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Next is your geophysical method; it is used for location of different strata, location
of different strata, soil strata, also used for location of water table also; it is an
approximate method. In geophysical method, there are two methods; 1 is there are 2 methods;
one is seismic method, other is your reflection method. Now part a, seismic method, let us
say 3 layers of soil say, layer 1, layer 2 and this is your say layer 3; A, B, C, where
geophones many installed regular interval in the ground surface.
This is v 1, v 2, v 3; v 1, v 2, v 3, then v 2, then v 1. So, this is o, this point is
o.
What is the procedure? Procedure is first shock wave generated at point or created created created by a hammer, say at
point o. Then a shock wave travels through soil, the observation of first wave, first
arrival wave first arrival wave recorded by geophones located at point A, B, C; geophone
converts, it converts ground vibration ground vibration to electrical impulse, and transmitted
to your recording apparatus. Assumption is shock wave increases as depth increases as
depth increases; so, in this case v 3 is greater than v 2 is greater than v 1.
Now if we look at this seismic method, first of all geophysical method, this is an approximate
method, so used to find it out the different soil strata like if there is a ground surface
here, suppose there are 3 layers; layer 1, layer 2, layer 3; at what distance, at at
what distance from the ground surface say x 1, say x 2 or say x 3, how do you know that
at what distance at the ground surface below here, the sub soil, soil strata changes? It
can be done there are various methods by means of boring, auger boring or hand boring you
can do it or you can do it also geophysical methods without doing any boring. So as this
is an approximate method, there are also limitations; in this case, geophysical method has again
two two methods; 1 is your seismic method, other is your reflection method.
In seismic method, what is the procedure? If we look at here, in seismic method, wave
is created, this is called shock wave is created that means, suppose let us say this is point
o; at point o, shock wave has been created by means of hammer; here you hammers and shock
wave you created. At the same time, from this, this is called source; from source at equal
distance, you put geophones A, B, C, you put this geophones. Then what will happen? The
moment shock wave you create, it will first travel from here to here, it will be receiving
by this by velocity v 1, first geophone located at point A. Then the shock wave also will
travel at an at at a velocity v 1 in layer 1, then it will reflected in layer 2, then
again it will be refracted, so that you will receive wave at point B similarly, for third
layer, it will go you will receive wave at point C.
So first arrival means the movement you start create the shock wave from this, from ground,
from here source to here, this is source, and these are receivers. In this receivers,
first arrival of this waves at this from this point to here, it will be received at station
A, B and C. So, what is the principle of geophone? Geophone whatever located here, it converts
ground vibration, what happen? It converts the vibration to electrical impulse that means
ground vibration will be created by from the source by means of impact, and it will by
impact this vibration will start from layer 1 layer 2 layer 3; so, it will convert this
ground vibration to electrical impulse, and it record as an receiver, how much time, it
takes to receive this waves? Then this another limitations you can say
the assumptions is shock wave to be increases as depth increases; that means v 3 is greater
than v 2 is greater than v 1; v 3 is your velocity at layer 3 is greater than velocity
at layer 2 is greater than velocity at layer 1. Let us say this, how this how you are going
to find it out H 1 and H 2. This is my layer 1, and height is called let us say this height
is called H 1, and this height is called H 2, and this height is called H 3.
If I plot this arrival time for first wave, arrival time for first wave say t, so distance
from the source, it is distance from source, this is alpha 1, alpha 2, alpha 3, x 1, x
2; if I write this is my v 1 and this is your v 2 - tan alpha 2, v 3 is equal to tan alpha
3; this will be we can say t 1 plus t 2 arrival time say, this is my t 1, this is my t 2.
For a certain distance say x 1, x 1,the direct wave in layer 1, layer 1, the direct wave
in layer 1, for a certain distance x 1, it reaches first, it reaches first. Similarly,
at this point two lines intersect, which indicate direct wave travelling at an distance with
your velocity v. If we look at here from this graph, these two points intersect; here is
your direct wave you are getting at an distance velocity v 1; this is your x 1.
