Bearing Capacity of Strip Footing Supported by Two-Layer c-<f> Soils

Transcription

1 56 TRANSPORTATON RESEARCH RECORD 1331 Bearing Capacity of Strip Footing Spported by Two-Layer c-f> Soils G. AZAM AND M. c. WANG The ltimate bearing capacity of an embedded strip footing spported by two-layer c-f> soils has been investigated sing an elastoplastic finite-element compter program. n the program the footing material is treated as linear elastic and the fondation soils are idealized as nonlinear elastic perfectly plastic materials that obey the yield criterion of Drcker and Prager. The program also considers initial stresses, interface behavior, and tension failre of soil. The analysis was performed on a VAX 11/785 compter. Three soils-a commercial kaolin, a silty clay, and a clayey sandwere selected for analysis of a representative nmber of soil layer combinations. The analysis was performed for a constant footing width and varying levels of top-layer thickne. The propagation of plastic yield zones nder progressive increments of footing load was investigated, and a generalized procedre for determining bearing capacity from compter-generated pressre-settlement crves was proposed. Meanwhile, on the basis of the analysis reslts, a semiempirical eqation was developed for determining ltimate bearing capacity. A comparison with existing theories indicates that the developed eqation can provide rnorereasonable reslts than the existing ones can. Additionally, the developed eqation is relatively simple and can be easily applied. Shallow fondations are sometimes located on a soil layer of finite thickness overlying a thick stratm of another soil. The nderlying stratm may be either a bedrock or another soil possessing different strength properties. The bearing stratm of the two-layer deposits can be either softer or stiffer than the nderlying stratm. f the footing rests on a relatively thin stiff layer above a soft deposit, it may pnch throgh the top layer into the nderlying stratm. n sch a case, the settlement and ltimate bearing-capacity behavior of the footing will, to a large extent, be governed by the strength characteristics of the nderlying stratm. On the other hand, for a footing resting on a relatively thick soft layer overlying a stiff layer, bearing-capacity failre may be limited to the top layer. n both sitations, the settlement and bearing-capacity characteristics of the footing will be greatly inflenced by the thickness of the top stratm and the strength properties of the two soil layers. Bearing-capacity theories for two-layer soil deposits are scarce in pblished literatre, and the theories that have been proposed have limitations that restrict their se to idealized conditions. For example, most of the proposed eqations apply either to prely cohesive(!> = ) two-layer soils or to soil layers made p of a cohesionless (c = ) and a cohesive (!> = ) soil. Frthermore, the proposed eqations for two- G. Azarn, Directorate of Design and Consltancy, Engineer-in-Cl1icfs Branch, General Headqarters, Rawalpindi, Pakistan. M. C. Wang, Department of Civil Engineering, 212 Sackett Bilding, Pennsylvania State University, University Park, Pa layer clay soils sally assme that the top layer is stiffer than the bottom layer, that is, that c 1 > c 2. This paper presents the reslts of a stdy involving twolayer c-p soils in which the top layer may be either stiffer or softer than the bottom layer. The reslts of analyses have been sed to formlate a semiempirical bearing-capacity eqation, the reslts of which have been compared with the existing eqations. EXSTNG THEORES Researchers have proposed relationships for predicting the ltimate bearing capacity of footings on homogeneos twolayer soils. However, as mentioned, all of the proposed eqations have limitations. A review of the available bearingcapacity eqations and their limitations for two-layer soils is presented in sbseqent sections. Bearing-Capacity Theories for Prely Cohesive Two-Layer Soils The bearing capacity of strip footings on two-layer clay soils, for a stiff layer overlying a soft stratm and for its converse, has been analyzed by Btton (J). He assmed a general shear failre along cylindrical slip srfaces that emanate from the edges of the footing. He presented modified bearing-capacity factors (Ne) for!