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- 1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME337EXPERIMENTAL ESTIMATE OF ULTIMATE BEARING CAPACITYAND SETTLEMENT FOR RECTANGULAR FOOTINGSM. S. Dixit1and K. A. Patil21Research Scholar, Department of Civil Engineering, Government College of Engineering,Aurangabad (Maharashtra State), India, 431005.2Associate Professor, Department of Civil Engineering, Government College ofEngineering, Aurangabad (Maharashtra State), India, 431005.ABSTRACTThe estimation of load carrying capacity of footing is the most important step in thedesign of foundation. A number of theoretical approaches, in-situ tests and laboratory modeltests are available to find out the bearing capacity of footings. The reliability of any theorycan be demonstrated by comparing it with the experimental results. Results from laboratorymodel tests on rectangular footings resting on sand are presented in this paper. The bearingcapacity of sand below a model footing of rectangular shape with variation in size, depth ofsand cushion (Dsc=900mm) and the effect of permissible settlement are evaluated. A steeltank of size 900mm×1200mm×1000mm is used for conducting model tests. Bearing capacityfactor Nγ is evaluated and is compared with Terzaghi, Meyerhof, Hansen and Vesic’s values.From the experimental investigations it is found that, as the footing size increases, ultimatebearing capacity and settlement values show an increasing trend and Nγ decreases byincreasing the footing size.Keywords: Rectangular footing, model test, sand, depth, ultimate bearing capacity,settlement.1. INTRODUCTIONAmong several different approaches in determination of the bearing capacity ofshallow foundations, the famous triple-N formula of Terzaghi has been generally employedin the past decades, and can be written as given in equation (1)γγBNqNcNq qcult 5.0++=…(1)INTERNATIONAL JOURNAL OF CIVIL ENGINEERING ANDTECHNOLOGY (IJCIET)ISSN 0976 – 6308 (Print)ISSN 0976 – 6316(Online)Volume 4, Issue 2, March - April (2013), pp. 337-345© IAEME: www.iaeme.com/ijciet.aspJournal Impact Factor (2013): 5.3277 (Calculated by GISI)www.jifactor.comIJCIET© IAEME
- 2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME338Where, qult is the ultimate bearing capacity of soil mass, c is the cohesion, q is the surchargepressure, B is the foundation width and γ is the unit weight of soil mass. Similarly Nc, Nq andNγ are bearing capacity factors, which are functions of the soil friction angle. The second andthird terms in equation (1) have been known as the main contributor to the bearing capacityof shallow foundations on non-cohesive soils. There are several suggested values for the thirdfactor by different investigators such as Terzaghi (1943), Meyerhof (1963), Hansen (1970),Vesic (1973), Bolton and Lau (1989) etc. Although all these methods are generally based ona limit equilibrium solution, there are differences between their assumptions for boundaryconditions and consideration of the soil weight effect. The third bearing capacity factor i.e. Nγhas been computed by taking several assumptions in to account. Terzaghi (1943) assumedthat, the components of bearing capacity equation can be safely superposed. Bolton and Lau(1989) performed a study on the effect of surcharge pressure on computed Nγ and presented adimensionless factor Ω defined as the ratio of the surcharge pressure q to γB. They stated thatif this factor is equal to or less than 1.0, the effect of surcharge pressure leads to less than20% error in calculation of the bearing capacity factor (Nγ), which seems to be acceptable forpractical purposes. Beside these assumptions, almost all conventional methods assume aconstant value of soil friction angle to compute the bearing capacity factors. Considering thebearing capacity equation, the third term suggests an increasing tendency in bearing capacitywith an increase in foundation size. However, data from De Beer (1965), Bolton and Lau(1989) shows that the bearing capacity of shallow foundations does not increase with sizelinearly and the bearing capacity factor Nγ, decreases by increasing foundation size.2. EARLIER STUDIES CARRIED OUTA shallow foundation is load carrying structures that transmit loads directly to theunderlying soil. Shallow is a relative term, a foundation with a depth to width ratio less thanor equal to four (D/B ≤ 4) is simply called a shallow foundation (Das, 1999). A foundationmust satisfy two fundamental requirements: ultimate bearing capacity and settlement offoundations. The bearing capacity of soil can be defined as the foundation’s resistance whenmaximum pressure is applied from the foundation to the soil without arising shear failure inthe soil. The load per unit area of the foundation at which shear failure takes place is calledthe ultimate bearing capacity. By taking into account these two criteria, there are manytheories and many approaches in laboratory and in situ studies to determine the ultimatebearing capacity. Firstly, Prandtl (1921), and thereafter Reissner (1924) presented theoriesbased on the concept of plastic equilibrium. Later, the