 Welcome to advanced geotechnical engineering course. This is module 7 on geotechnical physical modeling lecture 8. So in the previous lecture we introduced ourselves to two aspects which are required for verifying the scaring laws or particle size effects. The one is that modeling of models or other one is that modeling of prototypes. So in this particular slide the schematic representation of the figure which is actually used for you know explaining the modeling of models is given again. So here on the x axis we have the prototype dimension. So this can be a footing size or it can be a wall size or it can be an embankment size. So anything in prototype dimensions particularly at g level is equal to 1 they represent the prototype dimensions if they are in full scale. Then here it is on the y axis on the g level. So here what we have discussed is that the technique of testing this modeling of models with the different g levels and this is basically done with the aim of verifying the scaring laws you know is called as the modeling of models. And we also have deduced a number of scaling laws or scaling relationships between different parameters and they require validity or assure that they follow the scaling laws and that can be done by using the principle of modeling of models. So the modeling of models technique is used whenever we are trying to model a new physical phenomenon in the centrifuge and the scaling laws for one or more parameters cannot be derived easily. So this is applied when we actually try to derive test a model which is a new phenomenon in this centrifuge and the scaling laws for one or more parameters could not be derived easily. So if you are having a prototype of say 10 meter dimensions and we can actually have the you know the model different models at different gravities so that they represent all these models represent a prototype which is actually projected here at 1g. Similarly when you have a particular prototype of 5000 unit size then we also have three different models representing the behavior. So what does it mean is that it means that if you are having the same prototype with same soil tested with identical boundary conditions then the performance of these models which are tested model 1, model 2, model 3 and if they are models of this particular prototype they represent the identical behavior as that in the prototype. So this is an interesting option for centrifuge based physical modelers for verifying the scaling laws and also to check the models whether they are free from particle size effects in case of geonormantal engineering whether it is free from the characteristic length effect. So let us look into the example which is you know on the test program for modeling of models which was originally carried out by this Olson in 1980. This was reported by Taylor 1995 wherein they have tested the test program basically consists of concentric loading of you know footing tests on the circular footings on a uniform dry sand. So here the void ratio more or less is actually has been maintained in all the tests as E is equal to 0.565 and the average particle size is between 0.3 to 0.6 mm. So it can be looked into is what has been done is that the number of you know models have been formulated and basically to see where the size effects are there and where the scale effects are going to be there. So in this particular chart here this is footing dimensions are given on the x axis on logarithmic scale and here also the g level which is actually given on the y axis. So this particular you know line indicates that dp is equal to 0.25 meter diameter footing and this is 0.5 meter diameter footing and this is 1 meter diameter footing and 2 meter 4 meter diameter footing. Now when you go down from this side then we can see that the footing sizes increases and the stress levels are different and when you go in this direction the footing sizes are same and represent the identical prototype in the field but they actually have you know the different g levels. So for example here this particular model tested at 7.1 mm footing diameter is subjected to you know certain g of 35.4 basically to simulate a 250 mm diameter of footing. Similarly here when we take you know the 1 meter size so this 28.3 mm diameter footing subjected to 35.4 to model you know a 1 meter diameter circular footing in the field. So this particular series of tests which are actually named as series B, F and series C and G and K and DHL and PUX these represent you know 1 meter diameter footing and the test J and then test R which are actually for 2 meter and 4 meter size footings. So for test J in order to model a 2 meter footing a footing diameter of 14.2 mm was considered but the g level is maintained as 141.4 so that means that in order to get Tp is equal to 2 meters what we have to do is that 14.2 mm into 141.4 it yields 2 meter you know the diameter footing. So the results were actually compared for you know the prototype footing having diameter 1 meter and all test corresponding to you know 1 meter when we see and the normalized load settlement curves for modeling of models are given. So we know that when we have you know load carrying capacity of a footing found to depend upon several parameters and we said that P by gamma D is the you know principle of the Python which actually has to be identical in model prototype. So wherein we have seen that you know one particular dimensionless Python called Dg by D that is you know which is not similar in model prototype even in the centrifuge based physical modeling. So in order to see whether what to what extent these effects will be there so in order to verify that what has been done is that you know this P by gamma D or which is actually for so this test data is for diameter of 14.2 mm tested at 70.7 to yield a footing of diameter of 1 