 Let us start our today's lecture for NPTEL video course on Geotechnical Earthquake Engineering. So, for this video course currently we are discussing with module number 6 which is Dynamic Soil Properties. So, a quick recap what we have learnt in our previous lecture as I have already mentioned the basic reference for this course. I will refer to my another video course of NPTEL that is on Soil Dynamics, module 4 of that course where I have discussed in detail about this Dynamic Soil Properties. Now, in the previous lecture we have discussed about what are the most important Dynamic Soil Properties. In that we need to know first about the density or unit weight of the soil then shear modulus which is a important Dynamic Soil Property and damping characteristics another important Dynamic Soil Property. We have seen how shear modulus is defined it is nothing but the behavior of any material for our case it is the soil when it is subjected to cyclic shear stress. So, this is the shear stress versus shear strain plot the slope of that curve will give us the shear modulus. So, it is defined as the ratio of shear stress to shear strain as we all know for a linear material that is a material which is behaving linearly we will find out that this tau versus gamma or shear stress versus shear strain relationship is something linear like this. Hence, we will get a single value of this shear modulus from this curve whereas for actual material or most of the material like for soil we will get it will behave like a non-linear material where the shear stress versus shear strain of the material will behave non-linearly like this and if we want to find out the slope of that curve that will keep on changing at different point the initial tangent of that will be considered as maximum shear modulus or G max. If we want to find out shear modulus at any higher shear strain value then from that point if we join to the initial point then the slope of that line will give us the second shear modulus and if we draw a tangent at that curvilinear portion of that material behavior the slope of that line will give us the tangent shear modulus. Now, where these three shear modulus are used for equivalent linear analysis we use G second modulus for linear analysis of course we use G max and for non-linear analysis we use the G tan then we have seen how we carry out the equivalent linear approach we generally define the material property in terms of G by G max non-dimensional parameter in the y axis. So, maximum value of this G by G max ratio will be obviously 1 and as the shear strain increases which is plotted in the x axis in the log scale the material degradation will show like this for a soil and we will say that it is almost close to 1 G by G max value for very low shear strain that is that is called the linear range where G equals to G max for low strain for that the low strain range should be within 3 into 10 to the power minus 4 percent. Now, how to find out this G max value or maximum value of shear modulus the measurement involves basically the three major methods one is direct field measurement by using this techniques or indirect field measurement by using this techniques or laboratory measurement using these techniques also from the shear wave velocity value v s value we can calculate the value of G max using this relationship using this density of the material or density of the soil as rho. Now, coming to various relationship of this G value with respect to SPT n value that is standard penetration test n value several researchers has obtained correlation between the corrected SPT n value which is n 160 with respect to G max also in the laboratory one can find out using resonant column test like this that what is the value of G max at the resonant frequency from this plot of the distortion at different frequency on the resonant column the torque applied on it also from cyclic triaxial test one can find out the G max value another way to obtain the G max value is from in situ test parameters using various empirical relationships which are available worldwide like SPT n value CPT on penetration value DMT dilatometer test value PMT pressure meter test value. So, from each of these test we can get these empirical relationships for different types of soil as proposed by various researchers worldwide, but we need to remember these relationships are developed for limited number of data set point and also for a typical soil of that region. So, acceptability of these empirical relationships is always needs to be checked when somebody is trying to do a rigorous analysis for obtaining the G max value and further use of that G max for dynamic analysis. The variation of this G by G max with respect to cyclic shear strain for different values of plasticity index was reported by Wussetik and Dobry in 1991 which shows like this type of variation and also with respect to the number of cycles that is if number of cycle increases then there will be a change in the G max value obviously it is going to decrease as can be seen from here. The another important parameter damping behavior which we have discussed in our previous lecture like at low strain we will expect low damping ratio whereas at high strain we will get high damping ratio value and the variation of damping ratio with respect to cyclic shear strain for a typical soil material will be something like this. This result is also given by Wussetik and Dobry in 1991 for different values of plasticity index for fine grain soils. Now, worldwide there are developments on the SPT N value versus the shear wave velocity