formulation was modified by Terzaghi(1943), Meyerhof (1963), Hansen (1970), Vesic (1973) and others.The ultimate bearing capacity depends on the size of the foundation for both square andrectangular footings. Therefore, small models of footings prepared in a laboratory aredifferent from real size footings with regards to behavior and stress distribution. This is calledthe scale effect, and it has been studied by numerous researchers for many years (Bolton andLau, 1989; Cerato, 2005; Kumar and Khatri, 2008; Veiskarami et al., 2011). The scale effectarising from the grain size of the soil has a significant role if the foundation width to grainsize ratio is less than 50-100. Therefore, caution must be taken in applying the results of verysmall-scale model footing tests instead of full-scale behaviors. One simple solution to solvepossible problems due to the scale effect is to use a larger footing, giving an acceptable sizeratio, B/D50 greater than 100 (Taylor 1995). Although it is necessary to test the actual sizefooting to understand real soil foundation behavior to do so is an expensive, time consuming
- 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME339and experimentally difficult process. For this reason, taking the scale effect into considerationmost researchers have only worked on small-scale footings of different sizes in the laboratoryto obtain the ultimate bearing capacity.Terzaghi, (1943) formed a semi-empirical equation for computing the ultimatebearing capacity of a foundation. Later, Meyerhof (1963) proposed a general bearing capacityequation similar to that of Terzaghi which included different shape and depth factors. He tookinto account the shear strength of the soil above the base level of the footing. Thereafter,Hansen (1970) modified the study of Meyerhof, Vesic (1973) used an equation very similarto that suggested by Hansen (1970). However, there are some restrictions and assumption inall of these classical formulations; therefore, they do not always give reasonable resultscompared to available experimental data. Because of the uncertain nature of soils and thedifficulties of experimental tests in laboratory and in situ, there is an increasing tendency toseek alternative bearing capacity prediction methods, other than the traditional computingtechniques, to obtain more accurate results.3. EXPERIMENTAL STUDY3.1 Materials used for the testing: sandThe test sand used in this study was dry sand collected from Godavari River nearPaithan about 50 km from Aurangabad in Maharashtra State of India. The aim of this work isto study the effect of variation in size, depth of sand cushion below the footing (Dsc)=900mmand permissible settlement of footing on bearing capacity of sand for rectangular footing. Thespecific gravity of sand is found to be 2.65, coefficient of uniformity (Cu) 3.20, coefficient ofcurvature (CC) 0.96 and effective particle size (D10) 0.42mm. Grain size distribution curve isshown in Figure1. The maximum and minimum dry unit weights of the sand were determinedaccording to IS: 2720(1983), (part 14). The maximum dry unit weight obtained is 18kN/m³and the minimum dry weight obtained by pouring into the loosest state is 15.3kN/m³. Thefriction angle of the sand at 82.90% relative density (Dr), as determined from direct shear teston dry sand sample, is found to be 40⁰.Figure 1: Grain size distribution of sand
- 4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME3403.2 Laboratory Model Tests3.2.1 Test set-upThe load tests were conducted in a rectangular steel tank of 900mm x 1200mm in planand 1000mm in depth. The model footings used for the tests were rectangular in shape. Thefootings were made of 10mm thick rigid steel plate of sizes 100mm x 125mm, 100mm x150mm, 100mm x 175mm and 100x200mm. A hydraulic jack attached to the proving ringwas used to push the footing slightly into the bed for proper contact between the soil andfooting. A schematic diagram of the test set-up is shown in Figure 2. In the present study theintensity of loading will be denoted by q and depth of sand cushion below the footing will bedenoted by Dsc.3.2.2 Preparation of test bedPluviation i.e. raining technique was used to place the sand in test tank. The height offall to achieve the desired relative density was determined by performing a series of trialswith different heights of fall. In each trial, the densities were monitored by collectingsamples in small aluminum cups of known volume placed at different locations in the testtanks, based on the minimum and maximum void ratios of the sand for each height of fall, therelation between the height of fall and the corresponding relative density was developed.Figure 2: Sketch of Prototype Model of size 900mmx1200mmx1000mm3.2.3 Testing procedureInitially the sand bed of 900mm depth was prepared in the steel test tank using thesand raining technique. The side walls of the tank were made smooth by painting with an oilpaint to reduce the boundary effects. After preparing the bed, the surface was levelled, andthe footing was placed exactly at the centre of the loading jack to avoid eccentric loading.
