Address for Correspondence

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1 Research Paper EXPERIMENTAL STUDY OF AN ANGLE SHAPED FOOTING UNDER DYNAMIC LOADING Pancham Kumar 1, Hemant Mahiyar 2 Address for Correspondence 1 Assistant Professor CWEM (Central University of Jharkhand) India 2 Professor, S.G.S.I.T.S, Indore (M.P) - India ABSTRACT: The bases of all the civil engineering structures rest on soil/rock. The size of open foundation depends upon the bearing capacity and compressibility of soil/rock. The footings are often subjected to eccentric and inclined loading. The experimental and finite element analysis of Angle Shaped Footings has proved their acceptability under eccentric vertical or eccentric inclined static loading. In Angle Shaped Footings a vertical projection which is an integral part of footing and remains embedded in soil is there if the footing is subjected to eccentric vertical load while the projection is inclined in case the footings are subjected to eccentric inclined loading. However, the quadrant of eccentricity has to be known well before providing such footings as the footing projection is always provided towards the eccentricity. The earthquake is a natural phenomenon the occurrence of which is not in the hand of human being, and the civil engineers have to design the substructure taking care of earthquake force since the effect shall be ultimately transferred to foundation. Thus the study of foundation under dynamic loading is conducted to assess the behaviour of Angle Shaped Footings under variable parameters of experimental studies. After conducting exhaustive experimental studies on Angle Shaped Footings it has been found that Angle Shaped Footings displaced less in the direction parallel and perpendicular to direction of shaking but the tilt is more as compared to normal footing. The overall displacement perpendicular to plane of footing is less. Thus it can be concluded that Angle Shaped Footings have their advantage over the normal conventional footings even under dynamic loading. KEYWORDS: Bearing capacity, Eccentric loading, Angle Shaped Footing, Footing Projection, settlement, tilt. INTRODUCTION: The Purpose of the foundation is to safely transfer the load of superstructure on to the underlying soil. In doing so the soil must not fail in shear and at the same time settlement as well as the tilt if any should be within the permissible limit. The eccentricity in loading causes the foundation to settle by different amount and hence it experience tilt. When the eccentricity exceeds 1/6 th width of foundation the lifting of the further end is expected to occur as soil is a no tension medium. Any foundation is subjected to eccentric loading due to (i) moment in addition to axial load transferred from the column, (ii) foundation being at the edge property line, (iii) foundation subjected to eccentric load and (iv) foundation subjected to inclined loading or wind loading etc. A large number of experimental and analytical studies on the Angle Shaped Footing under static loading show the uniform compression reduced overall settlement and increase in bearing capacity. The utility of such footing has been found even under eccentric inclined loading when the projections are also provided at some inclination. Dynamic load: A load is said to be dynamic if it leads to vibrate the whole system or can vary in time and space which is difficult to measure, analyse and estimate as compared to static load. The nature of dynamic load cannot exactly simulate with reciprocating or sinusoidal loads. Dynamic loads are due to earthquake, bomb blast and due to impact. Earthquake produces random ground motion which would lead to violent vibration of the foundation soil system if the structure lies close to the epicentre. LITRATURE RIVIEW Footing subjected to dynamic loading Al-Karni A. (2001) performed experimental studied on shallow footing subjected to horizontal acceleration and concluded that the initial shear fluidization acceleration is maximum acceleration sustainable by a shallow footing regardless of the static bearing capacity safety factor Houlsby G.T. (2002) studied on behaviour of rigid circular footing on sand subjected to a combination of vertical loading, horizontal loading and moment. The model makes use of the force resultant and allows predictions of response to be made for any load or displacement combination. The use of model then illustrated by some demonstration calculation for the response of footing. This example illustrate the principal purpose of the development, which is to allow a realistic modelling of foundation behaviour to be included as an integral part of a structural analysis Lu xilin(2004) performed experimental studies on dynamic soil structure interaction. The test result are analyzed and simulated in detail with ANSYS program. The simulation result shows that three dimensional finite element model is proper for the analysis of Soil structure interaction program. Moss Eric S. Robb (2010) used Shake Table testing of scale soil-structure models to mimic the coupled seismic response of underground structures and surrounding soil. Currently the seismic design of subway and other critical underground infrastructure rely on little to no empirical data fir calibration numerical simulation. Nawghares M. (2010) did the experimental studies on the bearing capacity of eccentrically loaded footing. The results also compared with central and eccentrically loaded footing. A reasonable agreement was found between the theory and test data. Asakereh A. (2012) studied the model strip footing subjected to a combination of static and cyclic loading. The results indicate that the reinforced soil footing system produce lower settlement compared to unreinforced soil.