relationship because many a times people cannot obtain the dynamic shear wave velocity at the soil site or field. So, instead of that people can reasonably use from the static test which is nothing but static penetration test SPT N value the value of V s which further can be used to compute the G max value and for further dynamic design. So, how it is done? The example we had discussed in our previous lecture for soil of Bangalore region in India Sitaram et al. in 2006 proposed this empirical relationship V s in terms of the corrected SPT N 160 value also corrected with respect to clean sand. So, N 160 C s in terms of that how one can obtain the V s value in absence of the actual data obtained through field test for the V s value also for other types of residual soil and silt sand and sand silt the upper bound and lower bound equations were proposed by this researchers. Another group of researchers they had proposed for soil of Chennai region in India Bhuminathan et al. in 2006 for clay soil and for sandy soil the relationship between V s and corrected SPT N value. Then the application of research for dynamic soil characterization of Mumbai city we had started in our previous lecture and the reference for that I have mentioned that Sumedh why maske's PhD thesis Dr. Sumedh maske who completed his PhD in 2011 at IIT Bombay under my supervision. So, first we had discussed what are the various hazards for Mumbai city that is shows the need of doing the study of geotechnical earthquake engineering for Mumbai city. This is the seismic zonation map of India as per IS 1893 part 1 of 2002 version which places Mumbai city in zone 3 and these are the seven original islands of Mumbai city which has been combined together by land filling et cetera over the period of time. And these are various earthquake history in and around Mumbai city which has been reported in this journal paper by maske and Chaudhary 2010 journal of applied geophysics Elsevier. This GIS based map shows the original seven island of Mumbai and the surrounding marshy land that is reclaimed land around Mumbai city which actually formed today's Mumbai city. Some other necessary information to study the Mumbai city area for this seismic hazard analysis first of all location of the Mumbai city is in seismic zone 3 as per IS 1893 2002 version part 1. So, earthquake of 6 to 6.5 intensity or magnitude is possible to occur. Past disasters earthquake occurred in the peninsular India not exactly in Mumbai, but in peninsular India and Mumbai is also a part of that. The Mumbai city population is more than 15 million as per the census of 2011. Active fault zone are present close to Mumbai like Panvel flexure, Thanek Creek and Dharmatar Creek as mentioned by these researchers. Also there are various 23 small active faults in and around Mumbai city as mentioned by Raghukanta Nayanagar in 2006. So, with these details we had completed our previous lectures. So, let us see how to take it forward today in our present lecture. Now, when we want to do any dynamic soil properties study on that for the Mumbai city first we should know the typical soil property of Mumbai. So, to find out the typical soil property you can see in this slide that for the entire Mumbai region various numbers of borehole data has been collected from reliable government and private agencies. So, that we get the soil profile of entire Mumbai city in this fashion and this GIS based map shows the locations of boreholes which are collected all around Mumbai city which is available in the paper of Musca and Choudhury 2011 geotechnical special publication of ASC. This is a typical soil profile for the Mumbai city at various locations like Girgao, Wadhala, Andheri etcetera. And this table shows the various stations borehole stations various soil types their depth SPTN value corrected originally recorded corrected groundwater depth and various other soil parameters like amount of gravel sand sealed clay liquid limit plastic limit specific gravity. So, all these informations were collected from reliable and authentic borehole data from various locations like Tilaknagar, Chambur, Mulund, Wadhala etcetera. This chart shows the worldwide used correlations available for SPTN value versus the shear wave velocity VS value like for all types of soil, Oba and Toru Munini in 1970 proposed this equation of VS versus N also several other researchers as shown in this table have mentioned different equations of VS versus M as reported over here which are used worldwide extensively and the details are available in this paper by Musca and Choudhury 2011 in the journal Natural Hazards published by Springer. So, in this you we should again remember that these empirical relationships were developed based on the soils collected from a particular region and also it is based on a certain number of data set points. So, application of these equations for any particular region one has to be very careful whether that type of soil exist at the same area or not or whether the soil behavior at the location is similar or not. If not then obviously this relationship should not be used and a new relationship is required to be developed for that particular area. So, now let us look at here that when we want to develop some particular relationship of that SPT N value versus the shear wave velocity VS for Mumbai region from the collected borehole data you can see over here. These are the typical average shear wave velocity values all around Mumbai city at various borehole locations which are digitized in the GIS map these details are available in this paper. Also