meter size. Similarly here this is 28.3 mm diameter tested at 35.4 to yield a footing of diameter 1 meter. Similarly here 79.5 mm and tested at 12.5 to yield a prototype diameter of 1 meter. Here also 56 mm tested at 17.7 to yield a you know footing of diameter of 1 meter. So this can be seen that most of the values which are number of tests have been carried out and the reproducibility and repeatability of the test was found to be very good and you know at delta by D is equal to 0.1 and at P by gamma D is found to be the range of 95 to 100. Similarly here also at delta by D is equal to 0.1 and with you know this P by gamma D is found to be the range of 95 to 100. So these test indicates that the model actually in the modeling of model holds very good and also for the type of the size of the footing which is actually considered the particle size effects are actually minimal or you know not it can be said that they are negligible. So here what has been done is that the value of the bearing capacities for different G-levels were actually plotted and the Overson 1975-79 work is actually compared with the Bicasa et al 1973 and Kutter et al 1988 and here it has been found that the x-axis has actually has got acceleration field N and bearing capacity is plotted in kilo Newton per meter square on the y-axis. So the horizontality of these lanes which are actually tested by the several investigators this indicates that you know the modeling of the model holds good value. So and then one more interesting thing we need to do is that it is not that you know all the tests are actually free from you know scale effects. There are some tests for example when you are having you know say 7.1 mm diameter footing which is almost like the size of a button then you know when these footing size is actually supported in a given horizontal line with let us say 0.5 mm diameter is the average particle size then you know about 15 number of particles. So in the field when you have say 250 mm diameter you know footing resting on the you know soil in the field same soil in the field there are innumerable number of particles are actually going to support the footing. So that indicates that you know if in order to avoid the size effects in order to avoid the scale effects there is a requirement that you know the footing size that is a d by d50 has to be you know they found that you know has to be in the range of 30 to 180 and if this range is actually maintained they said that you know the scale effects you know particularly due to particle size can be eliminated. So while selecting the dimensions particularly like a footing diameter or tomorrow if somebody is interested in modeling a pile then pile diameter to the average particle size need to be understood and if this ratio is found to be having adequately higher number or higher ratio that is dimension divided by dimension of the particular model like pile diameter d or footing diameter d divided by d50 has to be adequately large and then you know it implies that you know it resembles the conditions you know similar to that in the field. So in such situations we can say that the model is actually free from particle size effects. So like this and this modeling of models was actually applied for verifying the consolidation laws that means that you know the time of consolidation we said that tm by tp is equal to 1 by n square. So in that situation when we actually model you know the different clay layers of different thicknesses tested at different gravities and representing the you know a certain thickness of the layer in the field then you know the consolidation as time settlement behavior have to be identical. So this was actually if we are able to get the identical performance with you know identical response then we can say that you know the particular scaling law for example for time of consolidation in model and prototype that is tm by tp is equal to 1 by n square is bound to be validated. So and then you know while discussing you know the dynamic scaling considerations we said that you know there will be a conflict between diffusion and dynamic events and this is actually arises because the scale factor for the time which is you know for diffusion is you know 1 by n square times faster and that is the time in prototype is 1 by n time in model is 1 by n square times in that in prototype. So because of this what will happen is that the excess pore water pressure will not generate to the initial set total stress or the total stress at a particular point then what will happen is that there is you know the partial raise of the excess pore water pressure and then a rapid dissipation of pore water pressure takes place. But in principle in the prototype when you actually really monitor this it is difficult to get this data but if you are actually having this excess pore water pressure with time recorded in the prototype when at a location at the onset of say earthquake then it will have like this it will be a raise up to a certain level to the target desired total stress then it will be dissipation. So you can see that the slope of this line is much flatter than the slope of this line which is actually shown here and here and this indicates that you know this is the you know curve which we may get if you are actually having the centrifuge model with the model pore fluid. So we said that in order to avoid the conflict two schools of thoughts were discussed one is to reduce the gradation of the particle size the other one is to replace the conventional pore fluid with water with a pore fluid having higher viscosity. Then we said that you know there are number of you know different types of pore fluids have been used and but one thing is that you know we have to see that the pore fluid will not actually affect the strength properties and also you know will