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Computer Analyses of
Foundation Design
Investigation of the Utilization of Matlab to
Perform Foundation Design Analyses
A Graduate Final Paper for the Following Course:
Class: CEE 598 Topic: Foundations
Class Number: 75065
Instructor: Dr. Claudia Zapata
Meeting Times: TTh 10:30 a.m. to 11:45 a.m.
Semester: Fall 2012
Prepared For:
Dr. Claudia Zapata
Asst Professor
Sch Sustain Engr & Built Envrn
Faculty
Prepared By:
Joseph Harrington
Undergraduate Student
Ira A. Fulton School of Engineering
Barrett, the Honors College ASU
1. Abstract
This report investigates the use of a Matlab script to perform common, repetitive
foundation design calculations. An important contribution to the consultant
engineering business stemming from this research is the amount of time, and
subsequently, money, that implementation would provide. Common equations and
typical soil properties were compiled to write the script. The typical, or default, soil
properties incorporated into the program provides the user with the ability to
quickly analyze certain conditions for a location that may not have a geotechnical
report at that time, or may never due to the size and scope of the project. The result
of this research is the Foundation Design Program. It was determined this program
successfully analyzes bearing capacity and settlement conditions and would save
engineering firms a substantial amount of time if they chose to implement it.
Table of Contents 1–
Sections
1. Abstract ............................................................................................................................................ 1
2. Introduction ................................................................................................................................... 5
3. Background .................................................................................................................................... 5
4. Data Collected ............................................................................................................................... 8
5. User’s Guide ................................................................................................................................ 15
6. Conclusions ................................................................................................................................. 27
7. Recommendations ................................................................................................................... 28
8. List of Appendices.................................................................................................................... 30
Table of Contents 2–
List of Tables
i. Table 1- Typical Values for Soil Properties (Part 1 of 3) ...................................... 12
ii. Table 2- Typical Values for Soil Properties (Part 2 of 3) ...................................... 13
iii. Table 3- Typical Values for Soil Properties (Part 3 of 3) ...................................... 14
Table of Contents 3–
List of Figures
i. Figure 1- Notation for Vesic’s Load Inclination ......................................................... 10
ii. Figure 2- Selection of the Length Unit ........................................................................... 15
iii. Figure 3- Selection of the Force Unit .............................................................................. 15
iv. Figure 4- Depiction and Corresponding Text for Examples ................................ 16
v. Figure 5- Example 2 Soil Profile........................................................................................ 18
Table of Contents 4–
List of Equations
Equation 1- Allowable Bearing Pressure ......................................................................... 8 1.
Equation 2- Eccentricity of Bearing Pressure ............................................................... 8 2.
Equation 3- Min and Max Bearing Pressure ................................................................... 9 3.
Equation 4- Terzaghi’s Bearing Capacity (Square Foundations) ......................... 9 4.
Equation 5- Terzaghi’s Bearing Capacity (Continuous Foundations) ............... 9 5.
Equation 6- Terzaghi’s Bearing Capacity (Circular Foundations) ....................... 9 6.
Equation 7- Vesic’s Bearing Capacity ................................................................................ 9 7.
Equation 8- Ultimate Consolidation Settlement (NC Soils) ................................. 11 8.
Equation 9- Ultimate Consolidation Settlement (OC Soils – Case I) ................ 11 9.
Equation 10- Ultimate Consolidation Settlement (OC Soils – Case II) ............ 11 10.
Equation 11- Allowable Differential Settlement ....................................................... 11 11.
