 Welcome to lecture on advanced geotechnical engineering course in module 7 lecture 9 geotechnical physical modeling. So this is module 7 in lecture 9 on geotechnical physical modeling. So in the previous lecture we have introduced ourselves to different types of shaking systems and then different types of containers which are required for earthquake based experiments. So this is the typical two dimensional shaking system available at RPI Newark and wherein you can see that the swing basket package will come out of the chamber along with the earthquake actuator. The earthquake actuator fitted in a sole basket and they use this for performing earthquake experiments and for the rest of the experiments they will use a different basket. So this particular slide shows the use of earthquake actuator mounted on the swing basket. You can see that this is the portion which is actually subjected to shaking in this direction and in this direction. So this is actually a typical two dimensional shaking systems there are also some three dimensional shaking systems which are available in Japan and other countries wherein they can actually have shaking in x direction, y direction and z direction. So this is the view of a laminar container which we have seen earlier and wherein the dynamic stiffness of the soil will be identical as that in the along the edges as well as within the soil. So in this way what will happen is that in the event of shaking the soil actually takes the form of the shape which is exerted by the body subjected to this motion. So here for example a pile subjected to the earthquake shaking is being studied. We can see that different types of instrumentations are actually placed to monitor during the earthquake. So this is a typical laminar box at the Schofield centrifuge center where in you can see that you have got different types of aluminum disc which are actually placed and contained in this direction as well as so for shaking in this direction and also they contained in this direction. So this is set the distance is set depending upon the whatever the amplitude is allowed. So this is a typical model container in national industry of Singapore small one dimensional shaking system and wherein we have the earthquake actuator. So after having seen the different avenues for inducing earthquake and then scaling considerations by using the knowledge which we have gained let us try to look into this problem. So in a full scale structure a Ksp2A type sheet pile wall section having EI that is the flexural rigidity EI is equal to 24 into 10 to power of 4 kilo Newton meter square for retaining a soil having a cohesion of 15 kilo Pascal's and a friction angle of 30 degrees was used. A model vertical wall is constructed with the same soil and is subjected to constant angular velocity of 104 revolutions per minute in a beam centrifuge of radius 4.5 meter and is required to be tested for its dynamic behavior physically. The breadth of the model is 300 mm and the measured radius from the center of the shaft to the top surface of the model is 4.085 meters. Now we are required to find out what will be the thickness of the model wall made of aluminum plate that is take E is equal to 72 into 10 to power of 6 kilo Newton meter square that means that 72 GPa and take bulk unit weight of the soil as 18.2 kilo Newton per meter cube and what will be the magnitude of exerted dynamic force during shaking if the model is subjected to 10 cycles of 50 cycles per second frequency with an amplitude of 1 mm if the weight of the laminated container including the weight of the model wall and instrumentation transducer is 300 kg and also find duration of the shaking in the model and duration of the shaking in the model and prototype and frequency in the prototype and also amplitude in prototype and error due to Coriolis effect. So here we have been asked a number of things so this is basically a sheet pile wall retaining wall problem so what we have is that a model retaining wall is required to be selected so for that based on the scaling considerations which we have reduced earlier. So E i in model divided by E i in prototype is equal to 1 by N power of 4 so by where N is equal to the scale factor N or gravity level in order to get that we know as we know the model weight model height and model height then what we can do is that we can actually calculate what is the radius up to the point where the stresses in model prototype are identical that is effective radius R e is equal to R t plus H m by 3 and after having obtained that by using N g is equal to R e omega square what we can do is that you can calculate what is the rpm you know the rpm then you can calculate the N and by using that N value we can calculate what is the thickness of the plate because here E of aluminum is not equivalent to E of this material which is actually used. So here the E is not specified but what we can do is that that is the prototype E i value was given so what we can do is that we can take this E i value and divided by N power of 4 and you will be able to get by knowing the E value of the model sheet per wall you get the I value and based on that we can actually calculate by using BT cube by 12 and by knowing the breadth of the model you can actually calculate what is the thickness of the aluminum sheet which is actually required for modeling you know E i is equal to 24 into 10 to the power of 4 kilo Newton per meter square after having obtained now determining the weight so by knowing the dimension by knowing the weight we can actually calculate what is the model weight and based on that one can calculate what is the by knowing the acceleration by taking by picking up from the acceleration magnitude and once we assume that this is subjected to a sinusoidal motion and by multiplying with the mass and then acceleration you will get the dynamic force and then you know by taking the 10 cycles of 50 years frequency so in the model what is the duration and amplitude has to be you know N times that of you know in the model so the details can be obtained and by picking from the velocity magnitude by calculating from the