not actually alter the constitutive behavior of the soil and also you know the damping characteristics and secondly is that you know we also have to see that how these are this is you know validated or is required. So in this case you know what we do is that we will have a detailed discussion about a particular pore fluid and then we will try to verify the requirement of this thing. So from theory point of view what we said is that you know this is required and this actually simulates the situation of you know the what exists in the field. So once again you know the quality of qualities of an ideal substitute pore fluid one is that the density has to be close to that of water and this is very much required because to have identical effective stresses you know as that in the prototype. Suppose if you are actually selecting a you know pore fluid which is actually heavier than water then you know for example like zinc chloride solution if we take then you know we cannot actually simulate you know this you know identity in the effective stresses. And the surface tension will be same as that in water and it should be Newtonian fluid so where you know the and then also it should be chemically polar and available in the you should be available in the wide range of viscosities and the viscosity should not change with the age of the you know the preparation of this solution and it should be stable and it should properly should not change in time from the experimental from the time frame of experimental preparation and easy to manufacture and non-toxic and soluble in water and should be in it. So these are the you know qualities of an ideal substitute pore fluid then number of pore fluids actually have been you know oh the first one to be used is that silicon oil and classified has hazardous waste and resistant to most solvents and thus determination of the dry density of saturated soil with silicon oil and the clean up of the equipment is difficult and unit weight is less than that of water necessitating the corrections to be implemented and relatively expensive and you know some laboratories they actually have you know their own trademark pore fluids and for that one example is that technical university Delft the Netherlands the composition not known but evaluated through physical permeability and monotonic and cyclic triaxiuses and said that you know the Delft pore fluid fulfills the required qualities of an ideal pore fluid. Then glycerin and water mixers which are actually also used non-toxic and easily mixable with water in any concentration. So different combinations of glycerin and water were actually tried and this is also one of some investigators I have actually used. So in the recent past methyl cellulose which is a methyl ether and which is biodegradable and relatively easy to clean up and available in the wide range of viscosity and unit weight of the solution will be identical to that of pure water and the components are inexpensive readily and available and not subjected to any proprietary protection. So this methyl ether or a metallose which is popularly called as is you know the pure pore fluid which is of discussion. So we also said that you know particularly when we have you know replaced the model pore fluid we have that is conventional pore fluid with a model pore fluid having high viscosity then you know we actually have said that the permeability will remain same that is Km is equal to Kp and when Km is equal to Kp then Vm is equal to Vp and with that what will happen is that you have got time in model prototype Tm by Tp is equal to 1 by n. That means that we have slowed down the diffusion event by replacing conventional pore fluid with a pore fluid having higher viscosity. So if you are actually scaring down model by say 50 times then we need to replace the pore fluid that is conventional pore fluid with a pore fluid having you know viscosity of 50 centimeter strokes because water at a standard temperature it actually has got 1 centimeter stroke you know the kinematic viscosity. So if you look into this here the constant head permeability test given by presented by the Volcker et al 1999 on sand which were actually conducted and then it says that you know for example water as the pore fluid when it was actually taken then the as the G level increases either because of you know either because of the Im is equal to Nip or because of Km is equal to Nkp which we have discussed earlier what actually happens is that with in increasing G level the permeability increases. So for water as pore fluid K increases with G level and increase was found to be all linear and if you are looking for a metallurys as a pore fluid then you can see that K1g whatever we have is found to be equivalent to Kng and very marginal variation can be noticed. Here the slope of this line is 0.0155 so if you take the inverse of that you will get as 32. So this is the test which is actually carried out at you know it should be you know this marginal differences could be due to you know the difference in the preparations of the sample. So you can see that this is very the slope of this line is 0.000478 and this is 0.0155 so it can be seen that you know by replacing you know the conventional pore fluid with a model pore fluid having higher viscosity that is particularly here metallurys actually has been tried then you know the permeability value which is coefficient of permeability was found to be you know found to be you know marginal having marginal variation. So the properties of metallurys in particular the chemical name of metallurys is hydro hydroxy propyl methyl cellulose and it is a water soluble cellulose ether and it is in the form of fine white powder and metallurys is tasteless orderless and it is also harmless and metallurys solutions of desired viscustis can be prepared by