CNM16 Soil Dynamics and Seismicity
s
School of the Environment
Semester 1 Examinations 2006 - 2007
CNM16
SOIL DYNAMICS AND SEISMICITY
Instructions to Candidates:
Time allowed: TWO hours
Answer THREE questions only out of FIVE
Data sheets and graph paper supplied
Friday 26 January 2007 9:30-11:30 hours
Page 1 of 12
CNM16 Soil Dynamics and Seismicity
Question 1
(a)
Briefly describe the principles of the reflected and refracted seismic
survey techniques.
(6 marks)
(b)
The geometry of a two layer problem is shown below,
Soil
density 1
seismic velocity v1
H
Rock
density 2
seismic velocity v2
Derive the following expression relating the depth H of the upper layer
in terms of the p-wave velocities v1 and v2 for each layer and the critical
distance xc for the simultaneous arrival of the direct and refracted
(head) waves.
H
xc
2
v2  v1
v2  v1
NB: Snell's law sin ic = v1/v2 and cos2ic+sin2ic = 1 where ic is the critical
incidence angle.
(10 marks)
(c)
A seismic refraction survey was performed to determine the thickness
of a surficial layer of soil over competent bedrock. The results are
tabulated below.
Geophone
Distance of
geophone from
shot location (m)
p-wave arrival
time (msec)
1
2
3
4
5
6
7
8
10
20
30
40
50
60
70
80
10
20
30
40
50
55
57.5
60
From these data calculate:
(i)
the p-wave velocities for each layer
(ii)
the thickness of the surficial layer of soil
Page 2 of 12
CNM16 Soil Dynamics and Seismicity
(17 marks)
Question 2
(a)
Briefly explain how a recurrence law is established and how it can be
used to estimate the return period of an earthquake greater that a
certain magnitude.
(8 marks)
(b)
Earthquakes have been recorded over a 175 year period. From all
available data, it appears that the earthquakes have been distributed
as follows:
MOMENT MAGNITUDE
3–4
4–5
5–6
>6
NUMBER OF
EARTHQUAKES
1790
200
15
3
(i)
By plotting the tabulated data derive the Gutenberg-Richter
recurrence relationship for the region.
(9 marks)
(ii)
What is the probability that at least one earthquake of magnitude
greater than 5.5 in a 10 year period, and in a 200 year period,
will occur?
(8 marks)
(iii)
Determine the earthquake magnitude that would have a 10%
probability of being exceeded at least once in a 50 year period.
(7 marks)
Page 3 of 12
CNM16 Soil Dynamics and Seismicity
Question 3
(a)
Explain what is meant by the terms tangent modulus, secant
modulus and equivalent linear soil model.
(5 marks)
(b)
What limitations are associated with an equivalent linear soil model.
(4 marks)
(c)
Data from a stress controlled triaxial test is presented in the table
below. The test is conducted under undrained conditions such that the
shear strain, 
a ), i.e  = 1.5a
Time
(Secs)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Deviator
stress, q
(kPa)
75
68
49
21
-9
-40
-62
-75
-73
-57
-32
0
21
56
72
75
Axial strain
%
0.11
0.12
0.12
0.1
0.05
0
-0.05
-0.09
-0.12
-0.12
-0.09
-0.05
0
0.05
0.1
0.11
From the experimental results plot the backbone curve for the soil and
determine:
(i)
the secant shear modulus (G) and damping ratio for the test
(10 marks)
(ii)
the secant and tangent shear modulii at 0.05% shear strain
(9 marks)
(iii)
estimate the maximum shear modulus Go
(5 marks)
Damping ratio   
1 Aloop
4 Atriangle
Page 4 of 12
CNM16 Soil Dynamics and Seismicity
Shear stress  = q/2
Question 4
(a)
Explain briefly the following phenomena:
(i)
Flow liquefaction
(ii)
Cyclic Mobility
(10 marks)
(b)
A site investigation of a container port showed 13 - 15m of clean sand
(D50 = 0.29mm) with a permanent water table at about 2.4 m below
ground level. The cone penetration tests (CPT) data for the site is
tabulated below.
Evaluate the liquefaction potential of the site if subjected to a peak
acceleration of 0.15g. Plot the factor of safety against liquefaction with
depth.
Assume that the saturated weight of the soil is 18 kN/m3, and the
stress reduction factor is as given in the table.
(18 marks)
Depth
(m)
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
(c)
Normalised cone
resistance qc1
(MPa)
6.5
5.7
5.2
4.9
5.1
6.3
6.9
7.6
rd
.98
.97
.96
.95
.94
.93
.92
.91
What measures could be taken to reduce the liquefaction potential of
the site described in (b)?
(5 marks)
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CNM16 Soil Dynamics and Seismcity
Question 5
(a)
Briefly explain the four main steps involved in seismic hazard assessment,
highlighting the difference between the Deterministic and Probabilistic
approaches.
(6 marks)
(b)
The site shown below in is located near 4 active seismic sources. The
fault types have been classified as:
Fault A
Fault B
Fault C
Fault D
Normal fault
Strike-slip fault
Strike-slip fault
Reverse fault
(i)
Using an appropriate relationship (Wells and Coppersmith)
determine the likely moment magnitudes (M) for each fault or linear
segment of fault (assuming only the linear segments may rupture at
any one time).
(6 marks)
(ii)
Using this information together with an appropriate attenuation
relationship perform a deterministic seismic hazard assessment
analysis and calculate the maximum peak horizontal acceleration
that might occur at the site.
(21 marks)
(70, 50)
Fault A
(70,40)
(0, 40)
(20,30)
Fault B
(50,30)
(0,20)
(50,20)
Fault C
(62, 20)
Site
(60,15)
(10,10)
Fault D
(40,0)
(co-ordinates in km)
Page 6 of 12
CNM16 Soil Dynamics and Seismcity
Data Sheet:
SEISMIC HAZARD AND ATTENUATION RELATIONSHIPS
Attenuation relationships
Cornell et al.
ln PHA (cm/s/s) = 6.74 + 0.859M - 1.80ln(R+25)
M = Earthquake magnitude; R = Site to source distance.
Empirical relationships between moment magnitude (M) and surface rupture
length (L in km)
Wells and Coppersmith
Fault type
Strike-slip
Reverse
Normal
Relationship
M = 5.16+1.12 log L
M = 5.00+1.22 log L
M = 4.86+1.32 log L
Guttenberg - Richter Recurrence Law:
log m = a - bM
m = mean annual rate of exceedance: M = Earthquake magnitude
PSHA:
Poisson Model:
The probability P[ ] of a random variable N, representing the number of
occurrences of a particular event during a given time interval is given by
PN  n 
 n e  t
n!
where  is the average number of occurrences of the event in the time interval
If  is the average rate of recurrence of an event (EQE) in the time interval t
then