these stations and soil type depth SPT N value are shown over here and this is the equation which has been developed for Mumbai city by Musca for his PHD work under my supervision and these are the ranges of values of SPT N value and corresponding shear wave velocity value in and around Mumbai at different locations. So, one can easily see it is not in the similar range in all the places it depends on location to location it varies from location to location. So, one needs to be very careful when somebody is planning to do any earthquake engineering study or analysis or design at different locations of Mumbai incorporating this dynamic soil properties. This result shows the correlation between shear wave velocity in the unit meter per second versus SPT N value and this is uncorrected SPT N value it may be noted. So, from the present study this is the observed and proposed equation that is V s equals to 72 n to the power 0.4 for entire Mumbai city soil and field observed or field measured actual shear wave velocity at three different locations are obtained at different values of SPT N value and corresponding V s values are plotted which are matching very well with the proposed entire region Mumbai soil. This result shows the correlations between shear wave velocity V s in meter per second unit versus the cleans and corrected SPT N 160 value. So, this is cleans and corrected SPT N value you can see the equation proposed here is V s equals to 40 n 160 C s to the power 0.47. So, there is a minor change from the uncorrected SPT N value to the corrected SPT N value. This is observed from the Dr. Mascis PhD thesis as reported over here and also it was concluded from the study that there is hardly any large variation or significant variation between the use of original raw SPT N value or corrected cleans and SPT N value also by previous other researchers why because there are very several uncertainties involved in the SPT N value corrections also. So, instead of adding up the uncertainties it is also suggested that for basic study or first step of study or design it is better to use the basic equation of V s equals to 72 n to the power 0.4 for the Mumbai city soil from the uncorrected SPT N value where it will give reasonably correct result for the shear wave velocity as it is also verified and authenticated from the field measurements as shown in this slide. Now, coming to this comparison of various Indian soils what are the different correlations available between shear wave velocity V s and uncorrected SPT N value as reported by four researchers group for four different city as on today it is available like this that is shear wave velocity V s in meter per second unit in the y axis and in x axis it is SPT N value uncorrected this line the top one shows the results for Delhi city which is given by Hanumanth Rao and Ramana 2008 that is the researchers from IIT Delhi they have developed this equation V s equals to 82.6 n to the power 0.43 for Delhi city this is the equation proposed to be used whereas Anbazagan and Sitaram in 2010 this lower most line with the circles symbol they proposed for the Bangalore city V s equals to 80 n to the power 0.33 as the proposed equation for the soil of Bangalore city. Maheshari et al in 2010 as shown by this dark triangles which is for Chennai city V s equals to 95.64 n to the power 0.301 is the proposed equation for soils of Chennai city and for Mumbai city the present study shows the results which is star marked over here this one V s equals to 72 n to the power 0.4 is the proposed correlation for Mumbai city soil that is from SPT N value how to calculate the shear wave velocity. So, it can be seen that for this four major cities in India like Delhi city Bangalore city Chennai city and Mumbai city these are the corresponding proposed correlations between SPT N value and the shear wave velocity V s value which will help finally to compute the maximum shear modulus G max value from this V s value for that particular region of soil and that will be finally used for the seismic design of any structures in that locality. In the similar fashion it is today's necessity that for most of the seismically active region or important locations where major construction is required or proposed there to carry out the seismic design or earthquake resistant design it is necessary to find out this kind of relationship of V s versus SPT N because at many places we will not be able to carry out the shear wave velocity test at field due to several reasons one of that as I have mentioned in previous lecture because of presence of several obstruction. If obstruction is present many a times s s w m a s w results will give us the wrong result because it is not giving the result of that V s value of that particular soil but it is giving a result of shear wave velocity passing through composite material that is whatever structure or hidden objects are present in the soil that material including the soil that does not capture the exact value of the stiffness or shear wave velocity etcetera of that particular soil. So, that is the reason why it is also proposed worldwide and also in India it is today's need to find out this kind of V s versus N relationship for most of the important cities and locations and the seismically active regions. This GIS based map shows the thematic map of average soil shear wave velocity more than 100 meter per second for the Mumbai city. You can see over here all these red color patches are nothing but those region where shear wave velocity average shear wave velocity to a particular depth is greater than 