Table of Contents 5–
List of Examples
5A. Example 1 – Problem 2.14 ................................................................................................... 17
5B. Example 2 – Example 3.4...................................................................................................... 18
5C. Example 3 – Problem 5.5 ...................................................................................................... 21
5D. Example 4 – Problem 6.4 ...................................................................................................... 23
5E. Example 5 – Problem 6.6 ...................................................................................................... 25
Table of Contents 6–
List of Appendices
A. Appendix A – References ...................................................................................................... 31
B. Appendix B – Spreadsheet Program Output ............................................................... 32
C. Appendix C – Foundation Design Program Script .................................................... 33
Table of Contents 7–
List of Symbols
Symbol Description
q Allowable Bearing Pressure
P Vertical Column Load
Wf Weight of Foundation
A Base Area of Foundation
uD Pore Water Pressure at Bottom of Foundation
e Eccentricity
M Applied Moment Load
B Footing Width
qult Ultimate Bearing Capacity
c' Effective Cohesion for Soil Beneath Foundation
ɸ’ Effective Friction Angle for Soil Beneath Foundation
σzD’ Vertical Effective Stress at Depth D Below Ground Surface
γ' Effective Unit Weight of the Soil
D Depth of Foundation Below Ground Surface
δc Ultimate Consolidation Settlement at the Ground Surface
Cc Compression Index
Cr Recompression Index
e0 Initial Void Ratio
H Thickness of Soil Layer
σz0’
‘
Initial Vertical Effective Stress
σzf’ Final Vertical Effective Stress
δDa Allowable Differential Settlement
Өa Allowable Angular Distortion
S Column Spacing (Horizontal Distance Between Columns)
Computer Analyses of Foundation Design
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2. Introduction
This report investigates utilizing Matlab to perform foundation design analyses. This
is an important aspect of engineering because nearly every engineering project
requires geotechnical analyses. Furthermore, the Matlab script, the Foundation
Design Program, was designed to expedite repetitive processes common to this
essential aspect of engineering projects. This report contains a user’s guide, which
provides a thorough explanation of the Foundation Design Program along with
multiple examples covering the extent of the program’s capabilities.
3. Background
Successful consultant engineering firms are able to complete projects at a high
quality and a lower rate than their competitors. Typically, this is accomplished by
applying aspects from previous projects to the current project. Therefore, it is clear
that the ability to expedite repetitive processes has a large impact on the success of
all consultant engineering firms. This is because it enhances the chances for
selection for a project by allowing the firm to charge, or bid, a cheaper price
resulting from the reduced amount of time on these tasks. For these reasons, this
report includes research into applications of expediting processes to foundation
design were researched. This report includes the findings.
Computer Analyses of Foundation Design
Foundation Design 6 Fall 2012
Graduate Final Paper
The most common program that is used by consultant engineering firms to
complete repetitive tasks is Microsoft Excel. While there are many reasons for this,
one of the main reasons is its convenience with formatting results into reports. In
addition, the familiarity with Microsoft Excel also leads to its wide use. However, as
entry-level engineers become increasingly proficient with computer programs,
other programs have emerged that transcend the capabilities of Microsoft Excel.
One of these programs is Matlab. Matlab provides more freedom with the design of
the program, including enhanced graphical user interface possibilities. Due to the
fact that the intent of this research was to expedite processes, it was determined
that utilizing Matlab to perform the analyses was desirable. While part of the reason
for this selection was convenience for programming complex, iterative calculations,
the primary reason was the integration with consultant engineering firms.
The opportunities for decreasing calculation time are typically with professional
engineers that have been in the industry for many years. With these opportunities,
the issue is not technical competency, but rather these engineers comprising
previous generations are typically not as accustomed to utilizing computer
programs to perform repetitive calculations. They are used to completing the
calculations by hand and due to the accuracy, are satisfied with the result and
subsequently, the process. However, as younger engineers are coming into the
industry with computer literacy integrated into their educational experience, they
are able to perform repetitive calculations quickly and efficiently. While accuracy of
engineering calculations is always in high demand, the speed is of particular interest
to many engineering firms with the recent economic issues. With lower budgets on
projects, firms are under more pressure to utilize their time as efficiently as
possible. This shows the necessity for senior engineers to become integrated with
computer based analyses. Unfortunately, some of these engineers have such a steep
learning curve that they are not able to utilize extremely useful Excel spreadsheets
due to their unfamiliarity with the program. With Matlab, this is not an issue
because of the graphical user interface capabilities.
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From this research, a code, or script, was created that provides the user with the
ability to analyze allowable differential settlement, consolidation settlement,
bearing pressure, and bearing capacity. This report contains a user’s guide that
provides instructions to ensure the user understands the intent of each input.
