Foundation Design Principles and Practices 3e
Donald Coduto, William Kitch, Man-chu Ronald
Yeung (Solutions Manual All Chapters, 100%
Original Verified, A+ Grade)
Chapter 1 has no Solutions manual
Chap. 2 Uncertainty and Risk in Foundation Design
2.1 Classify the uncertainty associated with following items as either aleatory or epistemic and
explain your reason for your classification: average wind speed over a 30 day period, location of
a certain applied load, change in strength of a soil caused by sampling method, capacity
determined by a certain analysis method, magnitude of live load caused by vehicles travelling on
a bridge, soil shear strength as measured by a certain method.
Solution
• Uncertainty of the average wind speed is aleatory. This is a random process that we
cannot affect.
• Uncertainty of location of an applied load is mostly aleatory. There is a certain accuracy
with which a structure can be built and the designer had little or no control over this
accuracy. In theory there is some epistemic uncertainty in that could be reduced with
better construction techniques, but from a practical standpoint this uncertainty is aleatory.
• Uncertainty in the change in strength of a soil caused by sampling method is an epistemic
uncertainty. Improved sampling techniques can reduce this uncertainty.
• Uncertainty in the capacity determined by a certain design method is generally epistemic.
With improved analytical tools we can reduce this uncertainty.
• Uncertainty in magnitude of live load caused by vehicles travelling on a bridge is
inherently aleatory. This is a random process which we cannot affect.
• The uncertainty in the soil shear strength as measured by a certain method is a
combination of epistemic and aleatory uncertainty. The uncertainty caused by the quality
of the equipment used and the care of the technician making the measurement is
epistemic and can be reduced by the use of more precise equipment and better training of
the technician. However, there is aleatory uncertainty in the soil strength inherent in the
natural processes that created the soil.
, Chap. 2 Uncertainty and Risk in Foundation Design
2.2 Figure 2.1 shows the PDF for a normal distribution determined from the unconfined compression
tests shown in the histogram. Does the mean and standard deviation of this PDF represent
aleatory or epistemic uncertainty? Explain.
Solution
The mean and standard deviation of this PDF contain both aleatory and epistemic uncertainty.
The mean of 20.8 and standard deviation of 7.30 are estimate valued of the true mean and
standard deviation of the unconfined compressive strength of this sandstone. The epistemic
uncertainty is associated with the number of samples used to estimate the parameters. If we had
taken more samples, we would have better estimates. However, this particular sample obviously
contains a large number of measurements. Therefore the estimated standard deviation is
probably very close to the aleatory uncertainty and testing more specimens is unlike to reduce
the uncertainty significantly.
Solutions Manual
Foundation Engineering: Principles and Practices, 3rd Ed 2-2
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from
the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying,
recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458
, Chap. 2 Uncertainty and Risk in Foundation Design
2.3 List three sources of epistemic uncertainty associated with determining the soil strength at a
given site and describe how you might reduce these uncertainties.
Solution
Source How do reduce
Small sample size Take and test more samples
Sloppy laboratory techniques Improve laboratory methods
Old or poor quality testing equipment Acquire improved testing equipment
Disturbance of soil samples before or Use better sampling and testing methods
during testing
Mixing up results from different samples Improve documentation methods to
eliminate mixing up samples
Solutions Manual
Foundation Engineering: Principles and Practices, 3rd Ed 2-3
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from
the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying,
recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458
, Chap. 2 Uncertainty and Risk in Foundation Design
2.4 Using a random number generator create a sample of 4 relative densities using the PDF
presented in Figure 2.2. Repeat the exercise to create 3 different sample sets. Compute the mean
and standard deviation of your sample. Compute the mean and standard deviation of each
sample set. Compare the means and standard deviations of your samples with each other and
with the mean and standard deviation of the original distribution. Discuss the differences among
the sample sets and the original distribution, including the type of uncertainties you are dealing
with. How many samples do you think are needed to reliably determine the mean and standard
deviation of the relative density of this particular soil?
Solution
There are an infinite number of solutions to this problem. The table below shows Excel
spreadsheet formula that can be used to generate the random sample sets.
A B C D
1 µ σ N Z
2 94.9 5.7 =NORM.S.INV(RAND()) =$A$2+$B$2*C2
3 =NORM.S.INV(RAND()) =$A$2+$B$2*C3
4 =NORM.S.INV(RAND()) =$A$2+$B$2*C4
5 =NORM.S.INV(RAND()) =$A$2+$B$2*C5
6 µ =AVERAGE(D2:D5)
σ =STDEV.S(D2:D5)
The table below shows three sample sets generated with the Excel spreadsheet shown above.
Note that the average of the samples ranges from 6.5 below the distribution mean to 6.8 above it.
Also one estimate of the standard deviation is nearly twice that of the original distribution. It is
possible, using sampling theory, to determine the number of sample required to have a certain
confidence level in the estimated parameters. However, this is well beyond the scope of this text.
Students should note that increasing the sample size to 3 to 7, significantly reduces the variability
of the estimated mean and standard deviation.
