STUDY OF RADIAL PORE WATER PRESSURE DISSIPATION DURING CONSOLIDATION USING PLUS & BAND SHAPE SAND DRAIN

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1 IGC 9, Guntur, INDIA Study of Radial Pore Water Pressure Dissipation during Consolidation Using Plus & Band Shape Sand Drain STUDY OF RADIAL PORE WATER PRESSURE DISSIPATION DURING CONSOLIDATION USING PLUS & BAND SHAPE SAND DRAIN M.V. Shah Ph.D. Student, Applied Mechanics Department, The M.S University of Baroda, Vadodara 3918, India. A.V. Shroff Professor Emeritus, Applied Mechanics Department, The M.S University of Baroda, Vadodara 3918, India. ABSTRACT: Paper presents experimental model of sand reinforced soft soil mass to expedite the in-situ settlement due to excess pore water pressure dissipation under preloading by radial drainage taking advantage of having more horizontal permeability than vertical. Experimental model has employed large size hydraulically pressurized modified oedometer having drainage control under any load condition and application of uniform load to soft soil mass by the help of convoluted rubber jack. The variation of geometry of sand drain has been varied to access the optimization of drain shape for better performance with respect to increase of quick strength by accelerating settlement and dissipation of excess hydrostatic pressure. The effect of sand drains of same n value (ratio of zone of influence to the diameter of drain) of 11.4 on consolidation characteristics of Kaolinitic clay were undertaken to investigate the dissipation characteristics using isochrones & settlement characteristics. Time-pore pressure dissipation and Time-settlement observations were recorded for different applied stress under long duration test. Average Degree of consolidation was computed using isochrones and the results were compared with author s theoretical solution by keeping time factor as constant parameter. The authors equal strain solution shows a fair agreement between measured and predicted values. 1. INTRODUCTION With the aim of providing an versatile solution particularly for soft soils for fast infrastructural development, there is an urgent need first to concentrate on regarding ground improvement by using vertical geodrains of locally easily available materials. The applied mechanics department of The M.S. University of Baroda, India started many years back research on finding most optimum drain in terms of materials (both natural and synthetic type), size (diameter of drain) and geometry to accelerate consolidation of soft marine clays with a complete set-up of hydraulically pressurized modified oedometer of different diameters with both conventional bishop pore pressure measuring system and electronic data acquisition system consisting of displacement transducers and pore water pressure transducers. Now days there are many commercially available GeoDrains in the market, which have replaced the use of conventional sand drains. Yet sand drains has its own advantage like easily installation, low skilled man power, economical, and where there is restrictions on imported equipment and material and in countries where there is an adequate supply of suitable sand. Out of many theories, the circular sand drains (Barron s, 1948) theory is still widely used for obtaining solutions by design engineers. Hansbo (19) gave theory on Band shape drain assuming equivalent circular shape is also used for band shape drains available now days in the market under different commercial names. More research is to be focused on installation techniques, material properties of sand drains. Sand drains of various geometries (shapes) are investigated using both development and dissipation of excess pore water pressure and out of which plus and band shape sand drains are selected for computing consolidation parameters. 2. SCOPE AND OBJECTIVE OF THE PAPER The aim of the present paper is to study consolidation of Kaolinite clay through radial drainage using plus and band shape sand drains and to provide guideline to the field engineers regarding optimization of drain geometry with reference to influence zone. The efficacy of experimental findings are also attempted to compare with field observations. The hydraulically pressurized Oedometer described by Rowe & Barden (1966) and further modified by (Shroff & Shah, 5) for pore pressure measurement during radial flow is employed in the present investigation. The sample in the Oedometer is a representative of one influence zone. The present investigation gives (a) Comparison of average degree of consolidation (Ur) of plus & band shape sand drain models computed from isochrones with authors theoretical solution. (b) Influence of drainage path on the consolidation process. (c) The rate of development and 329