Because the interface is very intuitive, it is expected that most users will not require
this user’s guide to utilize the program. However, in the case of the older generation
of engineers described previously, it will be a convenient reference. This program
allows engineering firms to save time in multiple ways. Firstly, it completes tedious,
repetitive calculations that are typical to all foundation design projects. Also, it
includes typical values for certain soil and other relevant conditions from reputable
sources. The intent of including these standard values also has multiple applications.
In the event that a small project also has a likewise budget, a geotechnical analysis of
the site may not be included in the scope. Therefore, if the engineer is advised to be
conservative with analyzing the site conditions, this program provides the user with
conservative, typical values for certain conditions that will be useful for design.
Another benefit of having standard values in the program is it provides a quick
estimate of the performance to be expected at the site before a thorough analysis is
needed. This could help with estimating bids and efforts that a design firm would
need to allocate to a particular project based on these quick results. Overall, this
program performs necessary analyses to save time and money for its users.
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4. Data Collected
Completion of the Foundation Design Program required a number of equations used
to complete the aforementioned repetitive calculations. It should be noted that
while each of the following equations are not cited individually, they are each taken
from the Coduto Textbook, which is supplemental to the CEE 598 course.
Additionally, descriptions of the variables included in the following equations (with
the exclusion of the bearing capacity factors) are defined in Table of Contents 7.
Finally, although intermediate calculations and equations were incorporated into
the Matlab script, it was determined that the following essential equations were
sufficient for inclusion in the report. With these considerations in mind, the
following are the main equations comprising the Foundation Design Program.
Bearing Capacity
In order to calculate the allowable bearing pressure, the following equation was
used (it should be noted that a similar equation per unit length was used for
continuous foundations, which is typical throughout the remainder of the applicable
equations listed in the report):
Equation 1- Allowable Bearing Pressure 1.
For situations that presented eccentricity with the loading, the following equation
was used to calculate the eccentricity:
Equation 2- Eccentricity of Bearing Pressure 2.
Computer Analyses of Foundation Design
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For those circumstances that loading eccentricity was present, the following
equation was used to calculate the minimum and maximum bearing pressure
(although an obvious application of the following equation shows the minimum and
maximum result to be the respective corresponding bearing pressure, it is worth
mentioning that the maximum bearing pressure corresponded to adding the
factored eccentricity by footing width, while the minimum bearing pressure
resulted from subtracting the aforementioned term in the below equation):
(
) (
) Equation 3- Min and Max Bearing Pressure 3.
For calculating the ultimate bearing capacity using Terzaghi’s Bearing Capacity
Equations, the following equations for different footing types were used:
Equation 4- Terzaghi’s Bearing Capacity 4.(Square Foundations)
Equation 5- Terzaghi’s Bearing Capacity 5.(Continuous Foundations)
Equation 6- Terzaghi’s Bearing Capacity 6.(Circular Foundations)
The other option for analyzing the ultimate bearing capacity is through the use of
the Vesic’s Bearing Capacity Equation:
c s g
s g
B s g
Equation 7- Vesic’s Bearing Capacity 7.
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In addition to Equation 7, another essential aspect to account for when using Vesic’s
Bearing Capacity Equation is the notation associated with the equation. In order to
effectively incorporate this into the Matlab script, the following figure was included
into the Foundation Design Program:
i. Figure 1- Notation for Vesic’s Load Inclination
(Coduto, 2001, p. 183)
Similar to other aspects of the program, inputs were created for the variables seen
above in Figure 1, which is described further in Example 5 of the report.
Consolidation Settlement
In order to calculate the consolidation settlement of the input scenario, it was
necessary to determine the appropriate analysis type for the soil behavior. These
different types included:
1. Normally Consolidated (NC) Soils (σz0’ ≈ σc’)
2. Overconsolidated Soils (OC) – Case I (σz0’ < σzf’ ≤ σc’)
3. Overconsolidated Soils (OC) – Case II (σz0’ < σc’ < σzf’)
Equations for each are listed on the following page.