100 meter per second. So, one can say these are relatively stiffer soil compared to other regions. Musk and Choudhury 2011 this natural hazards journal paper in Springer is available with all these details. This GIS map shows the geospatial contour map of average soil shear wave velocity V s with interval of 50 meter per second for typical soil of Mumbai city. So, with 50 meter interval 50 meter per second interval the shear wave velocity values are plotted and shown over here like 140, 190, 290 etcetera 240 are shown over here which is useful why because if somebody is planning to do any construction at any region say at Malad region then they know at this location typical remember this is the typical representation. It may vary within that location also but typically the range of shear wave velocity will be within this value whatever is mapped over here. So, these details are very much useful for practicing engineers and design engineers to further carry out the design earthquake resistant design or earthquake related design at that site. This GIS based map shows the value of maximum shear modulus G max value where it is more than 20 MPa for Mumbai city. How it is obtained from the values of V s it can be easily computed the G max value knowing the density of the soil. So, through that the G max of more than 20 MPa those locations are marked over here that means these are relatively stiffer soil zone. Now, this table shows the classification of the soil site into 5 different categories like soil class A, B, C, D, E with their description as hard rock, rock, very dense soil and soft rock, stiff soil and soft soil based on the dynamic property of the soil which is expressed in terms of average shear wave velocity V s 30. What is 30? 30 indicates the average shear wave velocity up to a 30 meter depth from the ground surface. So, that is why this number 30 came here. So, V s 30 of the soil in the unit meter per second that value is used to classify the soil into different classes. This soil site classification is based on as per Nihar standard of 2000 which is nothing but codal guideline or provision as mentioned in USA and practiced worldwide. So, for soft soil V s 30 value will be less than equals to 180 meter per second. For stiff soil it is between 180 to 360 meter per second, for very dense soil it is between 360 to 760 meter per second and so on. So, Mumbai soil what study has been carried out Dr. K. for his PhD thesis at IIT Bombay. It has been observed that most of the soil of Mumbai region comes under soil class D or E that means stiff soil and soft soil because their V s 30 value found out to be within this range of between 100 to 360 meter per second as mentioned over here. Now, coming to the another important topic, subtopic that is soil liquefaction. First I will mention that for the detail basic understanding of soil liquefaction one should refer and listen to my another video course that is on soil dynamics which is developed for this NPTEL course once again and for that soil dynamics video course module number 4 also discusses about this soil liquefaction. What is soil liquefaction? As mentioned in this book by Kramer in 1996 it is nothing but the transformation from a solid state to a liquefied state as a consequence of increased pore pressure and reduced effective stress for soil. And as mentioned by Osinov in 2003 if the shear resistance of the soil becomes less than the static driving shear stress the soil can undergo large deformations and is say to liquefy. So in the state of soil liquefaction soil liquefaction can occur due to several dynamic loads but earthquake is of course one of the reason. So due to earthquake also soil liquefaction can occur. Now soil liquefaction due to earthquake modern liquefaction engineering developed after Nigata 1964 earthquake and great Alaskan earthquake of 1964 after that the research etcetera extensively started in this area of soil liquefaction. So key elements of soil liquefaction as proposed by C Detol in 2003 are mentioned over here and we should always remember that every new earthquake whenever another earthquake comes it creates a new research area because we get lots of more data lots of more understanding about how the soil behave during and after the earthquake. So all those information whether it got liquefied if it has been liquefied what type of soil was there if it has not liquefied during a magnitude of earthquake why it has not liquefied what are the characteristics of the soil and then try to correlate between various physical and engineering soil parameters with respect to the liquefaction estimation and so on. So this assessment of likelihood of triggering or initiation of soil liquefaction needs to be carried out then assessment of post liquefaction strength and overall post liquefaction needs to be studied because after the liquefaction how much strength of the soil is remaining whether it can be further used for construction of structure or not. These are important to know assessment of expected liquefaction induced deformations and displacements assessment of consequences of these deformations and displacement then finally the implementation and evaluation of engineered mitigation if necessary at that site. Now susceptibility of the soil to earthquake induced liquefaction these are the parameters which influences like of course earthquake intensity and duration what type of soil is present there then soil relative density particle size distribution of the soil presence or absence of the plastic fines ground water table location that is amount of degrees