velocity magnitude and by knowing the V is equal to r omega r is known to us that is r is equal to r e omega is you know the rpm converted into radians per second we can actually calculate what is the model velocity so 2 V by V we can actually calculate the error due to you know Correlation effect so this is the problem basically it is a combination of you know the problem which is required combined with you know even in static experiments also you know in order to model the sheet pile wall we have to follow these considerations and the problem and the you know the problem for the figure for the problem one is actually shown here where in the dimensions are all are in millimeters and this is a typical laminar container and this is 150 mm distance embedded depth is 100 mm and this height is 300 mm and breadth of the model is 300 mm and this length is 350 mm so by knowing this the bulk unit weight of the soil we can actually calculate what is the gamma value and container and other associated value is given so entire mass is actually placed on the swing basket so we can calculate what is the dynamic force component. So another important aspect which you know we require to learn is that for any static experiment or dynamic experiments instrumentation is very vital so the aim of any centrifuge model test basically to get the data like displacements, water pressures or pore water pressures or accelerations and you know force changes and forces which are actually applied and stresses in the soil so in order to get that we have to learn about the instrumentation. So the aim of the model test in this interview is used to locate mechanisms and to get values or ratios for force or stress or displacement changes as well as to observe the response of pore and water pressures and degree of saturation, degree of concentration. So you know there are a number of types of transducers which are actually available for the centrifuge domain wherein you know we have to use them basically to get the displacements or loads and stresses and you know the accelerations etc. So with an aim to retrieve the information and also capture the exact mechanism of failure before failure and at failure and also to get the values or ratios for force, stress and or displacement changes and the instrumentation is vital. So in the instrumentation what we have primarily first is that contact type basically there are two types one is called you know linearly variable, linearly variable differential transformers the other one is called potential meters these are contact types and they are contact with the model. There are also some non-contact type you know displacement measurement transducers are there they are called as laser LODTs and they work on the principle of triangulation and the closer the smaller is the distance range then you know the resolution will be very high and there are also some force measurements like if you are applying a load on the pile or load on the retaining wall then you know if you wanted to measure what is the force which is actually applied then you know we need to know measure through a load cell. So there are basically compression type load cells and tension compression type load cells wherein they can take both tension and compression and suppose if you are pulling a pile out of the soil then you know you have to measure the tensile force and if you are trying to apply the axial load on the pile then you have to apply the compressive force on the pile and so in between the load application actuator and the object this particular load cell has to be fitted and to be connected to a data equation system for retrieval of the data and mostly and most widely used transducers are pore water pressure transducers PPTs wherein if you wanted to measure the so called water pressures within the soil pore water pressures then these done through miniature type pore water pressure transducers and one important thing we have to notice is that centrifuge based physical experiments because of you know the transducers which are actually embedded in the soil have to be miniature in size that means that they have to be as small as possible so that they will not actually have influence on the and they will not actually act like a some reinforcement inclusion in the soil. In addition to that if you are actually trying to measure the stresses on the soil then there are also now the pressure sensors are available and there are also now you know some pressure sensors actually can be available now they are called as you know some foil type disposable pressure sensors suppose if you are actually keeping below the base of the footing then you can actually measure the distribution of the base pressures on the soil at the onset of loading. And then for measuring strains we have the strain gauging technique and with the advent of the optical data equation systems image analysis and very recently the particle image velocimetry which is you know being widely used in centrifuge based physical modeling. Then we also have the accelerometers like the two basical types one is called piezoelectric accelerometers which are widely used and the other ones are now very recently have come they are called MEMS based you know accelerometers. So we will look into the details of you know different units in a brief way. So here in this particular slide what you see is a linearly variable differential transformer LVDT and wherein you have a core and a primary coil and a secondary coils. So one primary coil and two secondary coils are connected in series opposition. So whenever the core moves here and that actually registers as a change in voltage and that is actually measured as you know the voltage and this is a typical photograph of a typical LVDT and which actually has got contact type you know there is a this is the casing and this is called a core and to reduce the stresses and there will be you know small pads will be attached to this one so that the stresses on the soil will be reduced so that they will not pierce into the soil. So this is a contact type LVDT and the important requirement to calibrate is that you know we need