dissolving certain amounts of metallurys powder by weight in warm distilled and dehydrated water. So generally what is done is that you know the metallurys with higher concentration is actually prepared like for example 500 centistokes of metallurys and then you know suppose if you wanted at a concentration of say with viscosity of 50 centistokes then it will be diluted by mixing warm distilled and dehydrated water. So metallurys solutions of desired viscustis can be prepared by dissolving certain amounts of metallurys powder by weight in warm distilled and dehydrated water. So here in this particular chart effect of concentration age on the viscosity of metallurys is shown here. So if you see here you know viscosity which is actually measured by using viscometer and the concentration that is 1 percent, 2 percent, 3 percent so you can see that with increase in concentration there is an increase in the viscosity. Of course it is not linear but it is found to have a certain variation but as can be seen here viscosity when it is actually plotted with age in days for 1 percent concentration, 2 percent, 2.2 percent and 3 percent concentration. At 2 percent concentration itself you know the most of the you know test which can be done at 50 G can be achieved and here it is about 75, this is about 75 G that is 2.2 percent and the 203 percent concentration yields very high in a viscosity like 200 G. So most of the dynamic centrifuge model tests are carried out between 50 and you know 75. So it seems that 2 to 2 percent concentration is sufficient and another thing is that the marginal variation of viscosity indicates that it can be stable and will not actually alter its viscosity properties with the time and when you are actually having the ambient temperature of 21 to 24 degree centigrade whereas in you know the beam centrifuges which are actually there in the world so what will happen is that because of you know the cooling systems and because of the ventilation which are actually provide the temperature will remain in ambient conditions when the you know the test is in progress. And here the effect of temperature on the viscosity of the model of metallose so here it is says that with the increase in temperature definitely there is a decrease in the viscosity this is for 2.2 percent concentration which is shown here and it implies that you know if the temperature increase to 40 that means that there is you know a fall by about 30, 40 percent. However as said earlier when we are actually having the you know suitable ventilation systems in the beam centrifuge equipments in the world this particular you know factor is not a worry because the ambient temperatures will be maintained. So the effect of the metallose on the constitutive behavior of the sand was actually investigated and then strain controlled CO triaxial compression test were carried out on water and 60 centi stroke metallose saturated specimens of sand at place that 70 percent density fine sand place that 70 percent density and three cell pressures of 69 kilo Pascal's 138 kilo Pascal's and 207 kilo Pascal's were actually maintained. Then here when it is actually plotted with Q which is nothing but deviator stress sigma 1 dash minus sigma 3 dash with axial strain with this particular curve indicates the water as the pore fluid and this is the 60 centi stroke metallose you know pore fluid. And then here the pore water pressure generation is also shown here for a confining pressure of 69 kilo Pascal's this is a confining pressure of 69 kilo Pascal's. So it indicates that this stress strain behavior and pore water pressure generation with water and metallose were very very similar. So one thing the stress strain behavior and pore water pressure generation with water and metallose were very similar. And secondly when we plot the Q versus P dash and Q is nothing but sigma 1 dash minus sigma 3 dash and P is nothing but sigma 1 dash plus 2 sigma 3 dash by 3 then if you look for 69 kilo Pascal's and 207 kilo Pascal's with increase in the confining pressure the agreement is found to be in good order but what it actually indicates that the results indicates that the stress parts are very similar with water and metallose and found to be better with higher confining pressures and thus overall the constitutive behavior that is including the stress strain behavior, pore water pressure generation and the friction angle of sand was not altered significantly by use of the metallose instead of water as the pore fluid. So if a particular new pore fluid is actually being tried then there is a need to verify the properties particularly the constitutive behavior of the geomaterial which is being under consideration and how it is actually the considered pore fluid how it is affecting need to be investigated. So from this the example what actually has been given by DeWolf Curator 1999 it says that the stress parts were very similar with the water and metallose pore fluid and the overall constitutive behavior of sand was not altered significantly by the use of metallose instead of water as the pore fluid. And further this was actually verified in centrifuge by using a split container and the split container actually has got two compartments one actually has metallose as the pore fluid and other one actually has got water as the pore fluid and it separated by a leak proof separation and these are the horizontal accelerometer in horizontal direction, vertical accelerometer in vertical direction and these are the accelerometers in horizontal direction and these are the accelerometers in water as the pore fluid, these are the accelerometers with metallose as the pore fluid and these are the accelerometers, these are the pore water pressure transducers, these are the pore water pressure transducers. So here metallose of 60 centi stroke kinematic