# Mod-06 Lec-22 Dynamic Soil Properties (continued) Part -II

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 of 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 an 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 nonlinearly like this. If we want

to find out the slope of that curve, it 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 secant shear modulus. 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 secant 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 and non-dimensional

parameter in the y-axis. So, maximum value of this G by G max ratio will obviously be

1. As the shear strain increases, which is plotted in the x-axis in the log scale, the

material degradation will show like this for soil. We will say that it is almost close

to 1, G by G max value for very low shear strain. 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 three major methods. One is direct

field measurement by using these techniques or indirect field measurement by using this

technique or laboratory measurement using these techniques. Also from the shear wave

velocity value, that is 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 the various relationships 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 1 60 with respect to G max. Also in the laboratory, one can find out using

resonant column test like this. That is, what is the value of G max at the resonant frequency

from this plot of the distortion at different frequency on the resonant column with 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 cone penetration value, DMT dilatometer test value and PMT pressure

meter test value. So, from each of these tests, we can get these empirical relationships for

different types of soil as proposed by various researchers worldwide. But we need to remember

that these relationships are developed for limited number of dataset point and also for

a typical soil of that region. So, acceptability of these empirical relationships

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 Vucetic

and Dobryin 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 by G max value. Obviously, it is going to decrease as it can be seen from here. 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. 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 Vucetic and Dobry in 1991 for different values of plasticity index for fine

grained soils. Now worldwide, there are developments on the

SPT N value versus the shear wave velocity relationship because many 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 can further 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, Sitharam et al in 2006, proposed

this empirical relationship V s in terms of the corrected SPT N 1 60 value and also corrected

with respect to clean sand. So N 1 60 c s, in terms of that, how one can obtain the V

s value in the absence of the actual data obtained through field test for the V s value.

Also for other types of residual soil and silty sand and sand silt, the upper bound

and lower bound equations were proposed by these researchers. Another group of researchers had proposed

for soil of Chennai region in India, Boominathan 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. Reference

for that, I have mentioned Sumedh Y.Mhaske’s PhD thesis. Dr.Sumedh Mhaske has 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 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. These are the

seven original islands of Mumbai city, which has been combined together by land filling

etcetera over a period of time. This lists the earthquake history in and around

Mumbai city, which has been reported in this journal paper by Mhaske and Choudhury, 2010,

journal of applied geophysics, Elsevier. This GIS based map shows the original seven

islands of Mumbai and the surrounding marshy land that is reclaimed land around Mumbai

city, which actually forms today’s Mumbai city. We will see 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 disastrous earthquake occurred

in the peninsular India is not exactly in Mumbai, but in peninsular India and Mumbai

is also a part of that. The population in Mumbai city is more than 15 million as per

the census of 2011. Active fault zone are present close to Mumbai

like Panvel flexture, Thane 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 Raghukanth

and Iyengar in 2006. So, with these details, we had completed our

previous lecture. 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 Mumbai city, first we should

know Mumbai’s typical soil property. So, to find out the typical soil property,

you can see in this slide. 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. This GIS based map shows the locations of

boreholes, which are collected all around Mumbai city, which is available in the paper

of Mhaske and Choudhury, 2011, geotechnical special publication of ASCE. This is the typical soil profile for Mumbai

city at various locations like Gurgaon, Wadala Andheri, and etcetera. This table shows the various stations, borehole

stations, various soil types, their depth, SPT N value corrected, originally recorded,

corrected, ground water depth and various other soil parameters like amount of gravel,

sand, silt, clay, liquid limit, plastic limit, and specific gravity. So, all these information

were collected from reliable and authentic borehole data from various locations like

Tilaknagar, Chembur, Mulund, Walada and etcetera. This chart shows the worldwide used correlations

available for SPT N value versus the shear wave velocity V s value. For all types of

soil, Obba and Torimani, 1970, proposed this equation of V s versus N. Several other researchers

also, as shown in this table, have mentioned different equations of V s versus N as reported

over here, which are used worldwide extensively. The details are available in this paper by

Mhaske and Choudhury, 2011, in the journal Natural Hazards published by Springer.