Now similarly, at a distance time t 2, so refracted wave travelling with velocity v
1 and v 2 at a distance 2 h 1; if you look at here from here to here, it is your direct
wave you are receiving by means of geophone at an distance x 1, it comes first. Now come
to layer 2 that means in this case only h 1, in this case h 1 and h 2, it is travelling
what is the travelling distance? This is v 1, v 2 and v 3; v 1, v 2 and v 1, not this
is v 3; v 1, v 2 and v 1, to v 1 plus v 2; it is travelling with a distance H 1 plus
H 2. Now if I write x 1 by v 1, x 1 by v 1 is nothing but if I write x 1 is your distance
travel from to here to here by v 1 that is your time, that is your time t, which is equal
to also, which is equal to also 2 H 1 by v 1, because in case 1, case 1 you are getting
direct; in case 2, the wave is from this source it is travelling twice at the velocity v 1
and v 1. So, it will be 2 h 1 by v 1 plus x 1 by v 2 plus x 1 by v 2, which is equal
to again this is time t, you can get it from here, h 1 is equal to v 2 minus v 1 by v 2
into x 1 by 2. If I plot a graph between arrival time for
first wave t versus distance from the source; if you look at here, first this is this is
your first, it is your source. From here to here how much time it takes? It takes t 1;
from here to here it takes which is equal to distance travelled. What is your distance?
Distance is from here to here let us say x 1; so x 1 by v 1 that is your time. At the
same time at the same time, if you look at here at the same time, time t 1, because it
is within this frame of time t 1, this and this. At the same time, what will happen?
It travel from here to here with velocity v 1, then reflected with velocity v 2, then
refracted with velocity v 1; that means twice twice there is velocity v 1 with a height
of H 1. So 2 H 1 by v 1 that means it travel a distance,
in this case H 1 become a distance, here x 1 become a distance; in this case h 1 become
a distance, because it travel it travel from here to here that means it covers the distance
H 1, then it reflected, then it travel with a distance say x 1, then it then it it again
refracted back, again it travel with a distance H 1; that means 2 h 1 by v 1 x 1 by v 2 this
your time, from where you can get it, how much is your distance or may be H 1. At what
distance from the ground surface the layer changes that you will get it from this graph.
Similarly, similarly, you can find it out H 2; how do I get it H 2? I will take this,
this, this, this as well as this and this; that means in this case H 2, it will travel
from here to here with a distance H 1, in this case to find it out H 2, if you look
at here the source from layer 1, layer 2, layer 3, again it refract; that means H 1,
H 1 that means 2 H 1, 2 H 1 by v 1; then H 2, this is your v 2, then H 2 that means 2
H 2 by v 2 plus v 3 v 3 x 2 v 3 x 2 that means x 2 by v 3. Then you can easily find it out
what is the value of H 2? There are also empirical relations by means of impact shock, this is
given by this graph has been drawn based on your reflection as well as refraction by empirical
or impacts shock.
For impact shock, by means of empirical relation H 1 is equal to x 1 by 2 v 2 minus v 1 by
v 2 plus v 1; similarly, distance H 2, as I said distance H 2, how do you get it? H
2 is equal to 0.85 H 1 plus x 2 by 2 root over v 3 minus v 2 by v 3 plus v 2. So similarly,
you can find it out H 2 also by the method of principle of reflection and refraction,
so there are two assumptions in this case you can say, one assumption is that the movement,
the movement your shock wave generate, the movement shock wave generate, it will travel
by means of reflection or refraction, that is your one assumption; that means from here
this wave will generate, it will go, it will reflected here, again it will come start travel,
again it will be refracted and it will go; this is case 1. Case 2 is that impact shock;
it will travel impact by means of here and there by impact. So by means of method of
reflection and refraction, you can find it out H 1 as well as H 2; so H 1 I can get it,
v 2 minus v 1 by v 2 into x 1 by 2; H 2 I can get it 0.85 H 1 plus x by 2 v 3 minus
v 2 divided by v 3 plus v 2 root over.
Now, there are some standardizations; materials, then this is the velocity meter per second;
sand, sandy clay, gravel, rock, water in loose material, sand stone, then lime; in sand,
it is 180 to 365, sandy clay - 365 to 580 and gravel - 490 to 790, then your rock, rock
is your 400 to… Rock there are different types I can write rock tales 400 to 760, water
in loose material it is 1400 to 1830, then sand stone - 915 to 2750, then lime stone
lime stone is 1830 to 6100. These are well develop means, if this materials suppose say
I got the velocity, I got the distance H is like whatever the distance may be 2 meter,
5 meter, but whatever I get it from the velocity from here with this time, I get 1080 to 365
velocity meter per second square; that means it will say that with this distance H 1, there
is a sand layer, if it is 1080 to 365, then you can say this is sand layer; suppose it
is said like 1400 meter per second in that case, you can say that there are some loose
sand with water; that means water is there, with water is there loose sand with water
is there; so with this materials this has been standardized, so there are also limitations,
what is your limitations?