to calibrate for a given millimeter what is the you know all the you know the transducer which are actually you know placed on the in the model required to be calibrated. So the LVDTs are calibrated by subject into different millimeters like 0, 5 mm, 10 mm, 15 mm and for each displacement you measure what is the voltage and by plotting you know the displacement induced versus the measured output you can actually get you know a linear line and within that range what we get is that linear distribution. So sometimes you actually have minus 25 to plus 25 mm and minus 50 to plus 50 mm so this different depending upon the requirement of the travel the transducers can be selected and potentiometers are you know the which are nothing but attached to a spring which is you know subjected to the movement of the core induces a change in voltage and so that is also used for some you know non accurate measurements. And laser LVDT which is non contact type basically and the resolution is the function of distance between the transducer and measure measurement area and the shorter the distance better the resolution and the measurement principle is based on the triangulation and the measuring of the refraction of a laser beam. So what will happen is that you have a trans you know this laser transducer and which actually throws a you know a light on the subject or object so what will happen is that the refraction is actually received in a same transducer so with that what will happen is that the laser diode which is actually presents a visible spot on to the target space and the light reflected from this spot is actually directed through an optical receiving system on to a position sensitive element so with that what it does is that it measures the distance for example this laser LVDT is fixed to a moving you know object then there is a possibility that you will be able to get you know the profile of the system during the test. And the digital CMOS and CCD arrays use it to as a position sensitive measurement elements so the laser LVDTs are you know depending upon the resolution they actually have the accuracies which may be required for usage in the centrifuge model test. So this is a typical laser distance sensor non-contact type and so this is what actually is being shown with through this actually the light is actually shown then this is a connector to the data acquisition system. Now after having seen the displacement transducers then the miniature PPT transducer which is called pore water pressure transducer so this is a typical pore water pressure transducer you can see that the diameter is about 6.5 mm and length is about 12 mm so one can see that you know it has actually has got a diaphragm and onto this diaphragm there will be small miniature strain gauges will be pasted in a full scale of the full bridge of the Wittstein full bridge and so here the filter stone that is porous stone a ceramic stone has to be remain saturated always and so what happens is that in order to measure the positive pore water pressure water has to enter into this chamber between this diaphragm and you know the porous stone so through porous stone the water enters into it so it measures the head of water at the height of pressure above its mid height so this is actually taken as so as the water enters into this it exerts pressure on this diaphragm and this deflection of a diaphragm results in a change in the strain and that is recorded as a change in voltage so the pressure is this is calibrated again is induced pressure with change in voltage so when we plot the induced pressure with output in volts we can actually get a line which is a straight line passing through horizon and with that what we can get is that you know pressure by volts that is the calibration factor for a particular transducer. So these pore water pressure transducer available from 0.5 bar to up to 35 bar wherein they can actually measure that is about 3500 kilo Newton per meter square of pressure so this is a typical pore water pressure transducer is shown here and this is the you know protection for the sleeve here and then there is a cable which is actually running for the to the connected to the data distribution system so this is the casing of a stainless steel casing of a PPT which is actually shown here. And these are the typical load cells and which are used for tension compression these are after HPM and these load cells are actually used for you know measuring tension as well as compression and we also have miniature contact stress transducers and they are of the size of a button basically when the load is applied on the pressure sensitive area so it measures in results in a change in voltage so this actually also lead to the development of a pressure versus you know pressure versus change in voltage so in order to measure let us say later when you are actually trying to do a retaining wall problem we wanted to measure the pressure on the wall and all and this concept can be used. So then in sometimes when you are actually doing the partially saturated soils we need to measure the suction pore water pressure so in order to measure the suction pore water pressure as a soil is not completely saturated so here what will happen is that in the working principle of the suction pore water pressure is that here the diaphragm is actually filled with water and the ceramic disk is will be placed in position so here the difference is that water is actually thrown into the into the soil basically when it is being thrown into the surrounding soil it is actually relieved of the deflection so that actually results in you know change in pressure so water from the soil and water compartment depending upon the saturated and uncertain soils will be considered. So this type of transducers can actually measure up to minus 102 minus 200 kilo Pascal's of suction pressure and these are the typical strain gauges, foil type strain gauges are shown and the gauge length is actually shown here and which is actually having you know the backing what is called as a very important when you are actually trying to do on the particular say you know stiff material