So in this, you should again remember that these empirical relationships were developed

based on the soils collected from a particular region and also it is based on 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 exists 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 here that when we want

to develop some particular relationship of that SPT N value versus the shear wave velocity

V s for Mumbai region from the collected borehole data, you can see that these are the typical

average shear wave values all around Mumbai city at various borehole locations, which

are digitized in the GIS map. These details are available in this paper. These stations, soil type, depth and SPT N

value are also shown over here. This is the equation which has been developed for Mumbai

city by Mhaske for his PhD work under my supervision. 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 that 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. This is uncorrected

SPT N value and 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. 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 in Mumbai soil. This result shows the correlations between

shear wave velocity V s in meter per second unit versus the clean sand corrected SPT N

1 60 value. So, this is clean sand SPT N value. You can see, the equation proposed here is

V s equals to 40 N 1 60 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 Dr.Mhaske’s PhD thesis

as reported over here. It was concluded from this study that there is hardly any large

variation or significant variation between the use of original raw SPT N value or corrected

clean sand SPT N value. The same was concluded by previous other researchers. Why? Because

there are 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. It is also verified

and authenticated from the field measurements as shown in this slide. Now, let us see the comparison of various

Indian soils. The different correlationships available between shear wave velocity v s

and uncorrected SPT N value, as reported by four researchers group for four different

cities 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 Anumantrao and Ramana in

2008. 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 Sitharam in 2010, this lower most line with the circle symbol, they

proposed for the Bangalore city, that is V s equals 80 N to the power 0.33. This is the

proposed equation for the soil of Bangalore city.

Maheshwari et al in 2010, as shown by these dark triangles, which is for Chennai city

V s equals to 95.64 N to the power 0.301 is the proposed equation for the soil of Chennai

city. For Mumbai city, the present study shows the results, which is star marked over here.

This one, that is 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 these 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 finally help to compute

the maximum shear modulus G max value from this V s value for that particular region

of soil. That will be finally used for the seismic design of any structures in that locality.

In 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 to be carried out,

the seismic design or earthquake resistant design is necessary to find out this kind

of relationship of V s versus SPT N. Since, 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 is the presence of several obstruction.

If obstruction is present, many times SASW MASW results will give us the wrong result

because it is not giving the result of the that V s value of that particular soil. 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,

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 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 colored patches are nothing but those regions where

shear wave velocity, average shear wave velocity to a particular depth is greater than 100

meter per second. So, one can say that these are relatively stiffer soil as compared to

other regions. These details are available in Mhaske and Choudhury, 2011 Natural Hazards

journal paper in Springer. 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 per second interval, the shear wave velocity

values are plotted and shown over here like 140, 190, 240, 290 etcetera are shown over

here. It 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, typically, remember this

is a 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 engineer to further carryout

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, the G max value can be easily computed by 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, and E with their

descriptions 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 indicate the average shear wave velocity up to 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 NEHRP, standard of 2000 which is nothing but codal guide line or provision as mentioned

in USA and practiced worldwide. So, for soft soil, V s 30 value will be less than or equal

to 180 meter per second. For stiff soil, it is in between 180 to 360 meter per second.

For very dense soil, it is in between 360 to 760 meter per second and so on. So, for

Mumbai soil, a study has been carried out by Dr.Mhaske 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 was found out to

be within the range of 100 to 360 meter per second as mentioned over here. Now, coming to another important sub topic,

that is soil liquefaction. First, I will mention that for a detailed basic understanding of

soil liquefaction, one should refer and listen to my another video course on Soil Dynamics

which is developed for this NPTEL course once again. In that Soil Dynamics video course,

module number 4 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. 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 said to liquefy.

So, in the state of soil liquefaction, soil liquefaction can occur due to several dynamic

loads. Earthquake, is of course one of the reason. So, even due to earthquake liquefaction

can occur. (Refer Slide Ti me: 28:03) Now, let us see soil liquefaction due to earthquake.