of saturation hydraulic conductivity or permeability of the soil placement conditions or depositional environment of the soil aging and cementation of the soil structure overburden pressure and finally the historical liquefaction. So all these factors which influences the earthquake induced soil liquefaction now liquefaction susceptibility criteria there are several methods as can be seen over here for fine grained soil there are various methods to obtain the liquefaction susceptibility criteria both for fine grained as well as coarse grained soil Chinese criteria and modified Chinese criteria Andrews and Martin criteria of 2000 Ude et al 2001 criteria Cde et al 2003 criteria Brae et al 2004 criteria Brae and Sancio 2006 criteria Bolange and Idris 2006 criteria and various other studies. So among these the most important or maximum widely used one is this one this is by Ude et al 2001 this is maximum used worldwide for the liquefaction susceptibility estimation. Coming to Chinese criteria and modified Chinese criteria Chinese criteria was developed by Wang in 1979 based on the study on Haitian and Sanxian in 1975 and 1976 the criteria says that the percent finer than 0.005 mm should be less than 15 percent liquid limit should be less than equals to 35 percent and water content should be greater than 0.9 times of liquid limit for that fine grained soil this criteria is basically for fine grained soil. So, this is the typical plasticity chart as we know liquid limit versus water content this is the a line equation. So, modified Chinese criteria says that the fine soils that the plot above this one the a line shows in the figure are considered to be susceptible to liquefaction if these three conditions that is percent of clay present in the soil is less than 15 percent liquid limit is less than equals to 35 percent and in situ water content is greater than or equals to 0.9 times liquid limit. Then the Ude et al 2001 criteria is a combination of several other researchers findings and this is a kind of report or methodology proposed which is accepted worldwide so far. So, seed et al in 1985 developed the ratio of the CRR versus CSR curve for granular soil. CRR is cyclic resistance ratio and CSR is cyclic stress ratio the details about these things I have already discussed in my another video course for NPTEL that is on soil dynamics. So, I request all the viewers of this course also to go through my another video course on soil dynamics like module number four of that course. So, we can get all these basic details I am not covering it here. So, it has been proposed how to estimate this cyclic resistance ratio or CRR from corrected blow count SPT N 160. So, these are all the collected historical data points of earthquake from actual field test results that where the soil got liquefied and where it did not liquefy that shows the three curves like percent fines less than equals to 5 percent another is between 5 to 15 percent this range between 15 to 35 percent and more than 35 percent. So, like that this percent fine if it is less than equals to 5 percent then it is called SPT clean sand based curve and clean sand correction also required to be computed to estimate the CRR value from this curve and seed et al in 2003 they proposed these are the recommendations for fine grain soil that is plasticity index versus water content or liquid limit water content to liquid limit ratio of in the x axis they have divided into different three zones that is susceptible to liquefaction moderately susceptible and non susceptible. So, accordingly if somebody wants to put their soil in this region and try to find out whether it is coming in susceptible range or non susceptible range this recommendation may be used further bre et al in 2004 they proposed another methodology using the similar concept of plasticity index versus water content to liquid limit ratio like this and mentioned that liquid limit is not considered as the authors observed that a number of specimens with liquid limit greater than 35 percent were found to be moderately susceptible to liquefaction another set of researchers like Bray and Sancio in 2006 they proposed a criteria based on 10 numbers of cyclic simple shear test performed for the same soil specimen in addition to the test carried out as we have explained in the previous slide just now some observations of Chichi earthquake of 1999 as reported by Chu et al in 2004 are also incorporated in that and in the same pattern of plasticity index versus the water content to liquid limit ratio have been zonified into three zones one is susceptible to liquefaction another further testing is needed and another is not susceptible to liquefaction zone. Another criteria is mentioned by Bolange and Idris in 2006 where CRR of clay like material and CRR of sand like material has been considered as two boundaries with respect to the x axis plot of plasticity index p i. So, for different values of plasticity index the typical range from transition of sand like to clay like soil behavior is mentioned by these researchers which is showing the exhibit of cyclic liquefaction. So, fine grain soils having plasticity index less than three are named as sand like and they can exhibit the cyclic liquefaction type response whereas for fine grain soils with plasticity index greater than 7 are named as clay like material where they are expected to exhibit cyclic mobility type response. So, in one case it is cyclic liquefaction and another case it is cyclic mobility depending on whether it is sand like behavior or clay like behavior and in between range that is