Computer Analyses of Foundation Design
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∑
(
)
Equation 8- Ultimate Consolidation Settlement 8.(NC Soils)
∑
(
)
Equation 9- Ultimate Consolidation Settlement 9.(OC Soils – Case I)
∑
[
(
)
(
)
]
Equation 10- Ultimate Consolidation Settlement 10.(OC Soils – Case II)
Allowable Serviceability Requirements
While this section of the Foundation Design Program primarily incorporates typical
values, rather than complex equations, from the Coduto Textbook, the following
equation was utilized to evaluate the allowable differential settlement for the input
conditions:
Equation 11- Allowable Differential Settlement 11.
For the bearing capacity and consolidation settlement sections of the Matlab script,
one of the main features the Matlab script presents the user is the ability to perform
an analysis using typical soil properties. As described previously in the Background
section, this feature is useful in many scenarios where specific values for the desired
soil properties are not available. The Foundation Design Program requires selection
of the Unified Soil Classification System (USCS) group symbol in order to analyze
conditions using typical soil properties for the selected soil type. The typical soil
properties and the accompanying sources are included in the subsequent tables
starting on the following page.
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i. Table 1- Typical Values for Soil Properties (Part 1 of 3)
USCS Description
Default Soil Property Information
Dry
Un
it
Wei
ght
(kP
a)
Sou
rce
Satu
rate
d U
nit
Wei
ght
(kP
a)
Sou
rce
GP Poorly-graded gravel 19000
Tab
le 3
.2 (
Co
du
to, 2
00
1, p
. 50
)
20750
Tab
le 3
.2 (
Co
du
to, 2
00
1, p
. 50
) GW Well-graded gravel 19750 21500
GM Silty gravel 18250 20750
GC Clayey gravel 18250 20750
SP Poorly-graded sand 17250 20000
SW Well-graded sand 18000 21000
SM Silty sand 16750 19750
SC Clayey sand 17000 19250
ML Low plasticity silt 14500 16500
MH High plasticity silt 14500 16000
CL Low plasticity clay 15000 16000
CH High plasticity clay 15000 15250
Computer Analyses of Foundation Design
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ii. Table 2- Typical Values for Soil Properties (Part 2 of 3)
USCS Description
Default Soil Property Information
Cc
Sou
rce
Cc/
(1+e
0)
Sou
rce
Cr/
(1+e
0)
Sou
rce
GP Poorly-graded gravel -
Not Needed - Not Needed - Not Needed
GW Well-graded gravel - Not
Needed - Not Needed - Not Needed
GM Silty gravel - Not
Needed - Not Needed - Not Needed
GC Clayey gravel - Not
Needed - Not Needed - Not Needed
SP Poorly-graded sand -
Not Needed
Varies with DR Table 3.7, p. 71
Varies with DR
Table 3.7, p. 71
SW Well-graded sand - Not
Needed Varies with
DR Table 3.7, p. 71 Varies with
DR Table 3.7, p.
71
SM Silty sand - Not
Needed Varies with
DR Table 3.7, p. 71 Varies with
DR Table 3.7, p.