>-soils for varios vales of c 2 /c 1, c 1 and c 2 are the ndrained cohesions (or ndrained shear strengths) of the top and bottom layers, respectively. However, experimental data of Brown and Meyerhof (2) showed that Btton's (J) assmed failre modes were nrealistic and that the reslting bearing-capacity factors were on the nsafe side. They proposed the following bearing-capacity eqation for conditions in which the bearing stratm can be softer or stiffer than the nderlying stratm: q" = ltimate bearing capacity, q overbrden pressre eqal to the nit weight of soil times the depth of fondation, and Nm = modified bearing-capacity factor that depends on c 2 / c 1, the relative thickness of the pper layer (H 1 /B), and the footing shape. (1)

2 Azam and Wang Meyerhof and Hanna (3) have proposed a bearing-capacity theory for a strip footing spported by a two-layer clay in which the top layer is stronger than the bottom layer. n their failre mechanism, it is assmed that if the top layer is relatively thin, failre takes place when it is pnched throgh and the bottom layer ndergoes a general shear failre. However, if the top layer is relatively thick, the failre srface will be flly contained in the top clay layer. Ths, the ltimate bearing capacity of a strip footing can be expressed as q, = c,nc + 'Y1D1, Ne = bearing capacity factor = 5.14, D 1 = depth of fondation, and c = soil adhesion, a fnction of c 2 /c 1 (2) q = bearing capacity of a fictitios footing of the same size and shape as the actal footing bt resting on the top of bottom layer. Meyerhof (6) and Hanna and Meyerhof (7) have stdied the ltimate bearing capacity of footings on either a loose or a dense sand layer overlying a clay and have compared the different modes of soil failre with the reslts of model tests on circlar and strip footings. For a strip footing resting on a dense sand that overlies a soft clay, the bearing capacity was fond to increase with sand-layer thickness ntil abot Hif B 2'.: 2.5 (6); thereafter, it remained constant at a vale eqal to the ltimate bearing capacity of an infinitely thick dense sand layer. For a strip footing resting on a dense sand layer that overlies a firm clay, the test reslts showed a decrease in the ltimate bearing capacity with increasing sandlayer thickness. The bearing capacity decreases from the initial maximm vale (for a footing on an infinite clay layer) to the minimm for a footing on a thick sand deposit. For this case, Meyerhof (6) has proposed the following eqations: 57 Bearing-Capacity Theories for Sand Overlying Cohesive Soils Tcheng ( 4) has proposed a bearing-capacity eqation for a long rectanglar footing resting on a sand layer that is nderlain by a prely cohesive soil layer. He reported good agreement between his test reslts and the proposed eqation within the domain H 1 l.5b. He frther reported that the inflence of the bottom clay layer on bearing capacity becomes negligible when H 1 2'.: 3.5B. Tcheng's eqation is as follows: with a maximm for H,B = and a minimm for HJ B 2'.: H 1 /B (5) (6) (7) q = q: { l - 2{H 1 /B)tan l>(l + sin >) x exp[ - ( - )ta n 1>]} (3) H 1 is the failre depth. Satyanarayana and Garg (8) have proposed a simplified bearing-capacity theory for shallow fondations in c-> soils. According to their theory, the ltimate bearing capacity of a two-layer soil is given by q = bearing capacity of a long rectanglar footing resting on the sand layer, q = bearing capacity of the same footing resting on the nderlying clay layer, and > = angle of internal friction. Vesic (5) has proposed a more general bearing-capacity eqation, which is valid for rectanglar footings resting on a top layer with strength parameters (c 1,1> 1 ) that is nderlain by a weaker layer with strength parameters (c 2,j> 2 ). t is shown as (8) q = [q + (1/K)c 1 cot f> 1 ] exp[2(1 + BL) x K tan f> 1 (H/B)] - (1/K)c,cot 1> 1 l - sin 2 1> 1 K=, 1 + sin 2 1> 1 L = footing length, and (4) N Nq, N = bearing capacity factors based on l>av As is seen from the review, only one eqation proposed by Satyanarayana and Garg (8) is available for predicting the ltimate bearing capacity of two-layer c-f> soils. For this eqation, the proposers even cation abt applying the eqation to all soils.