or non-stiff material depending upon that you have to have a backing and then you know we have got the copper micron connected to a lead cables and that any change in the length is actually given as the change in strain so that is actually calculated as you know these you know the strains in particularly for example in model sheet pile wall or any geogrid layer if you wanted to measure you know then you have to have a suitable strain gauges which should be pasted along with a suitable backing material. So this is the typical installation of a strain gauge on a pile and for some convenience to avoid some roughness one can actually also take the leads through the pipe is actually hollow can be taken through the pile so these are the typical piezoelectric accelerometers. So piezoelectric accelerometers are the traditional transducers used to measure the acceleration between dynamic centrifuge experiments so when they are subjected to vibration a crystal within the instrument gets squeezed which in turn releases a charge so this charged output is converted into voltage using a charge amplifier. So these instruments have a natural inbuilt high pass filter meaning that they are ineffective at measuring accelerations at low frequency approximately below 5 heads. So this piezoelectric accelerometers are the traditional transducers used to measure acceleration dynamic centrifuge experiments and basically when they are subjected to vibration a crystal within the instrument gets squeezed which in turn releases a charge so this charged output is converted into a voltage using a charge amplifier. So this is also calibrated by a system wherein it can induce minus 1g to plus 1g and within that we have got a linear you know variation. So generally these accelerometers have calibration factors of the order of say some 7g per volt to 8g per volt. Then as I said earlier the MEMS based accelerometers that is micro, electro, mechanical system accelerometers. So these are you know MEMS accelerometers are small electrical devices they are basically used for measuring acceleration by measuring the force a mass applies to a spring. So the MEMS based accelerometers they are the small electrical devices and they are actually used to measure the acceleration by measuring a force a mass applies to a spring. So they also measure the inertial acceleration as well as the dynamic acceleration. So they have been used widely for field monitoring and have been used for 1g testing. So more recently they use in dynamic centrifuges has been investigated due to their small size and the small weight and significantly low cost compared to their piezoelectric counterparts. So these dynamic in the dynamic centrifuges the piezoelectric these MEMS based accelerometers are being used because of their small size and small weight and significantly low cost compared to their piezoelectric counterparts. So this is a typical you know MEMS based accelerometer which is actually shown. The principle is actually explained in the next slide. So here what we see is the schematic representation of the operating principle of a MEMS accelerometer and we can see that and this is the proof mass and there is one anchor point where the spring is attached and another anchor point one spring is attached and there are fixed plates and then there is another moving plate. So these plates are attached to you know they are the fixed plates and this plate is actually subjected to movement depending upon the application of the load. So the MEMS accelerometers are typically fabricated with a single crystal silicon wafers using micromachining to etch the defined patterns on a silicon substrate and these patterns take the form of a small proof mass which is actually shown here and that are free from the substrate and surrounded by fixed plates. So these are the fixed plates and the proof mass is connected to fixed frame by spring elements. So acceleration acting so this is the direction of acceleration acting on the proof mass is to dissipate and plates connected to the proof mass move between the fixed plates and this actually enables to measure the you know inertial as well as the dynamic acceleration. So in this particular slide working principle of MEMS based accelerometers is actually given. So here the MEMS based accelerometers actually have you know the movable plates and fixed plates and when the proof mass is actually connected to a fixed form by spring elements and acceleration acting on the proof mass causes it to displace and the movable plates plates will be subjected to you know vibration and the plates connected to the proof mass move between the fixed plates and that results in the you know lead for the change in voltages and which we actually measure as you know the accelerations. So the displacement causes a differential capacitance that is measured by the integrated electronics and is output as voltage that is proportional to acceleration acting on the proof mass. So you know this is you know the basic you know principle and the applications earlier applications include motion activated user interfaces such as in smart phones and game consoles and protection systems such as free fall protection of hard drives in laptops and airbag deployment in vehicles. So motion activated user interfaces such as smart phones and game consoles and protection systems basically for you know of the hard drives in laptops and airbag deployments in vehicles. So these are fitted with nowadays with MEMS based accelerometers. Unlike piezoelectric accelerometers which are only to measure the changes in acceleration MEMS accelerometers can measure both constant and changing accelerations. So these MEMS accelerometers noted to have you know lot of potential and you know the usage of this can lead to measure either constant and changing accelerations and this at the onset of the seismic perturbance particularly for dynamic centrifuge experiments. So after having seen different sets of you know the required you know the instrumentation. So then you know we can actually look into different you know construction process which are actually there. So before