71
SC Clayey sand - Not
Needed 0.1095
Average taken from Plasticity
Chart 0.01095 Assumed
Relationship
ML Low plasticity silt 1.5000
Table 8.3 (Holtz & William,
1981) 0.4286 Table 8.3 (Holtz &
William, 1981) 0.04286 Assumed
Relationship
MH High plasticity silt 4.0000
Table 8.3 (Holtz & William,
1981) 0.2739 Table 8.3 (Holtz &
William, 1981) 0.02739 Assumed
Relationship
CL Low plasticity clay 0.3125
Table 8.3 (Holtz & William,
1981) 0.1927 Table 8.3 (Holtz &
William, 1981) 0.01927 Assumed
Relationship
CH High plasticity clay 0.5000
Table 8.3 (Holtz & William,
1981) 0.2801 Table 8.3 (Holtz &
William, 1981) 0.02801 Assumed
Relationship *Unless otherwise noted, the table and figure references are in reference to Coduto Foundation Design
Computer Analyses of Foundation Design
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iii. Table 3- Typical Values for Soil Properties (Part 3 of 3)
USCS Description
Default Soil Property Information
Effe
ctiv
e
Co
hes
ion
(c'
)
Sou
rce
Effe
ctiv
e
Fric
tio
n A
ngl
e
(Φ’)
± + -
Sou
rce
GP Poorly-graded gravel - Not Needed 34.5 7.5 - - Figure 3.18, p. 88
GW Well-graded gravel - Not Needed 35.5 - 9 8 Figure 3.18, p. 88
GM Silty gravel - Not Needed 36 4 - - geotechdata.info.com
GC Clayey gravel - Not Needed 34 4 - - geotechdata.info.com
SP Poorly-graded sand - Not Needed 33 - 7 6 Figure 3.18, p. 88
SW Well-graded sand - Not Needed 33 - 7 6 Figure 3.18, p. 88
SM Silty sand 35192 geotechnicalinfo.com 32 - 6 5.5 Figure 3.18, p. 88
SC Clayey sand 42613 geotechnicalinfo.com 32 4 - - geotechdata.info.com
ML Low plasticity silt 43331 geotechnicalinfo.com 31 5 - - Figure 3.18, p. 88
MH High plasticity silt 45965 geotechnicalinfo.com 24 6 - - geotechdata.info.com
CL Low plasticity clay 49556 geotechnicalinfo.com 27 4 - - geotechdata.info.com
CH High plasticity clay 56977 geotechnicalinfo.com 22 4 - - geotechdata.info.com *Unless otherwise noted, the table and figure references are in reference to Coduto Foundation Design
Computer Analyses of Foundation Design
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5. User’s Guide
This section of the report contains a thorough guide to the Foundation Design
Program including examples explaining the extent of the program’s capabilities.
As mentioned briefly in the Background section of the report, the decision to
analyze the foundation design related calculations in Matlab was primarily due to
the user interface capability, which results in an easy-to-use program. Therefore, as
expected, there are minimal instructions necessary to effectively use the program.
One of the only explanations worth mentioning is the units associated with analysis.
No matter what type of analysis the user chooses to perform, the dialog menus
contained below in Figure 2 and Figure 3 are the first two steps to any analysis.
ii. Figure 2- Selection of the Length Unit
iii. Figure 3- Selection of the Force Unit
Computer Analyses of Foundation Design
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As seen in the figures represented on the previous page, the program is very
intuitive for all inputs. However, the user must keep in mind that after selecting the
desired length and force units for analysis, every subsequent input is anticipated as
keeping those units consistent. Therefore, it is essential to ensure that this is the
case throughout all inputs throughout the analysis. Furthermore, some background
on the Foundation Design Program worth mentioning is that all calculations are
completed in the base units of Newton and meters. There are additional function
scripts that convert input units to the base, or working, units using the desired unit
selections. This is important because it reaffirms the necessity to remain consistent
with units throughout all inputs along with providing an understanding of any
rounding error that may occur during the analysis. However, this is not expected,
and certainly not significant when analyzing the result. This is due to the fact that
each conversion factor was carried out to four decimal places to ensure precision.
While this is the only necessary instruction associated with the Foundation Design
Program, it was determined that examples for each of the program’s capabilities
would benefit its users in the event that any difficulties were experienced during
analysis. The examples begin on the following page and are all taken from the
Coduto Textbook.