2 A large number of experimental and analytical studies have been carried out on Angle Shaped Footings under static loading. It has been found that Angle Shaped Footings when subjected to static eccentric vertical load with a definite magnitude of footing projection the footings settles uniformly without any tilt. The amount of this uniform settlement is considerably low as compared to that of normal footing under same axial load. However, the response of Angle Shaped Footings under dynamic loading is yet to be studied. It is very difficult to carry in- situ tests on eccentrically loaded Angle Shaped Footing under dynamic loading. Considering this problem the tests are carried out in laboratory. Model footings of size B = 80 mm X 80 mm with different depths D of footing projection i.e. D/B are tested in the laboratory under controlled condition. The model footings for applying various static eccentric loads are marked at distance e x from center towards projection along x-direction. Thus objective of the present experimental research is to study the behaviour of eccentrically loaded Angle Shaped Footing under uniaxial harmonic motion. The effect of depth of projection, the orientation of Footing with shaking direction and duration of shaking has been investigated. The parameters investigated in this study includes the displacements, and tilting of Angle Shaped Footing under the dynamic load and compared with plain square footing under same conditions. EXPERIMENTAL INVESTIGATIONS An experimental study was carried out to investigate the behaviour of Angle Shaped Footings under dynamic loading. The study includes testing of 3 models of Angle Shaped Footings each having size 80 mm X 80 mm but having different footing projections of 20, 40 and 60 mm respectively. These models were tested under eight different orientations (Fig. 1) with respect to shaking direction. Plain square footings were also tested under dynamic and static loads. Each footing is subjected to same static vertical load but at different eccentricities in accordance to the equation of no tilt as recommended by Mahiyar Hemant (2000) i.e. D/B = 85.77(e x /B) (e x /B) (e x /B) eq. 1 Where, B = width of footing D = depth of footing projection; e x = eccentricity along x-axis towards projection projection of 80 mm width and 20 mm depth on one side, the third footing had a footing projection of 80 mm X 40 mm while the fourth footing had a projection of 80 mm X 60 mm. Thus ratio of depth and width (D/B) of projections are 0.25, 0.50, and 0.75 respectively. To bear the static load applied on the model footings a loading frame was prepared by two vertical channels welded on opposite sides of tank and one horizontal channel resting over the vertical channels. The top of horizontal channel is 1500 mm above the bottom of tank. To apply load on the footing hydraulic jack of capacity 20 kn is mounted on loading frame. With the help of hydraulic pump pressure was applied by extensible rod of 25 mm diameter. The rod is attached to hydraulic jack, is directly exerts pressure on Angle Shaped Footing through ball and socket arrangement. The models were tested under different static load and settlement, displacement in x- direction and y- direction were recorded. The x-direction was considered the direction of shaking and lateral to shaking is considered to y direction.the direction perpendicular to footing surface was considered as z- direction (See Fig. 1). The two dial gauges were kept at diagonally opposite corners of footings for measurement of displacements along z direction (i.e. settlement & tilt of footing) and two dial gauges, one for each displacement along x and y-axis respectively. In all four dial gauges were used. Description of test setup: A tank of dimension 400 mm X 400 mm X 250 mm has been fabricated and filled with sand (by rain fall method). The level of sand bed was made horizontal and footing was placed over it. After placing footing, the dial gauges were fixed and then load cell over the footing was placed. A steel ball is placed in between load cell and footing to transfer axial point load. The static load was applied with the help of hydraulic jack. The weight of tank with channels alone was kg while the weight of tank filled with sand, footing, hydraulic jack etc was kg. The schematic diagram of footing with dial gauges, load cell etc. is shown in Fig.2 Fig 1: Details of orientation of Angle Shaped Footing with respect to direction of shaking Description of test model footing under static load The models used in the experimental work were Angle Shaped Footing specimens. In all four model footings of mild steel of size 80 mm X 80 mm were taken. The first footing was normal footing the second one was given an angle shape by welding a Fig 2 Angle Shaped Footing with dial gauge arrangement Instrumentation for Dynamic Loading: For applying dynamic load, a special instrument was fabricated known as horizontal Shake Table. It is a unidirectional Shake Table which moves only in horizontal direction. The motion is a simple harmonic and works on the principle of crank mechanism, converting the rotary motion of the motor to linear motion of the Table. The sliding table is of size 500 mm X 500 mm to accommodate the steel tank filled with sand as mentioned above. The scaled model footings were tested under dynamic excitation and designed to carry a pay load of 200 kg. The Table has