viscosity was considered because the model is active 60 gravities and the red-density of the type of the sand which was adopted is about 70% and here basically to subject identical ground motions this particular type of you know the split container was actually was used and a level ground experiment was conducted to demonstrate the importance of substitute pore fluid in seismic centrifuge modeling of saturated cohesionless structures. So here the effect of the pore fluid on the model behavior was actually investigated and in this particular figure where this side is pore water pressure which is actually measured at three different points and this is Pm1, Pm2, Pm3 the locations we are shown once again Pm1 which is at the top Pm2 is in the middle of the container and Pm3 is the close to the bottom of the container, similarly PW1, PW2, PW3 they are in the water saturated pore fluid, their PW2 is in the middle of the container, PW1, PW3 are the top and bottom of the container. So when they can be seen that this is the initial vertical effective stress is 18.6 kilo Pascal's so you can see that the pore water pressure is actually raising up to that level and you can see here also that you know you have got you know that is on 0.2 kilo Pascal's and the pore water pressure also raising up to this level and this is with metallo as the pore fluid but the similar for the same similar ground motion the pore water pressure measured by using PW1, PW2, PW3 are plotted and shown here and here it can seen that the raise was actually very small and the dissipation is actually very fast. And you can see that there is a small raise and the dissipation is fast, so when the water actually has the pore fluid the accumulation of excess pore water pressure was reduced due to high permeability and however with metallo's due to slower dissipation higher excess pore water pressures could be generated and the rate of pore water pressure generation with the rate of pore water pressure dissipation with metallo's was considered to be smaller than with water. So this indicates that you know the pore water pressure generations you know the generation as well as the dissipation you know the dissipation particularly was actually slowed down because of the you know the pore fluid which is actually having higher viscosity than that of water. So here the time histories of the acceleration is actually shown here and the accelerometer which is actually placed at the close to the top middle and bottom are shown here and this is W1, W2, W3 which is in water saturated fluid as shown here they are distinctly different but this is you know the time histories of acceleration which is actually shown. So based on the observations like it is clear that neither the accelerations nor the excess pore water pressures indicated the occurrence of liquefaction in water saturated soil model because the excess pore water pressure you know as not generated to the level to which actually the liquefaction can be you know attenuated. But here you know this indicates that if you are actually taking a structure which is resting on you know in a certain water saturated model and it is subjected to say tested in a centrifuge then it indicates that you know it may lead to conservative results wherein we actually end up saying that the structure is safe from the liquefaction point of view. But however in the practice because of you know the difference in you know the pore water pressure generation as well as dissipation there will be you know the settlements and then there will be this lead to you know a different set of results which actually result in the destruction in the structure. So on the other hand the metallo saturated soil liquefied completely because the pore water pressure raised to the level of that particular stress and thus it was shown that the conflict between the dynamic and you know the diffusion time exists. So there is you know the conflict exists and this results of the seismic centrifuge test on water saturated soil models could underestimate the consequence of an earthquake that is what actually we have been discussing that if you are using water as the pore fluid in seismic centrifuge model text then you know the results can lead to underestimation because of the consequence of an earthquake. So this implies that a substitute pore fluid was actually necessary the substitute pore fluid is necessary for carrying out particularly the seismic centrifuge model test. But when we replace you know the water as the pore fluid even to saturate a fine signed a special saturation methods are actually required to be adopted and then they also take long time to for saturate and if you are actually having layered soil or if you are having clay and silt or silt and you know sand layers you know sometimes is very difficult to saturate with high you know pore fluids particularly if you are having a sand with up to say 20 to 30% that you know finds there is a possibility that you know the saturation may take longer time and special methods may be required. But the general methods which are actually you know adopted schematically are shown here one is the sucking water into the soil with a vacuum pump. So in this case a model pore fluid you know is sucked with the help of a vacuum pump to saturate the sample and the second one is that you know in this case a method of saturation with a silicon electric shown a fluid percolation in a vacuum chamber and actually happens then there is a possibility that you know this can actually get you know the saturation can actually happen. So in order to induce this you know the seismic turbulence to the models the schematic you know the there is a requirement of the inflate earthquake shaking system. So this inflate earthquake shaking system basically is required to be have high sophistication