For the steps listed in each of the following examples, there is an important
distinction between the different ways of inputting information into Matlab. The
following includes an example depiction and corresponding text for each type:
iv. Figure 4- Depiction and Corresponding Text for Examples
Computer Analyses of Foundation Design
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5A. Example 1 – Problem 2.14 (Coduto, 2001, p. 46)
Given:
Two-story department store
Columns 50-ft on-center
Desired:
Allowable total settlement
Allowable differential settlement
Steps using the Foundation Design Program:
1. Select the appropriate units
a. Select the length inputs units: feet
b. Select the force input units: lbs (although unnecessary for this
problem, selected for consistency and required by the Matlab script)
2. Select the desired analysis: Allowable Serviceability Requirements
3. Select the type of serviceability requirement analysis: Settlement (Total and
Allowable Differential Settlement)
4. Select the type of structure being analyzed: Typical commercial and
residential buildings
5. Input the column spacing: 50 (remembering that no units will appear and the
anticipation is that this input will be in accordance with the desired unit
length – feet, this is typical for all subsequent inputs in each example)
Results from the Foundation Design Program:
The allowable differential settlement is: 0.1 feet
The typical maximum allowable total settlement is: 0.164042 feet
Computer Analyses of Foundation Design
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5B. Example 2 – Example 3.4 (Coduto, 2001, pp. 76-77)
Given:
3-m deep compacted fill
Soil profile shown below in Figure 5
Consolidation test on a sample from point A produced the following results:
o Cc = 0.40
o Cr = 0.08
o e0 = 1.10
o σc’ = 70.0 kPa
v. Figure 5- Example 2 Soil Profile
Computer Analyses of Foundation Design
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Desired:
Ultimate consolidation settlement due to the weight of this fill
Steps using the Foundation Design Program:
1. Select the appropriate units
a. Select the length inputs units: m
b. Select the force input units: kN
2. Select the desired analysis: Settlement
3. Select the fill input type: Input Fill Properties
a. Input the unit weight of the fill: 19.2
b. Input the height of the fill: 3
4. Input the number of layers of different soil types: 3 (assuming two separate
layer types for the fine to medium sand due to the fact that the water table is
not at the middle of the layer and the program capabilities are limited to
evenly spaced sub-layers)
5. Input the depth of the groundwater table: 1.5
6. Input layer properties (top to bottom)
a. Layer 1
i. Input layer height: 1.5
ii. Select analysis for soil type: Normally Consolidated (NC)
iii. Input number of sub-layers: 1
iv. Select analysis for soil properties: Specific Values
1. Input soil properties into dialog box
a. Dry unit weight: 18.5
b. Saturated unit weight: 19.5
c.
: 0.008
d.
: 0.002 (assuming approximately one-third
of
)
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b. Layer 2
i. Input layer height: 2
ii. Select analysis for soil type: Normally Consolidated (NC)
iii. Input number of sub-layers: 1
iv. Select analysis for soil properties: Specific Values
1. Input soil properties into dialog box
a. Dry unit weight: 18.5
b. Saturated unit weight: 19.5
c.
: 0.008
d.
: 0.002 (assuming approximately one-third
of
)
c. Layer 3
i. Input layer height: 10
ii. Select analysis for soil type: Input Preconsolidation Stress
1. Input preconsolidation stress: 70
iii. Input number of sub-layers: 3
iv. Select analysis for soil properties: Specific Values
1. Input soil properties into dialog box
a. Dry unit weight: 0 (not given and not needed due
to the fact that the entire layer is below the
depth of the groundwater table)
b. Saturated unit weight: 16
c.
: 0.4/(1+1.1) (utilizing the computational
ability of inputs in Matlab)
d.
: 0.08/(1+1.1)
Results from the Foundation Design Program:
The total settlement for the given scenario is: 0.442025 m
An excel file containing a summary of the results (Please see Appendix B)
Computer Analyses of Foundation Design
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5C. Example 3 – Problem 5.5 (Coduto, 2001, p. 168)
Given:
5-ft square, 2-ft deep spread footing
Concentric vertical load of 60 k and an overturning moment of 30 ft-k
Groundwater table at a depth of 20 ft
Desired:
Determine whether the resultant force acts within the middle third of the
footing
Compute the minimum and maximum bearing pressure
Steps using the Foundation Design Program:
1. Select the appropriate units
a. Select the length inputs units: ft
b. Select the force input units: lbs
2. Select the desired analysis: Bearing Capacity Analysis
3. Select the type of bearing capacity analysis: Enter Specific Conditions to
Determine the Allowable Bearing Pressure, the Ultimate Bearing Capacity,
and the Factor of Safety
4. Select the desired code for use in computing the design load: ASD
a. Input loading conditions into the dialog box
i. Dead Load (D): 60000 (this is used because the given load is
not given as a combination of other loads, also note that 60000
is used due to the fact that 60 k converts to 60000 lbs per the
unit force selection, lbs, described in Step 1)
5. Select whether there is a moment load applied to the foundation: Yes
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6. Select the type of footing for the desired analysis: Square
a. Input footing dimensions into the dialog box
i. Width (B): 5
ii. Depth (D): 2
7. Select whether the top of the footing is at the ground level: Yes
8. Input the depth of the groundwater table: 20
9. Input the applied moment load: 30000
10. Although not required by the problem, further analysis of the problem is
available using either Terzaghi’s or Vesic’s Equations for the ultimate bearing
capacity for the foundation. However, if you wish to conclude the analysis,
click into the command window of Matlab and press CTRL+C (this can also be
used to conclude any analysis at any point if no further analysis is needed or
a mistake was made in a previous step). Also, it is important to note that this
would result in the program calculating a factor of safety given specific
inputs, which is not covered in any of the remaining examples.
