Momentcarrying capacity of pad foundations H.T.V.FonsekaUniversityof Moratuwa,Katubedda, Moratuwa Sri Lanka. [email protected]
lk Dr.L.I.N. De SilvaUniversity of Moratuwa , Katubedda, Moratuwa, SriLanka.
Abstract: Keywords: Bearing capacity; laterite soil; finiteelement analysis; Numerical modelling 1. IntroductionIsolated pad footings are getting morepopular due to construction of steel fabricated structures. And also due toconstruction of wind turbines and other towers also causes for the popularityof pad footings. Most important factor to be considered in designing a padfooting is bearing capacity. (Taiebat & Carter, 2000). Bearing pressure of padfoundations depends by the moment that induced on that foundation also. Thisstructures need to withstand for many lateral loads, such as wind loads. sothese structures need to be designed tocarry moments.
Moment carrying capacity of pad footingsis also a important factor when consider the stability of structures. Structures are designed byassuming previous results of tests conducted on clay soils. But it is notperfectly match with the Sri Lankan context. Sri Lanka has residual soils(laterite soils) in many places. So the moment carrying capacity of padfootings rests on laterite soils is a needing factor for economical designs. Otherwisedesigners will underestimate the moment carrying capacity of pad foundations.It will lead to a uneconomical design. (Patnaik, Nikraz, & Young, 2000)The moment carrying capacity can beincreased by increasing the dimensions of footing.
But it is not economical tochange the dimensions of footings always. (Patnaik, Nikraz, & Young, 2000).The moment carrying capacity of pad footings can be increased by changing thedepth of the foundation rests. But there is no proper investigation done tocheck the moment carrying capacity of footings with the embedded depth. 2.
Back ground Moment carrying capacity can beestimated by considering the bearing capacity of soil when there is aeccentricity load acting on the foundation. There are many equations toestimate the bearing capacity of the soil. Tazaghi(1943) have derived a equationto estimate the bearing capacity. But it does not cover about the moments somany other equations have been derived to overcome problems with this Tazaghiequation.
Vesic (1973), Meyerhof (1951),Hansen(1961) are some equations that have been derived to calculate momentcarrying capacity of foundations. In every above equation the moment carryingcapacity of foundations are estimated by define effective width (B’) andeffective length (L’) according to the moment induced. From that effectivedimensions the moment capacity will be estimated.In Tarzaghi equation of estimatingbearing capacity it is not considered that bearing capacity change with thedepth of the embedded depth of the foundations. But Vesic, Meyerhof , andHansen have considered the depth factor when estimating the moment carryingcapacity. Those shows that when embedded depth increases the bearing capacitywill also increase. 2.1 Failure equationsTazaghi bearing capacity equations havenot consider about moments and embedded depth when deriving the equation.
Sothat equation cannot be used to find the moment carrying capacity of footings.Bearing capacity of a foundation restingon cohesive soil subjected to a vertical loading can be estimated usingMeyerhof bearing capacity equation. (Equation 1) -(1)qu is ultimate bearing capacity on foundation.c is cohesive shear strength of soilq is vertical loading acting on the foundation.B width of the foundation Nc ,Nq ,N? are bearing capacityfactors.sc ,sq ,s? are factors whichconsider about the shape of the foundation.
dc ,dq ,d? are depth factors which consider aabout theembedded depth of the foundation. Bearing capacity of foundations restingon cohesive soils subjected to vertical loading can be estimate using Vesic andHansen’s equations. These equations have been modified to estimate the bearingpressure when there is inclination of load, ground, and base. qu is ultimate bearing capacity on foundation.c is cohesive shear strength of soilq is vertical loading acting on the foundation.
B width of the foundation Nc ,Nq ,N? are bearing capacityfactors.sc ,sq ,s? are factors whichconsider about the shape of the foundation.dc ,dq ,d? are depth factors which consider about theembedded depth of the foundation.ic ,iq ,i? are load inclinationfactorsgc ,gq ,g? are ground inclinationfactors.bc ,bq ,b? are base inclinationfactors. 2.
2 Finite element ModellingFiniteelement modelling is a method of analysing stress and forces of differentstructures. This modelling is used for the numerical analysis of pad footings.Finite element modelling can be done in 2D or in 3D plane. 2D analysis is easyto analysis and runs faster than 3D modelling.
But 3D modelling will gives usmost accurate answer. For the finite element analysis there are many softwareshave been developed. But Plaxis can be used for simple geometry problems, sinceit is more user friendly. Abaqus, Flac 3D, GTS-Nx Midas are also kind ofsoftwares used to model finite element modelling. These software can be used ifthe problem is more complex.
Such as when need to consider stability of pilesand walls. It is better to use more complex software.Inthe analysis it is assumed that foundation rests on a homogeneous lateritesoil. Model analysis it will take much time if the modelis complex. Time can beredused by making more simple the model.Since the foundation is Square foundation it can be assumed symmetric on bothtwo axis. So the modelling can be done for the quarter of the foundation. Fromthis assumption the analysis time can be reduced.