Sample # Trial 1 Trial 2 Trial 3
1 107.34 92.44 95.79
2 98.75 78.47 83.10
3 101.50 100.55 83.95
4 99.02 102.07 90.80
Sample mean 101.65 93.38 88.41
Sample Standard Deviation 3.99 10.80 6.01
Solutions Manual
Foundation Engineering: Principles and Practices, 3rd Ed 2-4
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from
the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying,
recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458
Donald Coduto, William Kitch, Man-chu Ronald
Yeung (Solutions Manual All Chapters, 100%
Original Verified, A+ Grade)
Chapter 1 has no Solutions manual
Chap. 2 Uncertainty and Risk in Foundation Design
2.1 Classify the uncertainty associated with following items as either aleatory or epistemic and
explain your reason for your classification: average wind speed over a 30 day period, location of
a certain applied load, change in strength of a soil caused by sampling method, capacity
determined by a certain analysis method, magnitude of live load caused by vehicles travelling on
a bridge, soil shear strength as measured by a certain method.
Solution
• Uncertainty of the average wind speed is aleatory. This is a random process that we
cannot affect.
• Uncertainty of location of an applied load is mostly aleatory. There is a certain accuracy
with which a structure can be built and the designer had little or no control over this
accuracy. In theory there is some epistemic uncertainty in that could be reduced with
better construction techniques, but from a practical standpoint this uncertainty is aleatory.
• Uncertainty in the change in strength of a soil caused by sampling method is an epistemic
uncertainty. Improved sampling techniques can reduce this uncertainty.
• Uncertainty in the capacity determined by a certain design method is generally epistemic.
With improved analytical tools we can reduce this uncertainty.
• Uncertainty in magnitude of live load caused by vehicles travelling on a bridge is
inherently aleatory. This is a random process which we cannot affect.
• The uncertainty in the soil shear strength as measured by a certain method is a
combination of epistemic and aleatory uncertainty. The uncertainty caused by the quality
of the equipment used and the care of the technician making the measurement is
epistemic and can be reduced by the use of more precise equipment and better training of
the technician. However, there is aleatory uncertainty in the soil strength inherent in the
natural processes that created the soil.
, Chap. 2 Uncertainty and Risk in Foundation Design
2.2 Figure 2.1 shows the PDF for a normal distribution determined from the unconfined compression
tests shown in the histogram. Does the mean and standard deviation of this PDF represent
aleatory or epistemic uncertainty? Explain.
Solution
The mean and standard deviation of this PDF contain both aleatory and epistemic uncertainty.
The mean of 20.8 and standard deviation of 7.30 are estimate valued of the true mean and
standard deviation of the unconfined compressive strength of this sandstone. The epistemic
uncertainty is associated with the number of samples used to estimate the parameters. If we had
taken more samples, we would have better estimates. However, this particular sample obviously
contains a large number of measurements. Therefore the estimated standard deviation is
probably very close to the aleatory uncertainty and testing more specimens is unlike to reduce
the uncertainty significantly.
Solutions Manual
Foundation Engineering: Principles and Practices, 3rd Ed 2-2
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from
the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying,
recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458
, Chap. 2 Uncertainty and Risk in Foundation Design
2.3 List three sources of epistemic uncertainty associated with determining the soil strength at a
given site and describe how you might reduce these uncertainties.
Solution
Source How do reduce
Small sample size Take and test more samples
Sloppy laboratory techniques Improve laboratory methods
Old or poor quality testing equipment Acquire improved testing equipment
Disturbance of soil samples before or Use better sampling and testing methods
during testing
Mixing up results from different samples Improve documentation methods to
eliminate mixing up samples
Solutions Manual
Foundation Engineering: Principles and Practices, 3rd Ed 2-3
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from
the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying,
recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458
, Chap. 2 Uncertainty and Risk in Foundation Design
2.4 Using a random number generator create a sample of 4 relative densities using the PDF
presented in Figure 2.2. Repeat the exercise to create 3 different sample sets. Compute the mean
and standard deviation of your sample. Compute the mean and standard deviation of each
sample set. Compare the means and standard deviations of your samples with each other and
with the mean and standard deviation of the original distribution. Discuss the differences among
the sample sets and the original distribution, including the type of uncertainties you are dealing
with. How many samples do you think are needed to reliably determine the mean and standard
deviation of the relative density of this particular soil?
Solution
There are an infinite number of solutions to this problem. The table below shows Excel
spreadsheet formula that can be used to generate the random sample sets.
A B C D
1 µ σ N Z
2 94.9 5.7 =NORM.S.INV(RAND()) =$A$2+$B$2*C2
3 =NORM.S.INV(RAND()) =$A$2+$B$2*C3
4 =NORM.S.INV(RAND()) =$A$2+$B$2*C4
5 =NORM.S.INV(RAND()) =$A$2+$B$2*C5
6 µ =AVERAGE(D2:D5)
σ =STDEV.S(D2:D5)
The table below shows three sample sets generated with the Excel spreadsheet shown above.
Note that the average of the samples ranges from 6.5 below the distribution mean to 6.8 above it.
Also one estimate of the standard deviation is nearly twice that of the original distribution. It is
possible, using sampling theory, to determine the number of sample required to have a certain
confidence level in the estimated parameters. However, this is well beyond the scope of this text.
Students should note that increasing the sample size to 3 to 7, significantly reduces the variability
of the estimated mean and standard deviation.
Sample # Trial 1 Trial 2 Trial 3
1 107.34 92.44 95.79
2 98.75 78.47 83.10
3 101.50 100.55 83.95
4 99.02 102.07 90.80
Sample mean 101.65 93.38 88.41
Sample Standard Deviation 3.99 10.80 6.01
Solutions Manual
Foundation Engineering: Principles and Practices, 3rd Ed 2-4
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from
the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying,
recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458