that let us look into we question ourselves after having discussed what is the requirement of physical modulators. You know we can answer this by considering the complex and non-linear stress strain behavior of the soil and made of interacting particles air, water and different surfaces. So this is one particular first reason that you know you require physical modalities at difficulty of numerical simulation of soil and soil structure systems at large strains and failure. So this is one thing where the numerical simulations have limitations and to validate and calibrate numerical methods like number of numerical methods which are actually available they are required to be validated and also have the once we calibrate this numerical methods just there is a possibility that we will be able to you know use them with contents. And then after having seen physical model test we said that physical model test can be that 1 is to 1 and 1 is to n and small scale then we also have said that the centrifuge model test are definitely superior to the you know the small scale model test performed at 1G. So definitely why centrifuge model test in the sense that since small scale model or models are cost effective and the cost of centrifuge base scale model test are very small compared to the cost of construction. So if you are able to do this in a before and then construct. So this is the reason why the many countries actually adopt ATM that is called analyze test and construct ATC policy analyze test and construct policy. So the small scale models are cost effective and soil properties are highly stress dependent so because of that you know the centrifuge model is the one of the obvious reason and centrifuge produces equal confining stresses in model prototype therefore same soil properties. So we also have said that you know because of the simulation of the stresses sigma v and sigma h and because of that there is same soil properties are there and so that is one advantage and then reasonable assumption that strains and deformations are also equal in model prototype and we also have seen that from the see page and consolidation point of view the time required for completion of the particular event of this thing is one by n square times smaller. So that means that you know they can also give you know rapid results particularly when we are actually having some contaminant migration or probably the pollutant migration studies where they actually take years to there but you know the centrifuge model test studies will be possible for you to do it in a short time. Now let us look into this particular example of you know effect of pile installation we actually have got different types of pile foundations like what we have is that precast driven piles and board castings with the piles. Then what we do in the you know in the installing these piles in the field is that a precast driven pile is actually driven into the ground by driving the piles into the soil. Now once we look into that that is the construction process wherein a precast driven pile is the length of the embankment or cut off of a pile is actually selected based on the soil strata which actually has been obtained from the soil investigation. And if you are actually going for board castings with the pile so what has been done is that with by auguring technique the hole is actually drilled and then the reinforcement case is actually placed and by using if it is underwater by using the Terny method the concreting is done. So that is so if you look into this when we have got pile installation through precast pile the surrounding soil is actually subjected to additional confinement or compression and that results in a different behavior and the surrounding soil is preloaded and then you know it actually has better k value but in case of board castings with the pile because of the removal of the soil from the surrounding soil there is a possibility of release of the relief of the stresses which actually takes place. So because of that the k value or coefficient of earth pressure will be less in case of board castings with the piles. So if you are actually having you know a typical pile installed let us say through a driving into the soil then if you are actually having a case where in the field if you are actually measuring a pile which is actually driven into the soil and measure the applied load versus settlement by using say pile load test. So in that case we may get the profile what we get like this. So virtually if you are actually installing the pile at normal gravity if you are installing the pile at normal gravity and you know test the pile at n-gravities then you may get actually something like a applied load settlement behavior will be like this and which is drastically different from the one in the field. But if you are actually having a system where you have got a soil body and into which the pile is actually driven into the soil body by using certain type of a robotic actuator and once the pile is actually driven and if you actually test the pile then you know the applied load settlement behavior was found to be very close to that in the full scale. So the reasons actually need to be understood between the soil stresses which are actually going to happen when the pile is actually installed at 1g and when it is actually taken to ng what will happen particularly in the form of a stress parts we can actually explain what is the effect of pile installation and why you know pile installation should be performed in flight and that question cannot be answered by applying our knowledge of soil mechanics with the stress parts. So now let us say that if you have got a model pile installed at 1g so when you actually have model pile installed at 1g so you actually have sigma that is the stress and the sigma means sigma h or the you know if you take an element very close to the pile then sigma v is the vertical stress and sigma h is the argon stress. So because of the low stresses the stresses are low there is a sigma v and then there is a sigma h which is actually low stress which is actually acting on the pile surface. By driving pile