This analysis it is assumedmoment will apply on a one plane only. (Keyghobadi, Ardakani, Deshghani, & Dezfooli, 2014) It isassumed that the foundation is made of concrete. And concrete properties have been included to the modelanalysis. Since this rest on laterite soil it is assumed that foundation isrigid foundation.
Previously foundexperimental soil parameters are also included for the analysis.Analysisis done mainly for two conditions. 1. Forthe experimental model conditions.
2. Forthe real type foundation.FirstExperimental all 3 conditions will be analyse using this method. Then a realfoundation dimensions will be given and analyse it also.Whenanalysis is done by giving a pure moment it cannot be identify the failurepoint. Because when the moment increase the displacement also increase. So thefailure point cannot be clearly identify.
For that foundation can be subjectedto a horizontal force other than moment. So the with the increase of moment wecould recognize the failure point with the help of horizontal load.Displacement vs horizontal load curve will shows a maximum peak value.
On thatpoint displacement can be taken as the failure displacement. Correspondingmoment will be the max moment. (Taiebat & Carter, 2000) Figure 1 shows vertical and horizontal forcesvariation with the increase of vertical load. Figure 1: horizontal and vertical responses withdeflection (Taiebat & Carter, 2000)Finiteelement Analysis need to be done bydefining a mesh.
The accuracy and the analysis running speed depends on themesh size we defined. Figure 2 show a mesh which was done to investigatebearing capacity of square foundations by using plaxis 3D software.Figure 2 : results of square foundation bearingcapacity analysis. (Keyghobadi, Ardakani, Deshghani, & Dezfooli, 2014)2.3 Experimental TestsExperimentaltests will give more accurate and reliable answers with comparing totheoretical and numerical analysis. Because those analysis were done byassuming some assumptions. Experimental analysis are done without any analysis.
So the experiments need to be more accurate. Other results are compared withthe experimental results.Firstit is need to do some tests, to find soil parameters. Laterite soil parametersfind by doing some different tests. Tri axial test, sieve analysis ,proctorcompaction tests are some test that need to do. From that we need find soilclassification, soil shear parameters, maximum dry density, Modules ofelasticity, and Poisson’s ratios etc. the rest and expected results are showntable1.
Table 1:Soil test andexpected results Test name Soil parameters Parameter Notation Triaxial test Modules of Easticty E Poissions ratio ? Friction angle Ø Cohesion C Sieve analysis Classification – Proctor compaction test Optimum moisture content ? Maximum dry density ? Foundationsize, embedded depth, and soil parameters will affect the moment carryingcapacity of pad footings. Even the size affect the moment carrying capacity itis proposed to have only 300×300 size foundation. The model foundation isexpected to made of steel plate and connect a steel rod which will act as acolumn. So the loading can be giventhrough it. Moment carrying capacity isdetermine of the laterite soil. So it is not needed to change the soil type. Test is proposed to change the embedded depthof the foundation and determine the moment capacity.
It is proposed to testmoment capacity at 300mm,600mm and 750mm depths.it is proposed to conduct thetest on a Perspex box. The bearing capacity can affect 2X width of thefoundation area. So the minimum size of the Perspex box will be 1500mmX1500mmbox. Soil is proposed to compact 75mmthick layer by layer with coloured soil. So the failure pattern can be observedafter failure. Digging will done along the centre line.
Compaction is proposedto have more than 90% compaction. Theloading will be done laterally with help of steel rod. It is proposed to have apully and loading system externally. Figure 3 shows how the loading (moment) willapply to the foundation.
Figure 3: Loading system (Patnaik, Nikraz, & Young, 2000) 2.3 Data analysisData obtained by experimental, numericaland theoretical results are need to be compared and analyse. Results can be analyseby graphical or tabular methods. This analysis will lead us to buildrelationship between theoretical and Numerical with the experimental results.
Thiswill helps us to compare all test.From these analysis it will helps topredict actual moment carrying capacity of real type foundations. And also thiswill helps to find the reliability of each equation for the laterite soils. 3. ConclusionExperimental values will gives us moreaccurate and real answers compared to theoretical and numerical analysis, sofrom that results, numerical and theoretical results need to be adjust andrepresent for laterite soils. This will helps to analyse real size foundationsin more accurate way.
Finding moment carrying capacity of padfoundations leads for economical designs in Sri Lankan construction industry.AcknowledgementsThe authors who have done experimentsand numerical analysis. Presented the results more reliable way. And specialthanks goes to Dr.L.I.N.
De Silva who is my research supervisor, for advisingand guiding me to do a good research. References Keyghobadi, M. H., Ardakani, A. R., Deshghani, M., & Dezfooli, M. G.
(2014). 3d Numerical Analysis of bearing Capacity of square foundations on geogrid reinforced soil . International Journal of scentific research in knowlage, 416-424. Patnaik, A.
K., Nikraz, H., & Young, S. M.
(2000). Momentcarrying capaciy of shallow isolated footings resting on sandy soils. Australian Geomechanics, 47-52. Taiebat, H. A., & Carter, J.
P. (2000). Numerical studies of the bearing capacity of shallow foundations on cohesive soil subjected to combined loading. Geotechnique, 409-418.