when plasticity index is between 3 to 7 a transition between this sand like to clay like behavior is proposed to occur and this figure provides a schematic illustration how this transition from sand like to clay like behavior is occurring. So, this criteria in the CRR versus plasticity index domain without a scale and distinction of sand like and clay like fine grain soil is based on solely on the plasticity index on the specimen and r u value that is pore pressure ratio as it is mentioned over here excess pore pressure ratio for fine for sand like soils initial liquefaction is achieved when excess pore pressure ratio r u becomes equals to 1. So, if it is less than 1 then it is not liquefying whereas for clay like soil it go undergoes cyclic mobility when this r u value exceeds 0.8. So, for sand like material it has to be equals to 1. So, that one can say liquefaction is going to occur for clay like material it should be more than equals to 0.8 then one can say it is going through the cyclic mobility. So, this r u based liquefaction susceptibility definition it requires the determination of CSR levels and the duration of the excitation. So, these things are the topic of research even on today in this year 2013 still further researches are carrying out their various research from the collected field test data of liquefied zone, non liquefied zone, transition zone etcetera and also doing the laboratory test and combining this data set of results as many data set are possible. So, that this interpretation of results and then further proposing some new criteria will be valid and can be used by various researchers. Now, coming to the seismic liquefaction hazard map of Mumbai city using this GIS and GPS the details of this work can be obtained in this journal paper by Maske and Choudhury 2010 in journal of applied geophysics Elsevier publication volume 70 number 3 page number 2162225. The evaluation of soil liquefaction like how it was carried out from the entire set of borehole data collected for the entire Mumbai region as the dynamic soil properties the V s value has been estimated and reported just few slides back as we have discussed here. Then for each borehole locations the soil liquefaction susceptibility is estimated using the simplified procedure for evaluation of liquefaction potential. The simplified procedure was basically proposed by seed and idriss in 1971. Further it was modified by Ud and Idriss in 1997 and the final one is Ud et al. 2001 which is widely used worldwide as I have mentioned. So, discussion about this simplified procedure to evaluate the liquefaction potential is available in my another video course of NPTEL which is on soil dynamics module 4 of that discuss about the simplified procedure for liquefaction estimation. So, these are the stepwise procedure in step 1 the surface data used to access liquefaction should include location of ground water table SPTN value share wave velocity value unit weight of soil fines content of the soil moisture content in the step 2 evaluate the total vertical stress and effective vertical stress that is sigma v and sigma v dash for all potentially liquefiable layer within the deposit and then one need to calculate this cyclic stress ratio or CSR as induced by the design earthquake. So, for a particular region we all know what is design basis earthquake as per the codal provisions or the zonation map or the seismic micro zonation point of view one can find out what is the value of this m x for a region that m x value can be used this g is acceleration due to gravity. So, this is just a number r d is nothing but stress reduction factor due to the flexibility of the soil and the sigma v is total vertical stress and sigma v dash is effective vertical stress. So, with that a non-dimensional parameter CSR cyclic stress ratio can be obtained which is proposed by C Dan Idris in 1971. Now, how to select this stress reduction coefficient r d there are various researchers who had proposed different ranges or values or equations for r d we can see over here as we go deeper and deeper inside the ground from the ground surface. So, from this ground surface where the depth is 0 if we go deeper below the ground as the depth increases in meter unit it is shown over here the r d value reduces also from 1 to this 1. So, 1 means there is no correction or stress reduction coefficient in this equation is not required 1 means that is at ground surface, but as we go deeper because of flexibility of the soil this stress reduction coefficient needs to be incorporated. One can see Idris in 1999 proposed this line to calculate the value of r d for a certain value of m s which is certain value of v s shear wave velocity 120 meter per second magnitude of moment magnitude of earthquake is about 6.5 p g a value of 0.2 g for that this is the line whereas, shittija etol 2009, kishida etol 2009 mentioned this line to be used whereas, set in etol 2004 mentioned this value to be used whereas, for another range of same soil that is v s value 120 meter per second, but under higher magnitude of earthquake when higher magnitude of earthquake m w of 7.5 is coming at that location these are the values of r d as proposed by different researchers. It is adopted from the research paper of Idris and Bolanje of 2010 one can easily see that there is a wide variation in the value of this r d which can influence this calculated value of this C s r. So, it is a question which is the correct value to calculate this r d. So, in absence of the correct value one can easily use the method proposed by you etol 2001 to calculate the