at 1g momentarily the argon stresses are more than vertical stresses and thereafter by you know subjecting to high gravities in centrifuge the vertical stresses are more than horizontal stresses. But when you take this into the centrifuge then what will happen is that the vertical stresses increases and pile is actually driven at 1g so the stress will remain same and it actually has picked up the raise to the value whatever the sigma v raises and corresponding to that it actually mobilizes. So installation at 1g in dense sand because have the low stress levels in normal gravity and lead to the greater dilation and higher k value and so this actually lead to basically the soil surrounding the pile actually experiences the greater dilation which is actually different from what actually happens in real practice. When let us say that we have got model pile installed at ng that means that you have a soil mass which is initial at 1g and when we take into this centrifuge the soil is sigma v that is vertical stress and the sigma h the stresses have been magnified because of the engine ornament and now when you are actually driving the pile then what will happen is that sigma h will be more than sigma v and then this results in because of the increase in the horizontal confinement because of the driving of the pile during flight. So installation at ng increases the horizontal stress and higher k value so here and this particular process was found to be very close to if you are able to test the pile which is driven in the normal gravity test the pile driven at ng gravities then there is a possibility that the load settlement behavior will be close to that observed in the field. So from the stress path diagrams we can actually plot so here on the x axis the s which is sigma v dash plus sigma h dash by 2 is plotted and t which is nothing but sigma v dash minus sigma h dash by 2 is plotted so and here it actually shown and this is the k0 compression line and effective stress paths followed by elements close to the pile for installation at 1g wherein that it follows that a, b, c and d. So it follows this path like a, b, c, d this is actually pile installed at 1g which is actually you know the different from the one actually happens in the field. In case if you are actually having a pile installation at ng it actually goes like follows this compression line ap and then you know pq and then qr. So this apqr is the stress path which actually taken or obtained for pile installed at ng. So let us explain this the horizontal stress may possibly increase even above the vertical stress so that it falls below the 0 bc at 1g and pq at nq that is that this horizontal stress increases because of the pile ride so it falls below 0 and bc in case of 1g installation and then pq in case of ng installation. If the above you know the variation occurs at low stress level then subsequent consolidation CD will seek to re-establish and stresses develop close to k0 line. So if the pore water pressure equilibrium is required after pile installation at higher stress levels that is qr at ng then the horizontal stress may perhaps not change significantly and the soil will be left with in situ radial stress before loading of the pile takes place. So here if the above variation occurs at low stress levels the subsequent consolidation CD will seek to re-establish and you know the stresses may develop close to k0 line that is you know the stresses may develop close to the k0 line that is actually this is actually being shown here. If the pore water pressure equilibrium is required after pile installation at higher stress level qr at ng then horizontal stress may perhaps not change significantly and the soil will be left in the in situ radial stress before loading of the pile takes place. So that means that here there might not be much change and then you know the loading of the pile takes place in this region the direction. So here once you look into this you know the if you are actually adopting you know this a, b, c, d stress path and a, p, q, r you know the process if you look into this is actually distinctly different from at pile install at 1g and pile install at ng that different. So because of that and this particular stress path is actually also analogous to the one is actually happens in the field. So in a way what actually understand is that in order to get the true results and the it is actually required now pile installation actually has to happen at ng and then subsequently load testing has to happen in order to have the results which are actually as close as to that in the field. So now let us after having looked into a particular problem wherein we have seen you know the typical problem wherein you have got installation of pile and then we said that installation of pile at ng and subsequent testing at ng is beneficial. Now let us also look we have the you know problem of construction process where it involves excavation in front of the wall. Suppose consider here you have a retaining wall and this is the soil which is actually back filled. Nowadays you know large amounts of works are actually happening and wherein you know if you are having a particular foundation and subjected to certain load what is the influence of excavation on the you know the building foundations that can be investigated and you know can lead to very interesting results. So if you assume that this excavation actually takes place in stages like stage 1, stage 2, stage 3, stage 4, stage 5, stage 6 excavations and this is the you can say that you know the dredge level or the bed level which is actually anticipated. Nowadays with increase in you know urban structures particularly in urban areas these are actually becoming quite common and so it many times many situations which is sometimes very difficult to model numerically. So these are actually tackled very well by using the centrifuge base physical experiments. So in this particular sequence in the field sequence what will happen is that excavation actually happens in stages and so that the soil support is actually removed to the wall and the wall is actually subjected to you