3 a stainless steel top containing array of tapered holes to facilitate mounting of the tank. It slides linearly over stainless steel guides. Drive Mechanism consists of a motor, belt and pulley arrangement, crank and connecting rod. The rotary motion is transferred to the crank and connecting rod through the belt and pulley. Crank mechanism has a locking screw arrangement that can be used to set the desired amplitude of motion. The connecting rod is connected between the crank and the Table, which also has a locking screw. Control mechanism is used to vary the frequency of the Table, by varying speed of the motor. Operating frequency can vary from 1 to 20 Hz. Control panel has various frequency bands for easy operation. The whole mechanism of the Shake Table is designed to make the working simple and electronic controlled; rather the motion is made as mechanically controlled. The idea behind is that it can be easy overhauled/repaired using the existing technical. The schematic diagram of tank placed over Shake Table is shown in Fig.3. Thus the shake designed here are quite economic as compared to those which are available in the market. Fig 3 Schematic Diagram of Tank placed over Shake Table Fig.3.1 Belt and pulley arrangement Fig: 3.2 Horizontal Shake Table Specifications of the Table: The Shake Table has following specifications Motion Type: Horizontal (uni-directional) Max pay load: 200 Kg Size of Table Top: 500 mm X 500 mm Frequency range: 0 5Hz (with pay load) Frequency range: 0 20Hz (without pay load) Frequency control: ± 5% Amplitude Range: ± 50 mm to 75 mm) Motor rating: 3HP, 3Phase, 440V, 1440 rpm, Control panel: 4 wires, 3 phases, 440 v input Controller mechanism: auto transformer The following stepwise methodology was adopted for applying the dynamic load over the model footings resting over sand bed and lying in a tank. 1) Ensure that there is no power supply 2) Switch the mains to On position 3) Press Start Button 4) Increase the frequency count, slowly by rotating arm the Increase Button; observe the motion of the Table for any frictional noise, relatively slow movement, oil leak etc 5) Then slowly increase the frequency to the desired value. Methodology Adopted in the Experimental Investigations The following test procedure has been adopted for testing the footing: The distance e x from the center of the footing was marked towards projection along the x-axis. The marking was done by drilling using a boring tool of diameter 3mm. The value of e x was obtained by eq. (1) Fill the tank with sand using rainfall method. Place the footing horizontally on the sand bed. Fix four dial gauges on footing (two for the vertical displacements placed at diagonally corners, one for displacement along X and one for displacement along Y direction. Ensure the verticality of load using plumb bob. The load was applied using the hydraulic jack. It was ascertained that in case of orientation no. 1 to 4 the edges of footing were parallel & perpendicular to the x-axis (i.e. direction of shaking). The skewed orientations were (i.e. orientation 5 to 8) set at 45 0 with respect to the direction of shaking.

