa applied in increment by uing teel frame. Each load increment wa maintained contant until the ettlement rate reache 0.0 mm/min and not le than one hour in any cae. 4. Experimental Reult Settlement in field wa recorded for different footing Figure 3. Settlement reading at urface uing dial gauge. Figure 5. Settlement reading in cae of urcharge uing quare teel box. ize and hape (circular, quare and rectangular) under different tree ranging between kn/m and kn/m. However, the ettlement ha been meaured at different relative denitie and at different depth (0.00 B), (0.5 B), (0.50 B), (0.75 B) and (1.00 B) for all kind of plate. From the meaured ettlement of coheionle oil the following relationhip are obtained Ultimate Bearing Capacity Uing Experimental Reult The ultimate bearing capacity of coheionle oil ha been determined from the relationhip between the tree and the meaured ettlement at urface and at different depth for all plate by tangent-tangent method according Egyptian Code. Figure 6 give an example of determination of the ultimate capacity. 4.. Determination of Subgrade Reaction k Uing Experimental Reult The allowable bearing capacity (q a ) i determined by dividing the ultimate bearing capacity (q u ) by F.S. =3.0, after which the correponding ettlement (S a ) i determined. Thu, k i calculated baed on dividing the allowable bearing capacity (q a ) by the correponding ettlement (S a ) a hown in Figure Effect of Foundation Depth on Subgrade Reaction k Figure 4. Settlement reading in cae of urcharge uing circular teel box. The effect of foundation depth on ubgrade reaction k ha been invetigated. However, the value of ubgrade reaction k have been obtained under different plate with different foundation depth a hown in Table 4. Figure 8 and 9 how example for the effect of footing depth on k for different angle of internal friction under different plate hape. Thee figure how that ubgrade reaction k of coheionle oil increae with increaing footing depth. Copyright 013 SciRe.

6 790 W. N. ABD ELSAMEE Figure 6. The relationhip between tre and ettlement of plate for determination of ultimate bearing capacity for circular plate diameter 355 mm. Table 4. Value of k (kn/m 3 ) of coheionle oil uing plate load tet diameter 305 mm, quare 305 * 305 mm (1 * 1) ft and rectangular 38 * 307 mm (equivalent area for 305 mm diameter). Angle of internal friction (Ø) Depth of k circular plate 305 mm diameter k quare plate 305 * 305 mm k rectangular plate 38 * 307 mm footing kn/m 3 kn/m 3 kn/m B B B B B B B B B B B B B B B B B B B B B B B B B Where: B = diameter of circular plate, width of quare plate or mallet dimenion of rectangular plate. Copyright 013 SciRe.

7 W. N. ABD ELSAMEE 791 Figure 7. Determination of ubgrade reaction k FRATIO (D/B) ANGLE OF INTERNAL FRICTION Ø=30 o circulare plate diameter=305mm Square plate 305 * 305 mm 0 Rectangular plate 38 *307mm SUBGRADE REACTION K (kn/m 3 ) Figure 8. The relationhip between ubgrade reaction k and depth of foundation for different hape of footing for angle of internal friction ø = FRATIO (D/B) ANGLE OF INTERNAL FRICTION Ø=36 o circulare plate diameter=305mm Square plate 305 * 305 mm Rectangular plate 38 *307mm SUBGRADE REACTION K (kn/m 3 ) Figure 9. The relationhip between ubgrade reaction k and depth of foundation for different hape of footing for angle of internal friction ø = 36. Copyright 013 SciRe.

8 79 W. N. ABD ELSAMEE 6. Effect of Foundation Size on Subgrade Reaction k The relationhip between ubgrade reaction k and footing ize for different hape of footing ha been obtained. Figure 10-1 how example for the effect of footing ize on k for different angle of internal friction. Thee figure how that ubgrade reaction k of coheionle oil increae with increaing footing ize for all type of foundation. In addition, ubgrade reaction k of coheionle oil increae with increaing angle of internal friction. 7. Effect of Foundation Shape on Subgrade Reaction k The value of ubgrade reaction k have been obtained for different plate under different foundation hape for different depth. Figure give example for the effect of footing hape on k. From thee finger it can be hown that ubgrade reaction k of coheionle oil under rectangular plate i higher than that under quare than that under circular one (at ame equivalent area). 8. The Obtained Value of k for Coheionle Soil Table 5 and 6 how the obtained value of k for coheionle oil. 9. Empirical Formula A convergence tudy wa performed to determine the ubgrade reaction (k ) uing SPSS tatitical cientific 0.6 FOOTING SIZE AREA ( cm ) 0.1 Ø=30 Ø=33 Ø=36 Ø=39 Ø=4 ANGLE OF INTRNAL FRICTION Ø=30 ANGLE OF INTRNAL FRICTION Ø=33 ANGLE OF INTRNAL FRICTION Ø=36 ANGLE OF INTRNAL FRICTION Ø=39 ANGLE OF INTRNAL FRICTION Ø=4 Circular plate at urface SUBGRADE REACTION K (kn/m 3 ) Figure 10. The relationhip between ubgrade rea ction k and footing ize at urface for circular plate [ize 305, 455 and 610 mm]. 0.6 FOOTING SIZE AREA ( cm ) 0.1 Ø=30 Ø=33 Ø=36 Ø=39 Ø=4 ANGLE OF INTRNAL FRICTION Ø=30 ANGLE OF INTRNAL FRICTION Ø=33 ANGLE OF INTRNAL FRICTION Ø=36 ANGLE OF INTRNAL FRICTION Ø=39 ANGLE OF INTRNAL FRICTION Ø=4 Square plate at urface SUBGRADE REACTION K (kn/m 3 ) Figure 11. The relationhip between ubgrade rea ction k and footing ize at urface for quare plate [ize equivalent area of 305, 455 and 610 mm]. Copyright 013 SciRe.