3 58 FNTE-ELEMENT ANALYSS A two-dimensional plane strain elasto-plastic finite-element compter program was sed for analysis. The program ses incremental stress-strain relations for elastic perfectly plastic materials and either Mohr-Colomb or Drcker-Prager (9) yield criteria to define soil yielding. t was specifically adapted and modified to inclde (a) capability for incorporating geostatic (initial) stresses to represent the stress state in the soil mass before the application of bondary loads, (b) interface elements to satisfy displacement compatibilities along the vertical bondaries between the fondation and soil, (c) footing material (reinforced concrete) modeled as a linearly elastic material, and (d) soil modeled as nonlinearly elastic in the elastic range. A complete description of the nmerical and mathematical formlations of the program, inclding validation, is available else (1). The finite-element compter program was sed to investigate the behavior of a reinforced concrete strip footing having B = 3. ft (91.4 cm) and D 1 = 3. ft (91.4 cm), shown schematically in Figre 1. The footing was spported by a two-layer soil deposit having for different layer combinations: a soft clay nderlain by a stiff clay, a stiff clay nderlain by a soft clay, a clayey sand nderlain by a stiff clay, and a stiff clay nderlain by a clayey sand. The stiff clay was a compacted kaolin, the soft clay was a compacted silty clay, and the clayey sand was a compacted mixtre of 9 percent sand and 1 percent kaolin. The strength properties of the three soils sed in the analysis are smmarized in Table l; determinations of these strength properties are docmented else (JO). n the analysis, the entire soil-footing system was represented by a finite nmber of eight-node qadrilateral elements interconnected at the nodal points. Becase in a continos footing, a plane of symmetry exists along the vertical-footing axis, only half of the model needed to be analyzed. The nodal FOOTNG SOL l SOL 2 BEDROCK FGURE 1 Schematic of footing-soil geometry. TRANSPORTATON RESEARCH RECORD 1331 points along the vertical side bondaries were restrained in the x-direction; those on the bottom bondary were restrained in x- and y-directions. To accommodate the nonlinear stress-strain characteristics of the fondation soils in the finite-element analysis, the geostatic stress and footing load were applied in increments. At the initial stage of loading, increments of no more than 1 percent of the total footing load were sed; at the final stage, the increments were redced to 1 percent. For each increment, generally three to five iterations of comptations were needed. The compter analysis was performed on a VAX 11/ 785 compter. The finite-element analysis provides stresses, strains, and yield condition of each element, pressre-verss-settlement (p-8) relationship of the footing and contact pressre at footing-soil interface, among others. The p-o relationships were sed to obtain the ltimate bearing capacity for each condition analyzed. As an illstration, a set of typical p-8 crves for soft clay nderlain by stiff clay, and its converse, for H 1 B = 1 and 8 are shown in Figre 2. These crves clearly demonstrate the variation in slope (stiffness) and the change in ltimate bearing capacity with changing H 1 /B for each layer combination. Sch crves are plotted for each condition analyzed, and from these crves the ltimate bearing capacities are determined sing the criterion discssed in the following. These ltimate bearing-capacity vales form the basis for sbseqent presentation and discssion. ULTMATE LOAD CRTERON The p-o crves obtained from the finite-element analysis do not always show a distinct point for the determination of ltimate bearing capacity. The point on the p-8 crve indicating ltimate bearing capacity depends on the mode of failre, sch as general, local, or pnching shear failre, which in trn depends on soil type, its relative density, compressibility, footing width, depth of fondation, and so on. Determining ltimate bearing capacity from p-o crves, therefore, reqires some degree of jdgment and experience. Researchers have proposed different approaches. For example, Vesic (11) has recommended that ltimate load can be taken as the point the slope of the p-o crve first reaches zero or steady minimm vale. Desai and Christian (12) have proposed either sing the concept of critical (or tolerable) settlement or choosing the load corresponding to the intersection of the tangents with the initial and ltimate portions of the p-8 crve. However, no single criterion is general enogh to apply to all types of soils and all modes of failre. Consideration of the critical-settlement criterion is jstified by the basic philosophy of fondation design, which regards the excessive settlement as a failre of the fondation. There is no single vale of critical settlement that satisfies failre conditions in all types of soils and all modes of failre. Observations in satrated clays (13) indicate that these settlements may be between 3 and 7 percent of footing width (B) for srface footings, increasing to 15 percent for embedded footings. For footings in sand, somewhat higher vales-ranging from 5 to 15 percent for srface footings and as high as 25 percent for embedded footings-have been proposed (14,11). Das (15) has sggested that for fondations at shallow depth