This method has also limitation; cannot use hard strata with a greater seismic velocity over lies
softer, cannot use hard strata lying over softer strata, cannot use area covered by
concrete, cannot use frozen soil. Case 1, it says cannot use hard strata lying over
soft strata; so it is if there are hard strata, then this is soft strata, so what will happen?
The hard strata it will refract, and whatever wave come to the soft strata, it will absorb
all these things; that means it should be soft, slightly softer, then this will be slightly
harder; this kind of assumptions should be there. Cannot use area covered by concrete,
if this area has been covered by concrete, this wave may not propagate beyond the concrete;
also cannot use this frozen soils; in European countries where the soil becomes always frozen
state, this method cannot be used.
Now we will go for solving one example; example from this seismic reflection method, refraction
method, so it says a seismic refraction study of an area has the given following data. So,
this is your distance from impact point point to geophone; time to receive waves; it is given 15, this is
in terms of meter, 15 meter 30 meter, and time to receive in you can say second, 15
30 60 90 120 and 0.025 0.05 second 0.10 0.11 and 0.12. So, what has been asked? Plot time
data, find find seismic velocity for surface and underlying layer; then find thickness
of upper layer. Now, with this data, first you plot your time versus this distance, travel
distance
This your 60, this is one point, this is other point, 15, 0.025 second, this is your say
30, this gives how much? 0.05; increase it, it gives 60, then it will go up to 0.10. Then
afterwards 90, this will give 0.11, then 0.12 and this will gave 120; this is your distance,
and this is fine time. First plot your time versus distance, you will find it out there
is a breakage in this line, clearly there is a reflection; if there is a reflection,
the line will change its path. So first up to 0 to 60; second, it goes straight line
with increase in with increase in time, the distance increases it goes straight line;
after 60 there is a reflection, you will find it out there is a reflection, so this is given
well documented and you can find it out say this is my v 1 and this is my v 2.
Now you can calculate from this formula v 1 is equal to 60 minus 15, 60 minus 15 divided
by 0.10 minus 0.025; velocity is equal to distance by time, so distance 60 minus 15,
so it will be 45 and 0.025 minus 0.1, so this will give 600 meter per second; similarly,
v 2 from this graph, I can find it out 120 minus 60 minus 60 divided by what is the time,
corresponding to the time 0.12 minus 0.10; it will be 3000 meter per second. Now this
is the velocity means, velocity profile you will get it, velocity is nothing but this
is your distance by time; from this graph distance by time, you can easily calculate
your velocity. Now once you will get velocity, then you can
calculate from here, what is your time means, what is your thickness H 1 as well as h 2.
Now find it out H 1, which is equal to x 1 by 2 root over of v 2 minus v 1 by v 2 plus
v 1; so which is equal to 24.5 meter; as it has been asked, thickness of only upper layer
in the question may be thickness of lower layer you can calculate. So the question is
plot time data, find seismic velocity for the surface and underlying layer; that means
this under lying layer is this is your under lying layer, because this velocity profile
it says it reflected; so v 1 and v 2 we calculate, then from there H 1 has been calculated.
Then with this v 1 and v 2, with this velocity, can we predict, what is the material? Or what
kind of soil it is, say soil 1, soil 2. As I said earlier from the chart as v 1 say 600
meter per second, so may be hard clay or maybe you can say clay, as it is 3000 meter per
second, it will be a sand rock; based on the velocity profile, whatever velocity we get
it, you can classify it may be hard clay and bottom one is sand rock. That means with this
method you will get, you can you can predict what is the probable of soil, what kind of
soil it would be; it may be a hard clay and layer 2 is sand rock; based on the clay means
detail detail soil classification you can confirm, whether it is hard clay or sand rock.
Then for soil 1, layer 1 and layer 2, thickness can be find it out; the thickness is your
first layer thickness is your 24.5 meter. Once you find this thickness, you can say
that up to this thickness, hard clay is there, beyond this it refracts; this has been refracted
or reflected. So, H 1 and H 2 we can easily find it out as well as what kind of material
is there inside, you can find it out