t n e  t
PN  n 
n!
Page 7 of 12
CNM16 Soil Dynamics and Seismcity
The probability of occurrence of at least one event in the time period t is given
by
PN  1  P[ N  1]  P[ N  2]  P[ N  3]  ...  P[ N  ]
 1  P[ N  0]  1  e t
P[ N  1]  1  e t
Using a recurrence law to describe the rate of recurrence of a particular
earthquake magnitude, then the probability of at least one exceedance in a
period of t years is given by
P[ N  1]  1  e  mt
GROUND RESPONSE
Solution to shear beam equation Gazetas (1982), assuming power law
variation of shear modulus.
m
 
 z 
 n  ss n (4  m)( 2  m)
G ( z )  Gb  
H 8
H
 n  n th circular frequency
Fundamenta l period
Tm 
16
H
(4  m)( 2  m)  m  ss
Values of n for first four modes of vibration of earth
dam/embankment for Gazetas solution model
n
m
0
1/2
4/7
2/3
1
1
2.404
2.903
2.999
3.142
3.382
2
5.520
6.033
6.133
6.283
7.106
3
8.654
9.171
9.273
9.525
10.174
4
11.792
12.310
12.413
12.566
13.324
Page 8 of 12
CNM16 Soil Dynamics and Seismcity
SEISMIC REFRACTION
For horizontal strata
Depth to refractor, z
z
xc
2
v2  v1
v2  v1
where xc is the cross-over point for direct and critically refracted arrivals
Time
Travel time curve
Distance
xc
Page 9 of 12
CNM16 Soil Dynamics and Seismcity
For dipping strata (refractor surface)
Angle of incidence of critically refracted
ray
1
v
v 
 c   sin 1 1  sin 1 1 
2
v
v

d
u

Angle of dip of strata (refractor)
1
v
v 
   sin 1 1  sin 1 1 
2
v
v

d
u

v1 = seismic velocity in layer 1
vd = apparent down dip seismic velocity
vu = apparent up dip seismic velocity
Page 10 of 12
CNM16 Soil Dynamics and Seismcity
LIQUEFACTION
Seed and Idriss (1971) Simplified Liquefaction Evaluation Method
 cyc  0.65
a max
 v rr
g
 cyc  CSRL v'
L
CSRL = critical stress ratio for liquefaction
Magnitude stress correction factors for Cyclic stress approach
Magnitude M
5.25
6
6.75
7.5
8.5
CSRM/CSRM=7.5
1.5
1.32
1.13
1
0.89
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CNM16 Soil Dynamics and Seismcity
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