4 Azam and Wang 59 TABLE 1 MATERAL PROPERTES OF FOUNDATON SOLS (1 psi= 6.9 kn/m 2 ) Material Propertiee Silty Clay Kaolin Clayey Sand nitial Modls in Compression, 667 2,88 6,1 psi Poisson's ratio Dry Unit weight, pci Unit cohesion, psi nternal friction anqle, deo nitial earth pressre coefficient Tensile strenoth, psi o. 54 nitial modls in tension, psi 1,55 7, 11, 3 Soil constant (Rrl a.so ) w V V w : p :> z H! ST! H CLAY sorr cy -, ' ' ' J.O FOOTNG DSPLACEMENT (ft) FGURE 2 Comparison of p-o crves for soft clay nderlain by stiff clay and its converse for H 1 /B = 1 and 8 (B = 3. ft, D 1 = 3. ft). and for those likely to fail by general shear, the ltimate load may occr at fondation settlement of 4 to 1 percent of footing width (B); however, for local or pnching shear failre, the ltimate load may occr at settlements of 15 to 24 percent of B. Ths, in the selection of a particlar vale of critical settlement, one shold take into accont not only the depth of fondation bt also the soil type and its likely failre mode. On the basis of these considerations and the fact that the soils of this stdy are not niform bt layered and contain a highly compressible clay and a sandy soil, a critical settlement eqal to 2 percent of B was chosen as one of the criteria for determining the ltimate bearing capacity. n addition, becase the ltimate load takes place in the state of failre, it is reasonable to take into accont the rate of yielding in the determination of the ltimate bearing capacity. Sch an approach, in which the yielding rate of soil elements is considered in conjnction with other techniqes, has been adopted here. The nmber of yielded elements is plotted against the applied pressre, and the yielding rate is observed from the slope of this crve. The point at which the crve exhibits a distinct change in the average slope, signifying accelerated plastic yielding, is an indication of the ltimate bearing capacity. The overall techniqe for determining the ltimate bearing capacity from p-8 crves adopted in this stdy is smmarized in the following: 1. f the p-'& crve shows a distinct yield point, then that point is taken to signify the ltimate bearing capacity. Sch a crve wold satisfy Vesic's criterion (11). 2. f the crve exhibits no distinct yield point, as in Figre 3, bt instead appears to sggest contined penetration, then the following steps are exected:

5 6 - The point given by the intersection of tangents to the initial and ltimate portions of the p-& crve is noted (Figre 3). This gives one possible vale of ltimate bearing capacity. -The point that indicates an increase in the rate of element yielding on the pressre-verss-nmber of yielded elements crve, sch as Point A in Figre 4, is noted. This gives a second vale of ltimate bearing capacity. - Whichever point is the lesser vale is chosen as the ltimate bearing capacity. 3. f the chosen vale is greater than that dictated by settlement considerations (i.e., pressre at a settlement of 2 percent of B), then the latter vale is taken as the ltimate bearing capacity. SPREAD OF PLASTC YELD ZONES Stdy of the plastic flow behavior gives insight into the progressive yielding of soil nder a load and can indicate the dominant failre mode. Selected figres depicting the spread of plastic yield zones in two-layer soils are presented here. Figres 5-8 illstrate plastic yielding for a weak clay layer nderlain by a stiff clay and its converse for two levels of the ratio of top-layer thickness to footing width, that is, H 1 /B = 1 and 4. Figre 5 shows that when the top layer is thin (H 1 /B = 1), the yield zones at the collapse stage extend into the bottom layer and propagate to the srface. The spread of yield zones to the grond srface indicates that at the collapse stage the soil yielding is analogos to a plastic flow nder sqeezing action. A yield-zone pattern of this type indicates a possible general shear failre involving both soil layers. When the top clay layer becomes thick (H 1 /B = 4), as in Figre 6, the TRANSPORTATON RESEARCH RECORD 1331 yielding is confined to the top layer. The yield zones appear to stop spreading into the stiff clay layer below, indicating that the elements in the lower layer have not yet reached their yield state. This behavior sggests that at H,B = 4, the ltimate bearing capacity will be dictated predominantly by the strength properties of the top layer, thogh some inflence of the lower layer may still be present. The yield pattern of Figre 6 frther indicates that the failre mode is a possible local shear failre confined to the top layer. Figres 7 and 8 show a stiff clay nderlain by a weak clay for H 1' B = 1 and 4, respectively. These figres reveal that the yield zones extend deep into the weaker layer below even when the top layer is sfficiently deep (e.g., H 1 /B = 4). This yield pattern is typical of a pnching shear failre of the top layer followed by a general shear failre of the bottom layer. Ths, the bearing capacity of sch a layer combination will be largely controlled by the strength properties of both layers. DSCUSSON OF RES UL TS The objective of this analysis was to establish the relationship between the ltimate bearing capacity (q ) and top-layer thickness for varios soil layer combinations. Accordingly, for soil-footing systems (H 1 /B = 1, 2, 3, and 8) were analyzed for the for two-layer combinations. Figre 9 shows the variation of ltimate bearing capacity (q ) with H 1 /B for two clay layer soils-soft clay over stiff clay and stiff clay over soft clay. t is noted from this figre that when the top layer is a soft clay, the bearing capacity decreases with an increase in the top-layer thickness and ltimately attains a steady vale eqal to its own bearing capacity at approximately H 1 1B = 6. The yield patterns given in Figres 5 and 6 can be sed to, 'M " Q, t!. l! z H t FOOTNG DSPLACEHENT (ft.) FGURE 3 p-8 crve for niform kaolin, illstrating the application of ltimate-bearingcapacity criterion (B = 3. ft, D 1 = 3. ft).