2 dissipation of excess pore water pressure under various stresses. (d) Gain in shear strength of clay sample at the end of consolidation test. 3. LABOTATORY INVESTIGATIONS 3.1 Materials Used China clay powder (inorganic clay of high compressibility, minerologically Kaolinite) obtained from Bhavnagar city, Gujarat state, India was tested by doing dehydration test with G = 2.592, LL = 67%, PI = 33.5 and belonging to CH group. The locally sand was used as filler material with specific gravity (G) as and coefficient of permeability (k) as cm/sec is used to form sand drains. 3.2 Modified Oedometer The large size diameter of Oedometer of 254 mm were used for testing the remolded samples (Fig. 1). A uniform pressure is applied by means of conventional hydraulic pressure system on the convoluted rubber jack which transfers uniform pressure on the soil sample placed in the cell. Pore water pressures are measured at the three radial points located at 1 degree each with r/re distances as r/4, r/2 and 3r/4 respectively. The important factor in all the above set-up is full control over drainage and uniform settlement measurement of the sample. For both the test diameter to height ratio of soil sample was kept constant. 3.3 Formation of Sand Drain The axial hole was formed with a thin walled mandrel (Fig. 2), having area ratio of.8 to 1.6 attached with template and guide frame connection. The drain was filled with de-aired saturated sand with the aid of small diameter flexible tubing by siphoning action to cause nearly no smear. The total surface area of both mandrels was kept same so as to achieve equal n value of Fig. 1 & 2: Plus Shape Mandrel and Installation of Band Shape Open-end Mandrel 3.4 Testing Program After installation of central drain and fixing top platen along with dial gauge, displacement transducers & pore pressure transducers connected to data logger system interfaced with PC along with bishop s apparatus are connected to their respective locations. Load increment is applied from constant pressure system to sample through water filed jacket, with closed position of the drainage valve at the top plate. Pressures are applied in the range of kpa, kpa,, kpa 1 kpa and 3 kpa with p/p = 1.. Each load increment is kept constant for about 96 hrs and secondary compression is also recorded. After completion of the test, the sample is taken for vane shear test to know post increase in shear strength after consolidation and to measure final moisture content. Also clay-drain interface study is made using SEMicroscopy. 4. RESULTS AND ANALYSIS Theoretical Review: Karl Terzaghi gave the general equation for consolidation due to radial flow. u/ t = Cvr [ 2 u/ r 2 +1/r u/ r] (1) Shroff & Shah (7) proposed a new mathematical theory whose general solution directly gives a clue to design engineers for selection of most economical drain. This theoretical treatment incorporates variation of compressibility and permeability during consolidation, type of the drain material, tortousity effect, k h /k v ratio under load variation, effect of n value (drain diameter) and drainage path. The lump parameter (λ) incorporates above all factors. The degree of consolidation (U R ) for different values of λ can be obtained using e eo U R = e1 eo = exp{ ( λ )} 2 Sin hλ R ( ) ( ) + + n 2 1. n Sin nπr π exp λ + n T Sin h n= 1 + n 4 π λ λ 2 π 4 { ( λ )} exp 2 Sinh λ ( ) ( ) 2 1 R ( ) n Sin nπr π exp λ + n T Sinh λ n= 1 λ + n 4 π 2 π 4 Isochrones for various positive and negative values of parameter λ are obtained from which degree of consolidation at various radial points against time factor is possible to deduce by the expression: ur U R = 1 where ur denotes the ui pore pressure at any radial distance r and u i is the initial value of pore pressure while in experimental studies will be the value of increment of pressure applied. The value of average degree of consolidation is computed using Simpson s rule as explained in Taylor (1948) and Lambe- Whitman (1969). We can obtain values of λ either positive or negative according to drain material, geometry and diameter of drain. From the results so far analyzed it is observed that maximum value of λ is +.7 and minimum.7. 33

3 4.1 Presentation of Results For comparison and analysis purpose, settlement and excess pore dissipation values at load of KPa, 1KPa and 3KPa are selected and shown here. The notations used for band shape sand drain as BSD and plus shape sand drain as PSD. In the analysis presented here 1kPa is taken as ideal engineering stress and all the results are shown thereof. (1-Ur/Uo)% radial dissipation log't' in min r1 r2 r3 Fig. 3: Dissipation of Excess Pore Water Pressure vs. log t in min for Three Radial Points (n = 11.4, PSD) radial dissipation log't' in min.1 1 (1-Ur/Uo)% r1 r2 r3 Fig. 4: Dissipation of Excess Pore Water Pressure vs. log t in min for Three Radial Points (n = 11.4, PSD) Ur/Uo% Exp Isochrones(1kPa).5 1 r/re t=.25 t=1 t=4 t=9 t=16 t=25 t=49 t=81 t= t=144 t=196 t=256 t=361 t=14 t=28 Fig. 5: Experimental isochrones at 1kPa for PSD From Figures 3 & 4 it is clearly observed that fastest dissipation of excess pre water is taking place for radial point r 1 as it very near to drain boundary while more time is taken for radial pint r 3. Also the Figures 5 & 6 representing experimental isochrones both for PSD & BSD gives the clear picture of dissipation nature of pore water with respect to time and radial distance. Influence of geometry on isochrones was very pronounced in case of PSD because of right angle corners hindering the flow path of pore water. Ur/Uo% Exp Isochrones(1kPa) r/re t=.25 t=1 t=4 t=9 t=16 t=25 t=49 t=81 t= t=144 t=196 t=256 t=361 t=14 t=28 Fig. 6: Experimental Isochrones at 1kPa for BSD (Ur/Uo)% Comparison of isochrones-psd r/re.5 1 Tr(T)=.22 Tr(T)=.47 Tr(T)=.75 Tr(T)=.17 Tr(T)=.145 Tr(T)=.192 Tr(T)=.252 Tr(T)=.337 Tr(T)=.482 Tr(T)=.542 Tr(T)=.627 Fig. 7: Comparison of Theoretical and Experimental Isochrones for PSD at 1 kpa Applied Stress Theoretical and experimental isochrones were compared both using Authors theoretical solution and Barrons theory (Fig. 7) and it found that experimental isochrones fits very well with theoretical isochrones both for PSD & BSD at all pressures and at all n values. From the above comparison it is clear that shape of isochrones gives us an idea of performance of drain w.r.t soil profile, drain material, drain diameter, shape of drain, drainage paths, tortousity effect, mechanics of solids (clay particle), and settlement rate at different times under different applied stress. 331