- 5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME341The footing was loaded by a hand operated hydraulic jack supported against a reaction frame.A pre-calibrated proving ring was used to measure the load transferred to the footing. Theload was applied in small increments. Each load increment was maintained constant until thefooting settlement was stabilized. The footing settlements were measured through the dialgauges whose locations are shown in the Figure 2. Table 1 shows the effect of intensity ofloading on settlement at depth of sand cushion below the footing (Dsc) =900mm, for 100 ൈ125mm rectangular footing.Table 1: Effect of q and Dsc=900mm.on settlement in mm, for 100 x 125mm rectangularfootingIntensity of loading (q) (kN/m²) Settlement in mm0 016 0.6832 1.9648 3.464 5.1280 7.8696 9.1112 10.6128 12.3144 13.84160 14.96Figure 3: Effect of q on settlement in mm at Dsc=900mm for 100x125mm rectangularfootingFigure 3 shows the effect of intensity of loading on settlement for depth of sand cushionbelow the footing (Dsc)=900mm.02468101214160 20 40 60 80 100 120 140 160 180SettlementinmmIntensity of loading kN/m2
- 6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME342Figure 4: Log Load vs. Log settlement for 100x125mm rectangular footing at 900mm depthAs shown in figure 4 log load vs log settlement relationship is plotted and twointersecting straight lines are identified in the data points. The load corresponding to point ofintersection gives the ultimate bearing capacity and corresponding settlement is obtained. Nγvalues are computed using the equation qult = 0.4γBNγ and they are computed for depth ofsand cushion Dsc=900mm. The results are compared with the theoritical values proposed byTerzaghi (1943), Meyerhoff (1963), Hansen (1970) and Vesic (1973). Similarly forrectangular footing of sizes 100x150mm, 100x175mm, 100x200mm effect of q and Dsc onsettlement in mm are found out and log-load vs log settlement curves are plotted.Table 2: Effect of q and Dsc on settlement in mm, for 100 x150mm rectangular footingIntensity of loading (q) (kN/m²) Settlement in mm0 013.33 0.7226.66 1.840 3.153.33 4.8666.66 6.880 8.0293.33 9106.66 10.1120 11.98133.33 13.1146.66 14.8160 16.31.31.41.51.61.71.81.922.12.22.30.2 0.4 0.6 0.8 1 1.2 1.4LogLoadLog Settlement
- 7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME343Table 3: Effect of q and Dsc on settlement in mm, for 100x175mm rectangular footingIntensity of loading (q) (kN/m²) Settlement in mm0 011.42 0.8422.85 2.8439.5 3.8845.71 4.9657.14 5.6868.57 7.8880 8.9291.42 10.46102.85 11.9114.28 12.86125.71 14.02137.14 15.28148.57 16.54160 17.74Table 4: Effect of q and Dsc on settlement in mm, for 100x200mm rectangular footingIntensity of loading (q) (kN/m²) Settlement in mm0 010 0.9820 1.5830 2.9640 4.7650 6.0460 7.7270 8.8680 9.490 10.42100 11.4110 12.78120 13.94130 14.98140 16.34150 17.18160 18.12
- 8. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME344Table 5: Effect of footing size on ultimate bearing capacity, settlement and NΨ valuesSr.no Footing size inmmUltimate bearing capacitykN/m2Settlement in mm NΨ1 100x125 95.49 9.12 106.12 100x150 104.71 9.54 96.953 100x175 109.64 12.02 87.014 100x200 114.81 12.58 79.72Thus from table 5, it is seen that as the footing size increases ultimate bearing capacity andsettlement goes on increasing. The bearing capacity factor NΨ decreases by increasing thefooting size. The values of Nγ calculated by Terzaghi (1943), Hansen(1970), Vesic(1973),and Meyerhof (1963) methods are 115.31, 95.41, 109.41 and 95.4 respectively.4. RESULTS AND DISCUSSIONFor depth of sand cushion of 900mm for rectangular footing of sizes 100mmx125mm,100mmx150mm 100x175mm 100x200mm, ultimate bearing capacity values are found to be95.49 kN/m², 104.71kN/m², 109.64kN/m²and 114.81kN/m² respectively. As compared to100mmx125mm rectangular footing, the percentage increase in the ultimate bearing capacityfor 100x150mm, 100x175mm and 100x200mm rectangular footing are found to be9.65%,14.81% and 20.23 % respectively. Thus it indicates that as footing size increases,ultimate bearing capacity goes on increasing.For rectangular footing of size 100x125mm,100x150mm,100x175mm and100x200mm depth of sand cushion below the footing Dsc= 900mm, the values of settlementsgoes on increasing. The percentage increase as compare to 100x125mm rectangular footingare found to be 4.60%,31.79% and 37.93% respectively. Thus it indicates that as footing sizeincreases, settlement also increases.The values of Nγ obtained from experimental investigations for various rectangularfooting of size 100x125mm,100x150mm,100x175mm and100x200mm depth of sandcushion below the footing Dsc = 900mm, show lower bound values in comparison withTerzaghi’s method (1943), Meyerhof’s methods (1963), Hansen(1970), and Vesic’s method(1973) for 900mm depth of sand cushion shows upper bound values. The values of Nγobtained show a decreasing trend for various rectangular footing.5. CONCLUSIONSBased on the studies carried out the following conclusions are drawn.• The percentage increase in the ultimate bearing capacity for 100 x 150 mm, 100 x175mm and 100x200mm rectangular footing are found to be 9.65%, 14.81% and20.23 % respectively. Thus it indicates that as footing size increases, ultimate bearingcapacity goes on increasing.• The value of settlement goes on increasing as footing size increase.• The values of Nγ obtained show a decreasing trend for various rectangular footing.• The bearing capacity factor Nγ decreases by increasing the footing size.