Modern liquefaction engineering is developed after Niigata 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 Seed et al

in 2003 are mentioned over here. 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 and lots of understanding about how the soil behave during and after the earthquake.

So, all those information like whether it got liquefied, or if it has been liquefied,

what type of soil was there, and if it has not been liquefied during an 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 and whether it can be further used for construction

of structure or not are important to know assessment of expected liquefaction, induced

deformations and displacements, assessment of consequences of these deformations and

displacement. And 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 susceptibility of the soil

to earthquake induced liquefaction. That is, earthquake intensity and duration, what type

of soil is present there, 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 influence the earthquake

induced soil liquefaction. For liquefaction susceptibility criteria,

there are several methods that can be seen over here. For fine grained soils and as well

as course grained soil, there are various methods to obtain the liquefaction susceptibility

criteria. They are Chinese Criteria and Modified Chinese Criteria, Andrews and Martin Criteria

of 2000, Youd et al 2001 criteria, Seed et al 2003 criteria, Bray et al 2004 criteria,

Bray and Sancio 2006 criteria, Boulanger and Idriss 2006 criteria and various other studies.

So among these, the most important or maximum widely used one is by Youd et al 2001. This

is maximum used worldwide for the liquefaction susceptibility estimation. Now, let us see Chinese Criteria and Modified

Chinese Criteria. Chinese Criteria was developed by Wang in 1979 based on the study by Haichen

and Tangshan 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 equal to 35 percent and

water content should be greater than 0.9 times of liquid limit for that fine grained soil.

This criterion 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, fine soils that

plot above the A line as shown in the figure are considered to be susceptible to liquefaction,

if these three conditions are met. 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 Youd et al 2001 criteria is a combination

of several other researchers findings. This is a kind of report or methodology proposes

which is accepted worldwide. So, Seed et al in 1985 developed the ratio of this CRR versus

CSR curve for granular soil. CRR is cyclic resistance ratio and CSR is cyclic stress

ratio. Regarding 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,

to also go through my another video course on Soil Dynamics, module number 4. We can

get all these basic details there and hence, 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 1 60. So, these are all the collected historical data points of earthquake

from actual field test results, as to where the soil got liquefied and where it did not

get liquefied. 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. Clean sand correction is also required to be computed

to estimate this CRR value from this curve. Seed et all in 2003, they proposed the recommendations

for fine grained soil. That is, plasticity index versus water content to liquid limit

ratio 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, Bray et al in 2004 proposed another

methodology using the similar concept of plasticity index versus water content to liquid limit

ratio like this. It is 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, proposed the criteria based on ten 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 Chi-Chi earthquake of 1999 as reported

by Chu et al in 2004 are also incorporated in that. In the same pattern of plasticity

index verses the water content to liquid limit ratio have been zincified 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 Boulanger

and Idriss 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 PI.

So, 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-grained soils having plasticity index

less than 3 are named as sand like and they can exhibit the cyclic liquefaction type response.

Whereas, for fine-grained soils with plasticity index greater than 7 are named as clay like

material and 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. In between range, that is when

plasticity index is in between 3 to 7, a transition between this sand like to clay like behavior

is proposed to occur. This figure provides the schematic illustration as to 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 grained soils, is based is solely on the plasticity index on the specimens and

r u value, that is pore pressure ratio as it is mentioned over here. Excess pore pressure

ratio 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.

For clay like soil, it 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, and then one can

say it is going through the cyclic mobility. So, this r u based liquefaction susceptibility

definition requires the determination of CSR levels and the duration of excitation. So,

these things are the topic of research even today, in this year 2013. Still further researchers

are carrying out various researches from the collected field test data of liquefied zone,

non liquefied zone, and transition zone, etcetera and also doing laboratory tests and combining

these dataset for result, as many datasets, so that, this interpretation of results and

then further proposing of some new criteria will be valid and can be used by various researchers. Now, let us see seismic liquefaction hazard

map of Mumbai city using this GIS and GPS. The details of this work can be obtained in

this journal paper of Applied Geophysics, Elsevier publication, volume 70(3), page number

216 to 225 by Mhaske and Choudhury. How is the evaluation of soil liquefaction

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. We have discussed here. Then for each borehole location, the soil liquefaction susceptibilities

are estimated using the simplified procedure for evaluation of liquefaction potential.