because we have said that you know for a model which is reduced by 1 by n times and subjected to n gravities the frequency has to be n times that in the prototype and the duration of the earthquake has to be 1 by n times that of the prototype. So this indicates that you know the inflate actuating system has to be very powerful and should be able to you know induce this earthquake shaking with wide range of frequencies. So in this particular a typical saturated sand with an appropriate pore fluid is actually shown here and the requirement of the one of the other requirements of earthquake shaking system is that the container has to be you know different if you are actually using you know normal rigid containers. So we actually have two types of containers one is for the static test the other one is for dynamic test. In case of the dynamic test with the recent evaluation is the laminar containers are actually evolved and these are actually are used and so we are going to discuss about the require why the laminar container is required for the seismic centrifuge experiments. So here the schematic representation is actually shown here and so this is the basket and this is the you know schematic of a typical shaking system mounted on the swing basket is shown here on this the you know the model which is going to be subjected to shaking is actually place. So for large equipments what is actually done is that the shaking will actually happen in this direction that means that if you are having you know in this direction that is perpendicular to the plane of rotation the shaking happens. So this actually has you know possibility that we can actually have you know large models can be tested in a large centrifuges with an appropriate in flight earthquake shaking systems. So here the HP is nothing but the thickness of the sand layer which is nothing but n times Hm if n is say 50g then that it represents about 50 times the Hm of the model which is under consideration. So please to be noted that this is a laminar container which is actually required and this container is actually fixed here and this depending upon the amplitude model which we are going to do and these are the you know the stoppers where in you know they actually prevent any detachment of you know the components at the onset of shaking. So this is the you know the typical centrifuge shaker during flight when the model is rotating this is this side is the center of the shaft and this is the you know the laminar container and this is the shaking system and these are the accumulators for pumping oil to the actuator and this is the basket. So this is actually mounted on the basket wherein actually this is actually shown for schematically for 50 gravities. So this implies you know this is a typical the centrifuge shaker during flight. So the first of all let us discuss what are the different shaking systems are required and then we will discuss what are the different you know why a laminar container is required. So in order to have you know the earthquake shaking number of ways of you know have been tried generally the earthquake like shaking the model in a flight requires a power source or actuator. So the actuator requires high frequency excitation and high forces need to be applied and the duration of shaking will be very short because the frequency is n times that in the prototype the duration is short and actuator must be kept. So in this short duration the actuator should be able to deliver peak energy flows almost instantaneously and the centrifuge itself could be subjected to unacceptable dynamic stresses if appropriate reaction masses are not designed to system. So basically the centrifuge itself need to be you know safeguarded to prevent any transfer of unacceptable dynamic stresses to the arm and you know the pedestal of the equipment. The actuator must be compact in size and a minimum mass and should be able to vary the, we should be able to vary amplitude and frequencies contents. Say for example we are having a you know amplitudes of about let us say 0.5 to 1 meter then we will actually model that let us say 500 mm by at 50g something like 10 mm amplitude. So in the frequency content let us say that the normal range of frequency which are actually possible in the field or about 1 heads to say 5 heads, 5 heads means very high frequency. Let us say that if we are having a earthquake of frequency of say 1 heads or 1 cycle per second. So based on the scaling loss if it indicates that if you are actually modeling at 50g then the frequency has to be you know 50 heads and it is subjected to say 10 cycles of 50 heads or 20 cycles of 50 heads. So you know that you know the sinusoidal motion has to be triggered by a suitable shaking system. So there are the different types of common shaking systems one of the traditional and bold which is now replaced by University of Cambridge that is called mechanical actuators and which was developed by using a simple concept. And a piezoelectric system which is UC Davis USA and electromagnetic system shaking system in Shimazu centrifuge in Japan and hydraulic actuator in University of Colorado USA. So this is you know bumping road indicator system wherein the bumpy road actuator was actually used. So what has been done is that the profile actually has been preset on the periphery of the centrifuge and the landing you know is activated and it you know moves along the the set profile which is there which is shown here which is shown here in the on the picture on to the you know the centrifuge chamber vertical wall and earlier traditionally this was actually used to study the earthquake motions in the University of Cambridge centrifuge. But nowadays this has been replaced with very powerful actuator. Now before looking into the different types of you know requirement of the containers