9 ) W. N. ABD ELSAMEE FOOTING SIZE AREA ( cm ) 0.1 Ø=30 Ø=33 Ø=36 Ø=39 Ø=4 ANGLE OF INTRNAL FRICTION Ø=30 ANGLE OF INTRNAL FRICTION Ø=33 ANGLE OF INTRNAL FRICTION Ø=36 ANGLE OF INTRNAL FRICTION Ø=39 ANGLE OF INTRNAL FRICTION Ø=4 Rectangular plate at urface SUBGRADE REACTION K (kn/m 3 ) Figure 1. The relationhip between ubgrade rea ction k and footing ize at urface for rectangular plate [ize equivalent area of 305, 455 and 610 mm]. 0.6 REA ( cm F OOTING S IZE A 0.1 ANGLE OF INTERNAL FRICTION Ø=30 o circulare plate diameter 305mm Square plate 305 * 305mm Rectangular plate 38 *307mm SUBGRADE REACTION K (kn/m 3 ) Figure 13. The relationhip between ubgrade reaction k and footing ize at depth of footing B = 0 (at angle of internal friction ø = 30 ). 0.6 FOOTING SIZE AREA ( cm ) 0.1 ANGLE OF INTERNAL FRICTION Ø=36 o circulare plate diameter 305mm Square plate 305 * 305mm Rectangular plate 38 *307mm SUBGRADE REACTION K (kn/m 3 ) Figure 14. The relationhip between ubgrade reaction k and footing ize at depth of footing B = 0 (at angle of internal friction ø = 36 ). Copyright 013 SciRe.

10 ) 794 W. N. ABD ELSAMEE 0.6 FOOTING SIZE AREA ( cm 0.1 ANGLE OF INTERNAL FRICTION Ø=4 o circulare plate diameter 305mm Square plate 305 * 305mm Rectangular plate 38 *307mm SUBGRADE REACTION K (kn/m 3 ) Figure 15. The relationhip between ubgrade reaction k and footing ize at depth of footing B = 0 ( at angle of internal friction ø = 4 ). Table 5. The obtained value of k for coheionle oil [MN/m 3 ] at depth of foundation = 0.00 B. Relative denity k circular plate 3 k [MN/ m ] k quare plate k rectangular plate Looe (Ø 30 ) Medium (Ø = ) Dene (Ø = 36-4 ) Table 6. The obtained value of k for coheionle oil [MN/m 3 ] at depth of foundation = 1.00 B. Relative denity k circular plate 3 k [MN/ m ] k quare plate k rectangular plate Looe (Ø 30 ) Medium (Ø = ) Dene (Ø = 36-4 ) program. From the experimental analyi the following empirical formula i preented. The empirical formula i derived to calculate ubgrade reaction (k ) for coheionle oil under the quare foundation uing regreion method: k 59.5D90.75 (6) qa a where: k odulu of ubgrade reaction, (kn/m 3 = M ); Ø = angle of internal friction; D = depth of foundation (meter); q a = Allowable bearing capacity, (kn/m ); a = Settlement at allowable bearing capacity (meter); k i dependant and D, Ø, q a, a are independent. One-way analyi of variance (One-Way ANOVA) i ued to calculate correlation coefficient of the reulting eq uation. The One-Way ANOVA procedure produce a one-way analyi of variance for a quantitative dependent variable by a ingle factor (independent) variable. Analyi of variance i ued to tet the hypothei. Thi technique i an extenion of the two-ample tet. The number of cae, mean, and tandard deviation, tandard error of the mean, minimum, maximum, and 95%-confidence interval for the mean were calculated. It hould be mentioned here that many trial were done to increae the accuracy of the derived equation (correlation coefficient = 0.95). However, the above empirical formula give an error % of ±10%. 10. Comparion between Value of k Obtained from Empirical Formula and Different Theoretical Method A comparion between the modulu of ubgrade reaction k o btained by the empirical formula and the literature data mention in Table 1 ha been preented in Table 7. The value of modulu of ubgrade reaction k were calculated uing Poion ratio υ = 0.3 and the following value of Young modulu E [kn/m ]: Looe (Ø 30 ) Medium (Ø = ) Dene (Ø = 36-4 ) E [kn/m ] From the above fair agreement ha been obtained be- tween value of k from the empirical formula at depth of footing = 0.00 B and Biot (1937) a well a Meyerhof and Baike (1965). Copyright 013 SciRe.