reasonable range or value of r d. In cyclic resistance ratio another parameter C r r at the reference magnitude of 7.5 can be calculated using SPT data of n 160 using this expression which is known as black's equation as proposed by black which is available in the paper of you and Idris 1997 and also you did all 2001. These are the x is in this equation x is nothing but n 160 corrected SPT a n value and various coefficients a b c d e f g h all are mentioned over here. And factor of safety against liquefaction is computed using this expression factor of safety against liquefaction is nothing but C r r 7.5 7.5 is nothing but at the moment magnitude of 7.5. If the earthquake of that zone for which the design is considered is different than 7.5 then corrections due to the magnitude correction needs to be carried out. So, C r r by C s r will give the factor of safety with respect to liquefaction. Using this concept this paper of musk and choudhury in journal of applied geophysics Elsevier classified the three ranges of factor of safety with respect to liquefaction their value to identify or remark their soil as critically liquefiable, moderately liquefiable and non-liquefiable soil. What is critically liquefiable when factor of safety less than 1? When factor of safety is between 1 to 1.3 it is mentioned as moderately liquefiable soil and when factor of safety is greater than 1.3 it is considered as non-liquefiable soil. So, using this ranges of factor of safety for entire Mumbai city in this paper the calculations for factor of safety against liquefaction with respect to depth and with respect to all boreholes were carried out. Finally, this is the GIS based map for entire Mumbai which shows the critically liquefiable area. Critically liquefiable means in these locations in these patches as shown by this color that shows a critically liquefiable area in Mumbai at a moment magnitude of 6. So that means if a moment magnitude of 6 earthquake comes in Mumbai these are the region where soil is going to liquefy as the present scenario is concerned. Critically liquefiable means factor of safety with respect to liquefaction will be less than 1. This is another liquefaction hazard map for Mumbai city which shows for moment magnitude of 7.5 if it comes in Mumbai these are the region where it is going to critically liquefy and one can easily see these are nothing but the areas where it is the reclaimed land. So that is why it is another kind of validation that as we know the reclaimed land or filled up land are more prone or susceptible for liquefaction during an earthquake which is also got validated from the property and from this liquefaction hazard map. So, how people can use this hazard map for further design? So, if somebody is planning to construct any big high rise building in these locations which is quite possible in Mumbai city extra design care and design measure needs to be taken for the foundation design and other design like if somebody is constructing a pile foundation in these locations then pile foundations need to be designed with respect to the liquefiable zone which I am going to discuss in subsequent lecture modules in this course. This table shows the various values of factor of safety against liquefaction for entire Mumbai city as obtained in this journal paper by Mascan Choudhury 2010 in journal of Applied Geophysics in Elsevier publication. One can see these are the different site address like Andheri, Bhandu, Baurivali, Bandra, Mallard, Dahisar etcetera. So, factor of safety against liquefaction for different moment magnitude are mentioned over here like moment magnitude of 5, 5.5, 6, 6.5, 7, 7.5 all values are given over here. One can see the non-bold values are perfectly fine. That means if in Mumbai magnitude of 5, 5.5 earthquake comes there is absolutely no problem in terms of liquefaction is concerned in these mentioned 10 locations in these 10 sites. But if magnitude of 6, 6.5 or more than that comes the soil tends to start liquefying at certain locations like one can see at Bhandu West if a magnitude of earthquake magnitude 7.5 comes the soil is going to critically liquefy that is it is going to fully liquefy that means the factor of safety less than one even at magnitude 7 also. Similarly, for other locations also the values are given over here which is very much useful for any designers to utilize this concept to further take protection and necessary design steps and methodology and construction steps for earthquake resistant design in and around Mumbai city using this data. So in concluding remarks we can say that typical shear wave velocity what we have obtained for the soil in Mumbai region between 3 meter to 10 meter range varies typically between 140 to 350 meter per second. And typical areas like Kandivali, Borivali, Goregaon, Malad of Mumbai city can be prone to critically liquefiable condition when an earthquake magnitude of 7.5 hits in and around Mumbai. The soil amplification factor for Mumbai which has been obtained earlier it can range between 2.5 to 3.5 if a similar type of Bhuj earthquake motion of 2001 hits Mumbai city. And from this known knowledge of geotechnical earthquake engineering one can further take precautionary measure to find out what are the significant effect of depth of this liquefying layer which needs to be considered for design of pile foundation and any other type of foundation even for shallow foundation also which are necessary to incorporate in the design. So with this we have come to the end of present module, module number 6. We will continue further in our next lecture.