This simplified procedure was basically proposed by Seed and Idriss in 1971 and further modified

by Youd and Idriss in 1997. The final one is by Youd et al 2001, which is widely used

worldwide as I have mentioned. So, discussion about this simplified procedure to evaluate

liquefaction potential is available in my other video course of N PTEL, which is on

Soil Dynamics. Module 4 of that discusses about this 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,

SPT N value, and shear wave velocity value, unit weight of soil, fines content of the

soil and moisture content. In step 2, evaluate the total vertical stress and effective vertical

stress, that is sigma v and sigma v dash for all potential liquefiable layer within the

deposit. Then, one needs 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 what is the value of this a max for a region.

That a max value can be used. This g is acceleration due to gravity. So, this is just a number

and r d is nothing but stress reduction factor due to flexibility of the soil. This 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

Seed and Idriss 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, so from the

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 one to this one.

So, one means there is no correction or stress reduction coefficient in this equation. It

is not required. One 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, Idriss 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.

Moment magnitude of earthquake is about 6.5 p g a value of 0.2 g. For that, this is the

line. Whereas, Kishida et al 2009 mentioned that this line to be used whereas, Cetin et

al 2004 mentioned that 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 adapted from the research paper of Idriss

and Boulanger 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 CSR. So, the question is, which

is the correct value to calculate this r d. So, in the absence of a correct value, one

can easily use the method proposed by Youd et al 2001 to calculate the reasonable range

or value of r d. Then, let us see another parameter cyclic

resistance ratio, also called as CRR. At the reference magnitude of 7.5, it can be calculated

using SPT data of N 1 60, using this expression which is known as Blake’s equation as proposed

by Blake. It is available in the paper of Youd and Idrisss 1997 and also Youd et al

2001. These are the x s’ in this equation. x is

nothing but N 1 60, corrected SPT N value and various coefficients a, b, c, d, e, f,

g, and h, all are mentioned over here. Factor of safety against liquefaction is computed

using this expression. Factor safety against liquefaction is nothing but CRR 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 correction due to magnitude correction

needs to be carried out. So, CRR by CSR will give the factor of safety

with respect liquefaction. Using this concept, this paper of Mhaske and Choudhury in journal

of Applied Geophysics, Elsevier, classified the 3 ranges of factor of safety with respect

to liquefaction. That is, 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 is less than 1. When factor of safety

is in 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 these 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 that, in

these locations, in these patches as shown by this color, shows critically liquefiable

areas 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 according

to the present scenario. Critically liquefiable means, factor of safety with respect to liquefaction

will be less than 1. This is another liquefaction hazard map for

Mumbai city. It shows for moment magnitude of 7.5, if it comes in Mumbai, these are the

regions where it is going to critically liquefy. One can easily see that these are nothing

but the areas where it is the reclaimed land. So, that is why it is another kind of validation.

As we know, the reclaimed land or field 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 designs. 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 Mhaske and Choudhury 2010 in journal of Applied Geophysics in Elsevier publication.

One can see these are the different site address like Andheri, Bhandu, Boriveli, Bandra, Malad,

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, and 7.5, all values

are given over here. One can see that the non-bold values are perfectly fine. That means,

if in Mumbai, magnitude of 5 to 5.5 earthquake comes, there is absolutely no problem in terms

of liquefaction is concerned, in these mentioned 10 locations. That is, in these 10 sites.

But, if magnitude of 6 to 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 is than 1, even at magnitude 7 also.

Similarly, for other locations also, the values that are given over here, which are very much

useful for any designers to utilize this concept to take further 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. 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 an around Mumbai.

The soil amplification factors 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.

From this known knowledge of geotechnical earthquake engineering, one can further take

precautionary measures 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 an necessary to incorporated in the design. So

with this, we have come to the end of the present module, module number 6. We will continue

further in our next lecture.