and then shaking systems let us look into the example problem. Consider that we have got a small volume which is 3 into 10 to the power of minus 2 meter cube is subjected to say 100 gravities and the equivalent volume is nothing but 3 into 10 to the power of minus 2 meter cube into 100 cube. Then let us say that this is actually subjected to 10 cycles at a frequency of 100 heads and with an amplitude of 1.5 mm. So the time model is about 0.1 seconds that is 10 by 100 is 0.1 second. Similarly in the equivalent in the prototype is that 10 cycles at a frequency of 1 head. So because the frequency is 1 head which is actually model at 100 G. So the model frequency is 100 heads the same motion but it is actually having 100 heads frequency here 10 cycles at 1 heads frequency. So the acceleration from the you know the deductions we have made that is amplitude into 4 this is the acceleration term in the equation which we have derived where 1.5 by 1000 into 4 pi square into 100 square. So with that what will happen this is the frequency with that what it actually says that if 592 meter per second square it is 60.3 G. Similarly the acceleration in the prototype is you know 0.15 that is amplitude into 4 pi square into 1 square is 5.92 meter square that is 0.6 G. So this is 1 G and so this is lateral acceleration is about 0.6 G. So if you know the unit weight of the soil then by multiplying 592 meter per second square into the mass of the you know the mass which is actually subjected we can actually calculate the lateral force that is due to the dynamic force due to this mass into the acceleration. So another thing which what we can try is that we have discussed that if you are having you know the velocity of moving you know particle within the model if it is actually you know let us say that you know say less than 0.05 times the model velocity we said that the Coriolis effect can be neglected but if it is in the ratio of 0.05 V2 to V we said that the Coriolis effect cannot be neglected then models have to be designed to safeguard again it is the Coriolis effects and if the velocity is say more than 2 times velocity model velocity we said that the Coriolis effect can be neglected because that is very very fast event example is that you know the you know the throwing of a sector due to triggering of a charge. So let us check for Coriolis effect for the same dynamic model which you have tested and V is equal to 30 meter per second so with that what we can say we can calculate by velocity by using velocity magnitude 10 which is nothing but Am is equal to 2 pi fm and where in the amplitude that is 1.5 into 10 to the power of minus 3 in meters 2 pi into 100. So with that what we have got is that 0.94 meter per second and firstly we let us check whether it is less than 0.05 V so 0.05 into 30 so about 1.5 meter per second so hence this is you know we can say that for the dynamic model here whatever we have done the error is actually 6.2 percent which is less than 10 percent. So the dynamic model under consideration where the Coriolis effect is negligible. So like this we are actually having any particular model dynamic model the Coriolis effect can be you know the presence or can be checked beforehand so this problem what we have done is that we have done a model which is subjected to the shaking and then you know we actually have calculated also whether the Coriolis effect is negligible or what is the error due to Coriolis effect that actually has been calculated. So now let us look into the typical shaking tables which are actually available in different parts of the world and this is a camshaft shaking table which was actually developed for inducing you know the shaking to the models. And this is electromagnetic shaking system which is actually you know which works on the principle of you know AC coil and DC coil. So you can see that this is the you know T shaped plate which is fixed here and with excitation of AC coil and DC coil the shaking table actually subjected to this is the you know the seismic excitation. So but one demerit of this electromagnetic shaking system is that the system actually actually is the payload is very high. So that means that you cannot actually take large models subjected to because electro shaking system itself will be very the self rate will be very high. So because of that you know the payload which can be mounted on the shaking table will be limited and also the you know the broad range of frequencies are also limited. This is another electromagnetic shaking system which was used at Shimazu centrifuge in Japan and this is you know typical hydraulic shaking system at Shimazu centrifuge wherein it has actually has got two servo walls and the that is the black color one which actually is indicates the shaking table. So this is you know the inflight shaking table system at Tongxi University in China wherein they this is after March 2006 where they actually mount the models on this shaking table. So this is you know inflight shaking table at Korea Water Resource Corporation, Kowakow where it actually has the payload of 1.5 tons about 15 kilo Newton and maximum shaking acceleration is about 45 G and shaking forces about 350 kilo Newton. So very high and shaking frequency range is 6 to 350 heads so it actually has got a wide range of frequency band and so this is you know a type of shaking table which is actually used in Korea. So after having seen the different shaking systems let us look into the boundary effects particularly when you are actually having earthquake modeling experiment we said that when you are actually having a static container you know that is the container that is rigid container which is used for say centrifuge model test then there can be possibility of multiple reflections of waves at the onset of earthquake motion. So the centrifuge