know ultimately subsequently the wall becomes unsupported. So this can be modeled by using number of techniques many people or many investigators actually have used different types of earthquake different types of excavation simulators like some of the simulators they include is that we have a blade which actually gets punched into the soil and then the blade actually drives takes over the soil mass and then drops into the certain area. So that is one process and now there is also another method which is actually called is that they replace this area so the wall is actually placed and then they replace this area with a heavy fluid like zinc chloride and you know the zinc chloride concentration selected such a way that you know you actually have identical stresses in both sides of the wall so that the k0 conditions can be simulated. But here this zinc chloride being you know the being actually having fluid the k0 is equal to 1 and particularly where horizontal stresses and vertical stresses will be equal and that leads to you know when you actually take a normal element soil element here the sigma v and sigma h the sigma h actually less than sigma v and this actually leads to you know sigma h and sigma v they are not equal but in case if you are actually simulating excavation by using you know the heavy fluid then you know the sigma h is equal to sigma v that actually can lead to some you know difference. So to address this many investigators actually have used and they do as an alternative to this actually there is also some plate support system will be put and then you know once you know reaching of certain gravity the plate support can moved away and that also can lead to you know differential movement. So this is you know the excavation in front of the wall by using heavy fluid in back drained in stages. So here also what will actually happen is that there will be a pore water pressure transducer and you connect it to a wall and with a solenoid wall. So once we wanted to decide to this so many centimeters of fluid to be drained the solenoid wall will be on remotely and drained into some other compartment then so it actually one by switching on and off will be able to construct you know the excavation. So this let us explain in terms of the stress pass again wherein we have got again S which is you know sigma v plus sigma h by 2 and T which is sigma v minus sigma h by 2. So here excavation stages is Apqrs, excavation by removal of the fluid pressure is that ABCDEFG. So here excavation in stages if you are actually doing then which is actually close to the prototype what you can say is that Ap and Q Apq. So these are actually you know they meet at a point here at a certain point here Apq and Qr andrs. So that is the you know the stress path which actually takes in the field but if you are actually removing the fluid then it actually takes like AB and then CD and EF and FG that is this direction FG. So you know if you look into this because of the stress dissimilarity this actually leads to the difference between the excavation through fluid as well as excavation stages. The stress paths are actually different one need to note down that the excavation stages in Apqrs what is actually if you have done through a proper excavation simulator and that simulates you know a system which is close to that in the field but we are simulating excavation by removal of the AV fluid then you know the stress path is distinctly different that we have to make a note in this particular slide. So let us dissect this excavation stages Apqrs, excavation by removal of fluid pressure ABCDEFG. So Ap which is actually consolidation and Apq is wall consolidation that is the removal of the load and Qr installation of wall andrs is the excavation. So if you look into this Ap is consolidation that is along the compression line and then we have seen that PQ wall consolidation so PQ is wall consolidation release and Qr is what we said is that installation that is the driving of the wall andrs is the excavation that is the rs is the excavation. So if you are actually pre-installing the wall then they actually meet at same point okay and so this is a stress path which is you know obtained by using excavation stages and excavation by removal of the fluid pressure so AP the consolidation 1g and BC over consolidation at 1g and CD is the installation of wall at 1g that means that here CD the wall is actually driven into the soil mass at 1g say in a clay when it is driven at 1g so at low stress levels kindly note here. Then DE is the excavation replacement of soil with heavy fluid that is DE is nothing but excavation you know and replacement with the heavy fluid and then subsequently where you have what EF the centrifuge acceleration changes from 1g to ng that is centrifuge acceleration changes from 1g to ng so there is an increase in the stress okay then fg is the excavation the draining of the fluid. So here the stress paths are actually distinctly different and the excavation stages if you are actually properly doing through a proper excavation simulator then we get very close to the what actually happens in the field is APQ rs in the excavation by removal of the fluid pressure that is actually A, B, C, D, E, F, G this is actually is obtained by you know in the field in the model by draining the fluid pressure. So for the excavation in front of the wall basically for a pre-installed wall once again this actually poses robotic challenges and the problem is you know the simultaneous removal of soil like horizontal stresses and vertical stresses and desirable to do this in stages leaving the real soil below each excavation level that is actually is the requirement and the ratio of the horizontal and vertical effective stresses before excavation will depend upon the soil type and the consolidation history of the soil and basically in sandy soil it might be as low as 0.3 in a stiff clay it can be as high as 3 horizontal stress. So practically the easiest way to applying varying load over a determining surface is to use the fluid pressure. So this is you know particularly the you know the application which was