4 Ensure horizontality of footing using spirit level. Ensure the appropriate frequency of Shake Table before testing. Ascertain the dial gauges are placed at appropriate positions. Note the initial readings of dial gauges and then apply static load. The resultant displacements caused by the applied static load were noted. To apply dynamic load, the horizontal Shake Table was turned in On position for desired duration of time and stopped after shaking. The displacements after shaking were recorded. The same procedure has been adopted for various parameters. Following parameters were kept constant Size of model footing = 80 mm X 80 mm Frequency of Shake Table = 90 rpm (1.5 Hz) with an accuracy of (+/-2 rpm) Amplitude =100 mm Following parameters have varied Magnitude of Static Load Intensity = kpa, kpa and kpa Duration of shaking= 3, 5 and 7 seconds D/ B Ratio = 0, 0.25, 0.50 and 0.75 Orientation of footing with respect to direction of shaking = Eight different orientations as per Fig. 1 For each parameter the procedure was repeated three times to see the variation in observations of displacements. In all 864 (3 static load x 3 duration of shaking x 4 D/B ratios x 8 orientations x 3 number of repetitions) tests were performed. The details of footing, its projections, self weight etc are shown in Table 1. The Plan & Elevations of Angle Shaped Footings alone are shown in Fig. 5 Properties of Sand: Following were the properties of sand used for the experimental work Gradation: - The grain size distribution curve is shown in Fig. 4 Density of sand corresponding to normal state = kg/m 3 Density of sand corresponding to Loosest state = kg/m 3 Density of sand corresponding to densest state = kg/m 3 Density Index = 0.96 Angle of internal friction = Φ =38 0 Table 1 Detail of Footing, projection etc e x(mm) D/B Footing size Depth of projection (mm) Self weight of footing(kg) 0 80 mm X 80 mm mm X 80 mm mm X 80 mm mm X 80 mm During performing a total of 864 set of tests the observations of displacements have been noted under static load and dynamic loads. It has been observed that the displacement along x and y direction due to static load were almost negligible whereas the displacement in z direction (settlement) was uniform. The dynamic load was applied in continuation without adjusting the displacement values. The displacement along x direction is denoted by U x, displacement along y direction is denoted by U y. The displacement along the z direction at near end is denoted by U z1 while the displacement along z direction at the far end is denoted by U z2. All these displacements as indicated by dial gauges placed were noted. The values of displacements are shown from Table 2 to Table 5. The tilt of footing in z plane is calculated as (U z1 U z2 )/B. Since the duration and orientation of shaking is what uncertain hence a number of bar charts showing variation of displacements along shaking direction at a given load intensity ( kn/m 2 ) and given D/B value (0.50) are shown in Fig. 6. Similarly bar charts for displacement perpendicular to direction of shaking at same load intensity and D/B values are shown in Fig. 7. Fig. 8 shows the bar charts for tilting at the same load intensity and D/B value. After studying the observations we can show the range (minimum & maximum values) of displacements along and perpendicular to direction of shaking and range of tilting for all the variables taken together. It has been from Table 6 to Table 8. Fig.6 Displacements along shaking direction at same load intensity ( kn/m 2 ) and D/B value (0.50) Fig.7 displacement perpendicular to direction of shaking at same load intensity ( kn/m 2 ) and D/B (0.50) Fig.8 Tilting at the same load intensity ( kn/m 2 ) and D/B value(0.50) Fig 5 Plan & Elevation of Angle Shaped Footing model RESULTS AND DISCUSSIONS:

5 Table 2 Displacement values for various parameters for D/B = 0 (Plane square footing) Orientation Orientation-1 Orientation-2 Plane square footing kn/m kn/m kn/m 2 time U z1 U z2 Tilt U x U y U z1 U z2 Tilt U x U y U z1 U z2 Tilt U x U y 3 sec sec sec sec sec sec Table 3 Displacement values for various parameters for D/B = 0.25 Orientation D/B= kn/m kn/m kn/m 2 time U z1 U z2 Tilt U x U y U z1 U z2 Tilt U x U y U z1 U z2 Tilt U x U y 3 sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec Table 4 Displacement values for various parameters for D/B = 0.50

6 Orientation D/B= kn/m kn/m kn/m 2 time U z1 U z2 Tilt U x U y U z1 U z2 Tilt U x U y U z1 U z2 Tilt U x U y 3 sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec

7 Table 5 Displacement values for various parameters for D/B = 0.75 Orientation D/B= kn/m kn/m kn/m 2 time U z1 U z2 Tilt U x U y U z1 U z2 Tilt U x U y U z1 U z2 Tilt U x U y 3 sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec sec