Results from the Foundation Design Program:
Based on the inputs, the design load for analysis is: 60000 lbs
The minimum bearing pressure (q_min) for the given scenario is: 1260.47
lbs/feet^2
The maximum bearing pressure (q_max) for the given scenario is: 4140.47
lbs/feet^2
Note: the first part of the desired section for this example is verified through the
answer. This is because if the resultant force does not act within the middle third of
the footing, the bearing pressure will not be calculated and the program will inform
the user to adjust the design accordingly.
Computer Analyses of Foundation Design
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5D. Example 4 – Problem 6.4 (Coduto, 2001, p. 197)
Given:
Dead load of 150 k and a live load of 120 k
3-ft deep spread footing
Soil beneath the footing is an undrained clay
o Su = 3000 lb/ft2
o γ = 117 lb/ft3
Groundwater table at the bottom of the footing
Desired:
Compute the width, B, required to obtain a factor of safety of 3 against a
bearing capacity failure
Steps using the Foundation Design Program:
1. Select the appropriate units
a. Select the length inputs units: ft
b. Select the force input units: lbs
2. Select the desired analysis: Bearing Capacity Analysis
3. Select the type of bearing capacity analysis: Enter Desired Factor of Safety to
Determine Minimum Required Width
4. Select the desired code for use in computing the design load: ASD
a. Input loading conditions into the dialog box
i. Dead Load (D): 150000 (note that 150000 is used due to the
fact that 150 k converts to 150000 lbs per the unit force
selection, lbs, described in Step 1)
ii. Live Load (L): 120000
5. Input the desired factor of safety: 3
6. Select the type of footing for the desired analysis: Square
a. Input the footing depth: 3
Computer Analyses of Foundation Design
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7. Select whether the top of the footing is at the ground level: Yes
8. Input the depth of the groundwater table: 3
9. Select the desired type of bearing capacity analysis: Terzaghi
10. Select the type of analysis for the required soil properties: Specific Values
a. Input soil properties into the dialog box
i. Dry unit weight: 117
ii. Saturated unit weight: 117 (while the given unit weight is not
specified as either dry or saturated, we can assume it is the dry
unit weight due to the fact that the groundwater table is at the
depth of the footing, however, for effective unit weight
calculations for other analysis types, this could have an effect,
therefore, it is advised to also input 117 lb/ft3 into this input as
well)
iii. Effective cohesion: 3000
iv. Effective friction angle (degrees): 0
11. Select the desired analysis type for displaying the answer: Yes, round to the
nearest specified length
a. Input the desired length to round the footing width result to: 3/12
(again utilizing the computation ability of Matlab when inputting
information by converting the rounded length, 3 inches, by the
selection for the input length: feet)
Results from the Foundation Design Program:
Based on the inputs, the design load for analysis is: 270000 lbs
The minimum footing width for the given scenario is: 6.25 feet
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5E. Example 5 – Problem 6.6 (Coduto, 2001, p. 197)
Given:
1.5-m wide, 2.5-m long, and 0.5-m deep spread footing
Soil beneath the footing has the following properties:
o c' = 10 kPa
o ɸ’ = 32°
o γ = 18.8 kN/m3
Groundwater table at a great depth
Desired:
Compute the maximum load this footing can support while maintaining a
factor of safety of 2.5 against a bearing capacity failure
Steps using the Foundation Design Program:
1. Select the appropriate units
a. Select the length inputs units: m
b. Select the force input units: kN
2. Select the desired analysis: Bearing Capacity Analysis
3. Select the type of bearing capacity analysis: Enter Desired Factor of Safety to
Determine Maximum Design Load
4. Input the desired factor of safety: 2.5
5. Select the type of footing for the desired analysis: Rectangular
a. Input footing dimensions into the dialog box
i. Width (B): 1.5
ii. Length (L): 2.5
iii. Depth (D): 0.5
6. Select whether the top of the footing is at the ground level: Yes
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7. Input the depth of the groundwater table: 2 (when the conditions show that
the groundwater table depth is at a great depth, the input must be greater