6 qo JJ, 75 P f -z 2 : ll ll. ti ii H t NTAL AVERAGE SLO.PB 2 - _ --,--,-.-r-r--.--t ,--, NUHBBR OF TBLOBD ELBHBNTS FGURE 4 Pressre-element yield rate crve for niform kaolin, illstrating the application of ltimate-bearing-capacity criterion. q l-: '- - Nl-U-H-ER-A-LS- 1-N-1-CA- T-E RATO OF ArPLEO PRESSURE TO ULTHATE BEARNG CAPACTY ;;;;::;==:=:::: = = = B l.o ft..,,. ll - '=.-5=" D - l.o ft..)9 == : 7 \. = =:. o.51 '= - - ". = '= = _, - 1 "1 n NO. OF ELEHENTS 2'6 = == = f = - - i- 11. OF NODES l _,_ FGURES Spread of plastic yield zones at varios pressre levels in two-layer soil with soft over stiff clays and H 1 /B = 1.

7 . 18 V,FOOTlllG 11. /NTERFACE NUHERALS NDCATE RATO OF APPLED PRESSURE TO ULTHATE DEARNG CAPACTY B J.O ft " - j De J.O Ct t: n 4 "' 1. NO. OF F.l.EHENTS n. Of NOl)F ,_ j H "' FGURE 6 Spread of plastic yield zones at varios pressre levels in two-layer soil with soft over stiff clays and H1/B = 4. q FOOTNG NTF.RFACE NUHERAl.S NDCATE llato or ArrLED rressure TO ULTHATE BEARNC CAPACTY ' J -= = = 8.J.O ft, Pr l. DC. 5 t: 1' -====-- -- :!., = - o. 18 'f ;.DO J.'GURE 7 Spread of plastic yield zones at varios pressre levels in two-layer soil with stiff over soft clays and H 1 /B = 1.

8 .6 FOOTlllG r Nl'ERFACE ii ' tluherals NDCATE RATO OF ArrLED rressure TO ULTHATE BEARNG CAPACTY t B J.O ft. -.:! - - H "1 n- 4 t; D 1 J.O rt a o. 75 l - 1. \ - - N!'\. ' :\,'\!"'-' ), j t: "' - FGURE 8 Spread of plastic yield zones at varios pressre levels in two-layer soil with stiff over soft clays and H 1 /B = o.. ;) " "' :i "' 8!::; = : STFF ClAY SOFT ClAY SOFT ClAY STFF ClAY B 1 B TOP LAYER THCKNESS TO FOOTNG VDTH RATO (_!) B FGURE 9 Variation of ltimate bearing capacity with top-layer thickness for soft clay over stiff clay and its converse (B = 3. ft, D 1 = 3. ft, H 2 = 3. ft). 12

9 64 explain the observed behavior. The greater bearing capacity at a smaller H 1 B ratio is possibly becase at small H 1 B ratios, the failre zone extends into the lower stiff clay layer and the higher strength of the lower layer contribtes toward a greater ltimate bearing capacity. However, when the top soft clay becomes thicker, the major portion of the failre zone is within the top layer. As a reslt, the lower strength of the top layer redces the ltimate bearing capacity. The trend of bearing-capacity variation for a stiff clay nderlain by a soft clay layer (Figre 9) is almost the exact opposite of the preceding case. The ltimate bearing capacity increases with top-layer thickness and ltimately attains a steady vale eqal to the bearing capacity of the top layer at approximately H 1 /B = 6. The explanation for this behavior, as before, is that at small H 1 /B ratios the failre zone extends into the bottom layer, whose lower strength redces the ltimate bearing capacity; at higher H 1 /B ratios the failre zone remains confined within the top clay layer, reslting in a greater ltimate bearing capacity. The variations of ltimate bearing capacity with top-layer thickness for a sand nderlain by a stiff clay and its converse are illstrated in Figre 1. The bearing capacity of the former case decreases with increasing sandlayer thickness from a maximm at H 1 /B = (i.e., the footing rests on the clay layer) to a minimm vale eqal