8 Table 6 The range of displacements along the direction of shaking D/B Ratio Load intensity 3 sec 5 sec 7 sec Min-max Min-max Min-max kn/m kn/m kn/m kn/m kn/m kn/m kn/m kn/m kn/m Table 7 The range of displacements perpendicular to shaking D/B Ratio Load intensity 3 sec 5 sec 7 sec Min-max Min-max Min-max kn/m kn/m kn/m kn/m kn/m kn/m kn/m kn/m kn/m Table 8 The range of tilting D/B Ratio Load intensity 3 sec 5 sec 7 sec Min-max Min-max Min-max kn/m kn/m kn/m kn/m kn/m kn/m kn/m kn/m kn/m CONCLUSIONS: Based upon the experimental studies conducted in the laboratory on a model footing of 80 mm X 80 mm under a constant frequency of 1.5 Hz following are the conclusions (A)Effect of varying Load Intensity The settlement and tilt of Angle Shape Footing increases with increase in load intensity. The displacements U x and U y decreases with increase in load intensity. (B) Effect of D/B value: Settlements (U z1 & U z2 ), displacements (U x & U y ) decreases while the tilt increases with increase in D/B values. (C) Effect of Duration of Shaking Settlement, displacements and tilt increases with increase in duration of shaking. (D) Effect of Orientation: Projection parallel to shaking produces lesser tilting than projection perpendicular to shaking direction. Projection parallel to shaking has tendency to tilt such that the free end is settled more than projected end. Skewed orientation shows more tilting, more displacements along and perpendicular to shaking than the orientation of projection perpendicular and parallel to direction of shaking. Displacement in lateral direction is very less as compared to displacement along direction of shaking. REFERENCES 1. Al-karni, A., Awad and Budhu, M. (2001). an experimental study of seismic bearing capacity of shallow footing, Proceeding: Fourth international conference on recent advanced in geotechnical earthquake engineering and soil dynamics 2. Moss S. Eric (2010). Shake table testing to quantify seismic soil-structure interaction of underground structure, Fifth international conference on recent advanced in geotechnical earthquake engineering and soil dynamics. 3. Asakereh A., S.N., Tafreshi, M. and Ghazavi, M. (2011). Strip footing behaviour on reinforced sand with void subjected to repeated loading, International Journal of Civil Engineeringvol,Vol.10, No Moghaddas Tafreshi, S.N., Mehrjardi, Gh. T. and Ahmadi,M. (2011) Experimental and numerical investigation on circular footing subjected to incremental cyclic load, International Journal of Civil Engineering,Vol.9, No.4, pp Mahiyar,H.K. and Patel,A.N.(2000). Analysis of angle shaped footing under eccentric vertical load,

9 Journal of Geotechnical and Geo-environmental Engineering Vol. 126, No.1, pp Joshi, D. P. and Mahiyar, H. K.(2009). Analysis of angle shaped square footings resting on soil under eccentric inclined load, Emerging Journal on Engineering Science and Technology. Vol 1, No.1, pp Mahiyar H.K. and Dayanand P. Joshi (2009) Angle Shaped Rectangular Footing with Variable Angle of Footing Projection under Eccentric Vertical Load Journal of Electronic Journal of Geotechnical Engineering vol.14 (2009). 8. Joshi, D. P. and Mahiyar, H. K.(2009). Effectiveness of angle shaped footings resting on soil under eccentric inclined load, International Journal of Theoretical and Applied Mechanics, Vol 4, No.1, pp Joshi, D. P. And Mahiyar, H. K. (2009). Moment tilt characteristics of angle shaped footing under eccentric inclined loading, International Journal of Theoretical and Applied Mechanics, Vol. 4, No.1, pp Gupta, D. (2000). Experimental studies on angle shaped square footing under uni-axial eccentric loading, M.E. thesis submitted to D.A.V.V., Indore. 11. Atulkar, K. and Narendra (2005), Optimization of angle shaped footing, M.E. thesis submitted to R.G.P.V., Bhopal. 12. Duwasa, Anand (2007), Experimental study of biangle shaped footing subjected to two way eccentric loading with pile under sand, M.E. thesis submitted to R.G.P.V., Bhopal. 13. Kanungo, A. (2004), Experimental study of angle shaped square footing on cohesive and cohesion less soil under eccentric loading, M.E. thesis submitted to R.G.P.V., Indore. 14. Rajput, D. (2006), Bi-angle shaped model footing subjected to one way eccentric load under mixed soil condition, M.E. thesis submitted to R.G.P.V. Bhopal 15. Verma, Narendra (2007), Experimental study of angle shaped footing subjected to eccentric loading with pile under sand, M.E. thesis submitted to R.G.P.V., Bhopal.