models are generally enclosed with finite boundaries provided by a model container and the artificial boundaries of the model container may distort the stress and strain fields and generate p waves among other superfluous wave reflections in the model and that are not present in the prototype. So in the prototype you know when the typical typically we will not actually have the reflection because of the infinite boundaries but in the model because of the confinement with you know very stiff walls in the model container like in rigid container there can be you know generations of p waves and also the reflection of other superfluous wave reflections. So the realistic boundary conditions at the boundary of model produce accurate model simulations of soil specific behavior basically that reflect the behavior observed in the semi infinite soil layers in the field. So now consider so this is what actually has been discussed when you are actually having in the prototype you actually have got when it is subjected to say certain ground motion and because of this infinite boundaries there is only the secondary waves are generated but when the centrifuge model with a rigid container is used because of the seismic excitation there is you know also the generation of p waves the compressional waves and also the other superficial waves which actually causes the multiple reflections so which may affect which are actually going to affect the let us say a particular structure being studied can be a possibility of you know leading to the misinterpretation of results. So this is you know it is typically the way how it is there in the prototype. So you can say that when it is subjected to a certain type of motion in this direction so there will be you know deformation in this direction this is the element before deformation this is the element after deformation at the you know you can see that at the center and along the edges you actually have got identical deformations but and then also there is you know at all points actually the soil stiffness dynamic soil stiffness is identical in you know in this direction. So and also there exists actually some conjugate shear stresses and the sigma v this is vertical stress and sigma h here this is at the element a which actually has got the stresses like this sigma vertical stress and then horizontal stresses. When we are actually having rigid container with a smooth wall so what we have is that the absence of the shear stresses can be noted here and the reflection of you know waves causes at the center the deformation may be identical that as that in the in the field but however the edges actually has got when the model is actually you know shaken in this direction subjected to shaking in this direction. So the soil column deformation at the edges is actually different so this actually can be noted so the deformations is they are different and also the absence of the conjugate shear stresses or complementary shear stresses. So the end walls are smooth and the stress dissimilarities would occur because of the lack of complementary shear stresses on the elements at a and b. So particularly when you are having a rigid container there is a possibility that the rigid container actually having very high stiffness as compared to soil in principle in the prototype the stiffness is actually identical so that causes also a problem. So this was actually resolved by with the number of you know different other options which were I tried like some of the earlier you know containers were like ESB type containers where in you know the aluminum and rubber alternate you know packing systems are used to induce some flexibility to the side walls of the container. But however in the latter stage the laminar container actually have been developed and this track ring devices originally developed for simple shear test have been increasingly used to simulate the free boundary conditions in earthquake modeling of soil deposits and this type of container is actually is called as a laminar container and the design concept of laminar containers is that of is that the container should have a limited contribution to the response of soil system and it should not cause you know the reflection of the waves and laminar containers are constructed by stacking lightweight rings separated by bearings that permit relatively free movement of the soil and rings during the shaking. And this also these laminar containers are actually found to simulate the actual behavior in the field so that it induces the you know the so called the you know the identical deformations at the edges as well as in the center. So this is a typical laminar container what you can be seen that when the model is actually subjected to shaking and this is you know a pile which is actually being subjected to some shaking. So you can be seen that like in the field the deformations are actually identical and then lead to you know the motion which is analogous to that in the field. So in this particular lecture we try to understand about the again the concept of modeling of models and then we also try to see why what is the necessary and how the you know the replacement of the pore fluid can be justified with replacement of conventional water fluid can be justified by using modeling of models experiments as well as the experimental evidence which we actually have said that the there is a requirement for dynamic centrifuge experiments the replacement of the modeling of the pore fluid is required. Then finally we have also seen that different types of shaking systems which are actually in work and then the laminar containers which are actually used for the dynamic equipments so that this actually simulates the identical behavior of the prototype in the centrifuge models particularly the dynamic centrifuge experiments.