11 W. N. ABD ELSAMEE 795 Table 7. The value of k for coheionle oil [MN/ m 3 ] from the preent work and the literature data. Method k [MN/m 3 ] Looe (Ø 30 ) Medium (Ø = ) Dene (Ø = 36-4 ) B iot (1937) Veic (1961) Meyerhof and Baike (1965) Selvadurai (1984) Author empirical formula (Depth of footing = 0.0 B) Author empirical formula (Depth of footing = 1.0 B) Concluion From the preent experimental tudy uing the in-itu plate load tet (P.L.T) t he following are concluded: 1) Subgrade reaction k of coheionle oil increae with increaing footing depth a well a footing ize; ) Subgrade reaction k of coheionle oil under rectangular footing i higher than that under quare and that under circular one (at ame equivalent area); 3) Subgrade reaction k of coheionle oil increae with increaing angle of internal friction; 4) The value of ubgrade reaction k for coheionle oil are preented; 5) An empirical formula i preented to calculate the ubgrade reaction k of coheionle oil for quare foundation; 6) Fair agreement ha been obtained between value of k obtained from the empirical formula at depth of footing = 0.00 B and Biot (1937) a well a Meyerhof and Baike (1965). REFERENCES [1] E. Winkler, D ie Lehre von Elatizitat and Fetigkeit (on Elaticity and Fixity), Praguc, 1987, p. 18. [] B. T. Iancu and O. T. Ionut, Numerical Analye of Plate Loading Tet Numerical Analye of Plate Loading Tet, Buletinul Intitutului Politehnic Din IASI Publicat de Univeritatea Tehnică, Gheorghe Aachi, Tomul LV (LIX), Fac. 1, Sectia Contruct II. Arhitectură (Iancu- Bogdan Teodoru and Ionut-Ovidiu Toma), 009, pp [3] M. K. Elamny, M. B. Eledeek and W. N. Abd Elamee, Effect of Depth of Foundation on Modulu of Elaticity E for Coheionle Soil, Civil Engineering Reearche Magazine of Al-Azhar Univerity, Vol. 3, No. 3, 010, p [4] S. K. Dae and Y. P. Seong, Relationhip between the Subgrade Reaction Modulu and the Strain Modulu Obtained Uing a Plate Loading Tet, 9th WCRR Lille World Congre, 011. [5] M. Aminaton, L. Nima, J. Maoud, Kh. Mehrdad, Kh. Mahdy, A. Payman and D. B. Ali, Foundation Size Effect on Modulu of Subgrade Reaction on Sandy Soil, The Electronic Journal of Geotechnical Engineering, Vol. 17, 01, pp [6] M. A. Biot, Bending of Infinite Beam on an Elatic Foundation, Journal of Applied Mechanic Tran. Am. Soc. Mech. Eng., Vol. 59, 1937, pp. A1-A7. [7] A. B. Veic, Beam on Elatic Subgrade and Winkler Hypothei, Proceeding of the 5th International Conference on Soil Mechanic and Foundation Engineering, Pari, 1961, pp [8] J. E. Bowle, Foundation Analyi and Deign, 6th Edition, McGrow-Hill International Pre, [9] K. Terzaghi, Evaluation of Coeffcient of Subgrade Reaction, Géotechnique, Vol. 5, No. 4, 1955, pp [10] ASTM, Tet Method for Denity and Unit Weight of Soil in Place by the Rubber Balloon Method (D167-94), In 1995 Annual Book of ASTM Standard, Vol. 4, No. 8, American Society for Teting and Material, Philadelphia, 1994, pp [11] L. S. Ping and L. W. Yang, Subgrade Reaction and Load-Settlement Characteritic of Gravelly Cobble Depoit by Plate-Load Tet, Canadian geotechnical Journal, Vol. 35, No. 5, 1998, pp [1] Egyptian Code, Soil Mechanic and Foundation, Organization, Cairo, 001. [13] Z. M. Reza and J. Maoud, Foundation Size Effect on Modulu of Subgrade Reaction in Clayey Soil, The Electronic Journal of Geotechnical Engineering, Vol. 13, 008, pp Copyright 013 SciRe.