to that for a footing resting on an infinitely thick sand deposit. The ltimate bearing capacity in this case attains a steady vale at abot H 1 /B = 3. This H 1 /B vale is in good agreement with the vale of approximately 2.5 obtained by Mt:yt:rhof (9) from model tests on loose sand overlying stiff clay and the vale of3.5 sggested by Tcheng (4). PROPOSED EQUATON TRANSPORTATON RESEARCH RECORD 1331 The bearing-capacity eqation is formlated by crve fitting. The data base for formlation is the bearing-capacity-versstop-layer-thickness relationship discssed earlier and presented in Figres 9 and 1. The variations of bearing capacity seen in these figres dictate that a semiempirical approach is most appropriate for formlating a single eqation for all for crves. Of the varios relationships attempted, the empirical parabolic interaction relationship appears to best fit the data base. On the basis of this relationship, the following bearingcapacity eqation is proposed: q = ltimate bearing capacity of strip footing over twolayer soil; q, = ltimate bearing capacity of the footing spported by an infinitely thick top-layer soil, compted by the traditional bearing-capacity eqation sing factors recommended by Vesic (5); qb ltimate bearing capacity of the footing spported by an infinitely thick bottom-layer soil, compted by the same method as q,; m layer factor, which is for two layers of clay (se of the lower vale is recommended if one clay layer is highly compressible, otherwise se the average vale) and.3 for a sand-clay layer combination; and (9) 24. c :;!::: " :! "' "' 8 ;!;!::; => STFF CLAY SAND SAND STFF CLAY 4 FGURE TOP LAYER THCKNESS TO FOOTNG 11DTB RATO ('.'!) a Variation of ltimate bearing capacity with top-layer thickness for clayey sand over stiff clay and its converse (B = 3. ft, D 1 = 3. ft, H 2 = 3. ft).

10 Azam and Wang 65 H 1 /B = top-layer-thickness-to-footing-width ratio, which is no more than 6 for clay-clay layers and no more than 3.5 for sand-clay layers. The reslts compted from Eqation 9 are compared with the available theories in Figres 11 and 12. The comparison reveals that the bearing-capacity variations predicted from eqations of Vesic (5) and Satyanarayana and Garg (8) attain steady vales at approximately H 1 B = 1 and 2, respectively, signifying that the bottom layer ceases to have any inflence beyond these top-layer thicknesses. On the other hand, the bearing capacity determined from Eqation 9 approaches a steady vale at a gradal rate, indicating a prononced inflence of the bottom-layer soil p to approximately H 1 /B = 6. Sch a gradal variation of bearing capacity with the top-layer thickness appears to be more reasonable ULTMATE BEARNG CAPACTY OF NFNTELY THCK TOP LAYl:R ' ' 15 1 so Veslc CJ> Satyanarayana and Garg () 3 Proposed Eqation R TOP!AYER THCKNESS TO FOOTNG YDTB RATO (_!) B FGURE 11 Comparison of proposed eqation with available theories for stiff clay nderlain by soft clay "' 2 '". 15. "' 1. :r:. t; 5 :::. i"'---2 l Satyanarayana and Garg (,!) 2 Proposed Eqation ""-1 "---r-- ' "-._ LTillATE BNG CAPACTY or NFNTELY THCK TOP LAYER ' ' 7 R TOP!AYER THCKNESS TO FOOTNG VDTB RATO (_!) B FGURE 12 Comparison of proposed eqation with available theories for soft clay nderlain by stiff clay.