actually used for applying the pressures initially and then withdrawing the pleasures by draining the fluid. So the unit weight of the soil is actually greater than the unit weight of water so this strategy is to use a heavy fluid such a ways that aqueous solution of zinc chloride can be used. So in a fluid if the horizontal and vertical stresses are of course always same in any level so an assumption might be made is more important to maintain the correct horizontal stresses on the pre-installed wall than to maintain the correct vertical stresses on the ground remaining in front of the wall. So this problem has actually has been described because of the Pascal's law the stresses in horizontal and vertical direction are same. So this can be addressed by using a combination of heavy fluid with air pressure this can be addressed by using a combination of heavy fluid with a air pressure to supplement differential vertical stress at the base eventually excavated soil in order to able to provide the separate control of horizontal and vertical stresses. So what actually you know people have done particularly Macanumara at all they have done is that they have used the you know the heavy fluid but at the bottom you know there is actually you know they actually added you know the so called air pressures. Very recently you know the work actually has been done at IIT Bombay is that combination of zinc chloride and you know the water draining has actually been adopted and this is actually also found to produce the identical stresses as that in the you know vertical stresses are actually stimulated to as the identical that in the model. That means that here what actually has been explained is that by using a combination of heavy fluid and you know water by draining heavy fluid and water simultaneously. So the weight of heavy fluid and weight of water such that you actually simulate sigma v like in the field and sigma h like in the field say for example for a normally consolidated soil when sigma h is equal to 0.5 as become v and those conditions can be simulated by easily by using this combination then there is no requirement of giving air pressure at the base of the container. So one example which can be taken is that you know suppose if you are actually having a particular slope and if you are having a pore water pressure transducer at file locations and if you measure the pore water pressure then you will get the reading like time versus pore water pressure like here this test was actually carried out at this figure which is actually shown as test was carried out to 30 gravities. So you can see that they you know at 24 cm of model you know 25 cm of model actually has got this much height of water and these are the pore water pressure transducers within the slope and this is at the toe you can see that the pore water pressure is low here. So this particular example problem basically consists of steady state seepage problem conditions were simulated for a slope having 12 meter height at 50 gravities and figure below shows us the you know periodic surface are given and these are actually obtained from the centrifuge model test and the slope portion as well as the base layer was most compacted in void ratio of 0.38 and the coefficient of permeability of the soil is 1.6 into 10 to power of minus 6 meter per second and what we need to do is that seepage velocity at the end of the 6th day and 12th day between points BC and BC that will be shown and pore water pressures and discharge per unit length of the slope at C and C and time of seepage. So average particle size is given as 0.22 mm and can you may discuss to the what is given as 1 centi stroke that is 1 into 10 to power of minus 6 meter square per second. So this is the typical problem statement and the solution can be addressed by using this particular formula. So if you want the velocity now we can actually between B and C and B and C that means that this is the periodic line for 6th day this is the periodic line for 12th day so water actually has prognosis from this direction. So by using this V is equal to K by gamma w K is the permeability of the soil that is 1.6 into 10 to power of minus 6 meter per second 1.6 into 10 to power of minus 6 meter per second gamma w that is 9.81 kilo meter cube delta P that is you know this difference the pressure difference that is 6.25 is the horizontal coordinate 13.21 and 10.34. So this is about 3 meter pressure difference over a horizontal distance of 6 meters. So delta P by L you get the velocity that is the discharge velocity now by knowing the porous void ratio N is equal to e by 1 plus 1e we can actually calculate what is the seepage velocity. So seepage velocity at the 6th day and seepage velocity at the time of 12th day can be found out and similarly by knowing the velocity you can also estimate what is the Reynolds number. So by knowing the velocity by knowing the particle size effective particle size and taking the kinematic viscosity we can get Reynolds number and then we can check whether the Reynolds number is less than 1 for a allowable limit. So what we have seen is that this particular problem statement and these are the periodic surface which are actually measured through experiment. So from the measured data how we can actually calculate you know basically the discharge velocities seepage velocities and pore water pressures at different points during the course of experiment and during the course of the seepage can be established. So this is a typical example wherein we can actually use the data and calculate whatever we have actually done through the experiments and through the discussions and lectures you can actually use and solve this problem. So in this particular lecture we try to understand about connected through different shaking systems as well as through the containers and then we try to understand two typical construction process one is the effect of pile installation whether installation of pile in NG is important or 1G is important and what is the consequence of that and also one construction process which we have discussed is that excavation in front of the war.