4 Ur% Average degree of consolidation.1 Tr.1 1 PSD-T PSD-E BSD-T BSD-E Fig. 8: Comparison of Average Degree of Consolidation vs. Time Factor for PSD & BSD at 1kPa Applied Stress Fig. 9: Sectional View of BSD & PSD at the End of Consolidation Considering the different factors affecting rate of consolidation as mentioned above, a lump parameter λ is introduced by Authors theoretical model. Average degree of consolidation (Ur) from pore water pressure dissipation is computed as per Simpson s rule for different values of λ (range from to.7) both for PSD & BSD and it is found that λ equal to.12 fits for BSD and λ =.11 fits for PSD. Figure 9 shows the sectional view of bsd and psd-clay interface at the end of 3kPa applied stress. There was no change observed in the shape of band drain at upper surface except some bulging is observed at the middle of the sample. In case of plus shape drain the corners could not remain intact along length but overall diameter of drain remained same as per original diameter. 5. CONCLUSIONS Author s theory of consolidation with radial drainage and equal strain deformation can predict the excess hydrostatic pore water pressure and average degree of consolidation with a fair degree of accuracy. With increase in the degree of consolidation the isochrones become asymptotic to the horizontal axis steep slope nearer to the starting of isochrones indicate early dissipation of pore pressure near the drain boundary. Isochrones for pore pressure at the radial distances for different degree of consolidation for a particular pressure fits satisfactorily with the author s theoretical solution as well as by Barron s equal strain solution. The degree of consolidation obtained from settlement readings matches very well with theoretical values. Authors have gone for long duration test and have observed that by using large size oedometer we get a clear picture of behavior of soft clay and its compressibility under steady state condition. It is very important to understand the behaviors of PSD and BSD both in terms of not only rate of consolidation but also in Terms of rate of pore pressure development for all pressures. It was observed that rate of pore pressure development is very fast in initial time but later on it rate reduces as we proceed towards zero excess pore water pressure and this phenomenon is observed for all n values and for all applied stress. Authors concluded that rate of development of pore pressure and rate of dissipation of pore pressure are not directly proportional to each other but it purely depends on non-clogging potential of drain material and drainage path made by pore water particulate. Faster rate of dissipation was observed in case of BSD in compare to PSD for kpa, 1kPa & 3kPa pressure while for initial pressures faster rate of dissipation was observed in case of PSD for n = At every stage of consolidation on each pressure it is observed that through equal strain condition is applied at the finite distance dissipation of pore water pressure must not be passing though equal gradient developed as a whole by each saturated particle though an equal surface area of drain is available. The mechanics of pore water pressure plays an important role in understanding the clay-drain surface interaction as horizontal permeability is found to be 8 to 9 times greater than vertical permeability as tortousity is one of the major factors. Coefficient of consolidation due to radial drainage(cr) calculated from pore pressure reading give more or less same value for a particular value of effective pressure at all the three radial points except in case of the inner most radial point. With increase in n value Cr value decrease for a particular pressure The nature of e V/s log p graph reflects clay to be normally consolidated. Shear strength increases after consolidation test. Shear strength obtained at radial co-ordinates are different than one another and increasing towards the drain. The above investigation clearly depicts that band shape is much better than plus shape as it achieves higher degree of consolidation at lesser time and also less disturbance is observed during its installation. Also sand is a best filler material whose maximum advantage can be taken where it is easily and cheaply available. Researchers and design engineers should come forward and make use of such plus shape drains in compare to conventional circular shape sand drains to consolidate soft soil mass to achieve economy. REFERENCES Barron R.A. (1948). Consolidation of Fine Grained Soils by Drain Wells, Trans A.S.C.E., Vol. 113, pp Hansbo S. (19). Consolidation of Clay, with Special Reference to Influence of Vertical Drains, Proc. Swedish Geo-tech Instt. No. 18, pp

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