11 66 TRANSPORTATON RESEARCH RECORD 1331 SUMMARY AND CONCLUSONS The ltimate bearing capacity of a shallow continos footing spported by two-layer c-> soils has been investigated sing an elasto-plastic finite-element compter program. Three soils- a soft clay (silty clay), a stiff clay (kaolin), and a clayey sand (9 percent sand + 1 percent kaolin)-were sed to form representative soil layer combinations. The effect of top-layer thickness (H 1 ) on bearing capacity was investigated for each layer combination. Footing width (B) and depth of fondation (D 1 ) were kept constant at 3. ft (91.4 cm). The reslts of the analysis led to the formlation of a semiempirical bearingcapacity eqation that is simple in its application. The reslts of the analysis indicate that when the top layer is a thin weak clay nderlain by a stiff clay, the failre mode is predominantly a general shear failre involving both clay layers. Bt when the top layer is a thin stiff clay nderlain by a weak clay, the plastic yield pattern sggests a predominantly pnching shear failre of the top clay layer. For a thin sand layer nderlain by a stiff clay, the yield patterns sggest a local shear failre limited to the sand layer. For a thin layer of stiff clay nderlain by sand, the failre mode is predominantly a pnching shear failre of the top clay layer. The thickness of top soil layer has a marked inflence on the ltimate bearing capacity. The bearing capacity decreases steadily with increasing top-layer thickness when the top layer is weaker than the bottom layer, and vice versa. The bearing capacity attains a steady vale at a specific top-layer thickness, depending on the strength properties of the two soils. The developed bearing-capacity eqation is compared with available soltions. Reslts of the comparisons indicate that the developed eqation can provide a more reasonable bearingcapacity vale than existing ones. ACKNOWLEDGMENT The stdy was partially sponsored by the National Science Fondation. This spport is grateflly acknowledged. REFERENCES 1. S. J. Btton. The Bearing Capacity of Footings on a Two-Layer Cohesive Sbsoil. Proc., 3rd nternational Conference on Soil Mechanics and Fondation Engineering, Zrich, Switzerland, Vol. 1, 1953, pp J. D. Brown and G. G. Meyerhof. Experimental Stdies of Bearing Capacity in Layered Clays. Proc., 7th nternational Conference on Soil Mechanics and Fondation Engineering, Mexico City, Mexico, Vol. 2, 1969, pp G. G. Meyerhof and A. M. Hanna. Ultimate Bearing Capacity of Fondations on Layered Soils Under nclined Load. Canadian Geotechnical Jornal, Vol. 15, 1978, pp Y. Tcheng, Fondations sperficielles en milie stratifie. Proc. 4th nternational Conference on Soil Mechanics and Fondation Engineering, London, England, Vol. 1, 1957, pp A. Vesic. Bearing Capacity of Shallow Footings. n Fondation Engineering Handbook (Winterkorn and Fang, eds.), Van Nostrand Reinhold, New York, N.Y., G. G. Meyerhof. Ultimate Bearing Capacity of Footings on Sand Layer Overlying Clay. Canadian Geotechnical Jornal, Vol. 11, 1974, pp A. M. Hanna and G. G. Meyerhof. Design Charts for Ultimate Bearing Capacity of Fondations on Sand Overlying Soft Clay. Canadian Geotechnica/ Jornal, Vol. 17, 198, pp B. Satyanarayana and R. K. Garg. Bearing Capacity of Footings on Layered c-l> soils. Jornal of the Geotechnical Engineering Division, ASCE, Vol. 16, No. GT7, 198, pp D. Drcker and W. Prager. Soil Mechanics and Plastic Analysis in Limit Design. Qarterly of Applied Mathematics, Vol. 1, No. 2, 1952, pp G. Azam. Stability of Shallow Continos Footings Spported by Two-Layer Soil Deposits with an Undergrond Void. Ph.D. thesis. Pennsylvania State University, University Park, Ag A. Vesic. Bearing Capacity of Deep Fondations in Sand. n Highway Research Record 39, RD, National Research Concil, Washington, D.C., 1963, pp C. S. Desai and J. T. Christian. Nmerical Methods in Geotechnical Engineering. McGraw-Hill, New York, N.Y., A. W. Skempton. The Bearing Capacity of Clays. Proc., Bilding Research Congress, London, England, 1951, pp E. E. De Beer. Bearing Capacity and Settlement of Shallow Fondations of Sand. Proc., Symposim on Bearing Capacity and Settlement of Fondation, Dke University, Drham, N.C., 1965, pp B. M. Das. Principles of Fondation Engineering. Brooks/Cole Engineering Division, Monterey, Calif., 1984, pp