- 9. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME345REFERENCES1. Terzaghi, K. (1943), Theoretical Soil Mechanics, John Wiley and sons, New York, USA.2. Meyerhof, G.G. (1963), “Some Recent Research on the Bearing Capacity ofFoundations”, Canadian Geotechnical Journal, 1, pp.16-26.3. Hansen, J. B. (1970), Revised and Extended Formula for Bearing Capacity, DanishGeotechnical Institute, Copenhagen, Bulletin, 28, pp. 5-11.4. Vesic, A.S. (1973), “Analysis of Ultimate Loads of Shallow Foundations”, Journal of thesoil mechanics and foundations Division, ASCE, 99, pp.45-73.5. Prandtl, L. (1921), “On the Penetrating Strengths (Hardness) of Plastic ConstructionMaterials and the Strength of Cutting Edges”, Zeitschrift fu Angewandte Mathematikand Mechanik, 1, pp. 15-20.6. Reissner, H. (1924), “Zum Erddruck Problem (Concerning the Earth–PressureProblem)”, International Proceedings of the first International Congress of AppliedMechanics, Delft, (Germany), pp. 295-311.7. De Beer, E. E. (1965), “Bearing Capacity and Settlement of Shallow Foundations onSand”, International Proceeding of the Bearing Capacity and Settlement of foundationsSymposium, Duke University, Durham, NC, pp.15-34.8. Bolton, M. D. and Lau, C.K. (1989), “Scale Effect in the Bearing Capacity of GranularSoils”, International Proceeding of the 12thInternational conference on Soil Mechanicsand Foundations Engineering, Rio De Janeiro, Brazil, pp.895-898.9. Kumar, J. and Khatri, V.N. (2008), “Effect of Footing Width on Bearing Capacity FactorNγ”, Journal of Geotechnical and Geo-environmental Engineering, ASCE, 134(9),pp.1299-1310.10. Veiskarami, M., Jahanandish, M. and Ghahramani, A. (2011), “Prediction of the BearingCapacity and Load-Displacement Behaviour of Shallow Foundations by the Stress-Level-Based ZEL Method”, Scientia Iranica, pp.16-27.11. Cerato, A. B. (2005), “Scale Effect of Shallow Foundation Bearing Capacity on GranularMaterial”, Ph.D. Dissertation, University of Massachusetts Amherst, 461.12. M. Alhassan and I. L. Boiko, “Effect of Vertical Cross-Sectional Shape of Foundationand Soil Reinforcement on Settlement and Bearing Capacity of Soils”, InternationalJournal of Civil Engineering & Technology (IJCIET), Volume 4, Issue 2, 2013,pp. 80 - 88, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316.13. K.V. Maheshwari, Dr. A.K. Desai and Dr. C.H. Solanki, “Bearing Capacity of FiberReinforced Soil”, International Journal of Civil Engineering & Technology (IJCIET),Volume 4, Issue 1, 2013, pp. 159 - 164, ISSN Print: 0976 – 6308, ISSN Online: 0976 –6316.14. Dr. S. S. Pusadkar and Sachin S. Saraf, “Interference of Adjoining Rectangular Footingson Reinforced Sand”, International Journal of Civil Engineering & Technology(IJCIET), Volume 3, Issue 2, 2012, pp. 447 - 454, ISSN Print: 0976 – 6308,ISSN Online: 0976 – 6316.

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