than or equal to the footing depth plus the footing width, as this is the
minimum requirement to forego any additional adjustments of the effective
unit weight of the soil)
8. Select the desired type of bearing capacity analysis: Vesic
9. Select the type of analysis for the required soil properties: Specific Values
a. Input soil properties into the dialog box
i. Dry unit weight: 18.8
ii. Saturated unit weight: 0 (due to the fact that the groundwater
table is at a great depth, it is not necessary to analyze the
saturated unit weight of the soil)
iii. Effective cohesion: 10
iv. Effective friction angle (degrees): 32
10. Figure 1 will appear, which displays the notation for Vesic’s Equations
a. Input the Vesic’s Equation Geometric Conditions into the dialog box
i. D: 0.5
ii. Alpha (degrees): 0
iii. Beta (degrees): 0
Results from the Foundation Design Program:
The maximum allowable load for the given scenario is: 1771.83 kN
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6. Conclusions
From the results of the Foundation Design Program, it was determined that Matlab
is a very useful tool for analyzing foundation design calculations. The many
anticipated benefits described in detail in the Background of the report were
affirmed with the results. The analyses are much quicker than hand calculations and
also provide the user with the ability to perform the calculations without refreshing
on the specific topics. The Matlab script also removes any chance of human error
throughout the calculations and provides great precision in the results with Matlab
storing up to 63 digits of each number used in all calculations. Again, the only
limitation to this precision is the four-decimal conversion factors if the desired units
for analysis are not Newton and meters.
In addition to these findings, the main feature that warranted its design, the ability
to analyze default values for different soil types, was determined relatively accurate
through Example 2 (Example 3.4 from the Coduto Textbook). While the values used
in the steps listed under Example 2 were specific values, the conditions were
analyzed again using default values contained in the Foundations Design Program
for the Fine to Medium Sand (SP) with Dr = 40% and the Soft Clay (CL). The default
value analysis resulted in a total settlement of 0.446 m compared to the 0.442 m
from Example 2 with the specific values. This result had a percent difference of less
than one percent (0.90%), which led to the conclusion that the default values were
appropriate for the settlement analysis. To increase confidence in this conclusion
and extend its application, further analysis into other types of soils and other
analyses types would be required. However, due to the scope and limitations of this
report, this analysis was determined sufficient.
With this in mind, the applications of the Foundation Design Program to save
engineering consulting firms time, and subsequently money, is very large.
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7. Recommendations
The recommendation deduced from the investigation of utilizing Matlab to compute
repetitive foundation design calculations is to implement the Foundation Design
Program into geotechnical engineering firms if a license of a program to do similar
calculations has not already been purchased. The intent of this is twofold. Firstly,
implementing the Foundation Design Program would save engineers a considerable
amount of time for every project that requires some type of bearing capacity or
settlement analysis. Furthermore, it would ideally have a psychological effect for
some engineers that were not aware of such capabilities of computer programs
saving a substantial amount of time on each project. While these engineers may not
be proficient in Matlab, they may have competency in another program, which they
could use to start incorporating repetitive tasks into computer based calculations.
As mentioned previously in the report, with the current economic struggles of our
nation at this point in time, the demand for efficiency is at an all-time high.
For firms that do not have a license for a similar program and have the luxuries of
the required time and resources, it is also recommended to expand on the
capabilities of the Foundation Design Program. Specifically, the methods for
analyzing settlement in shallow foundations also include repetitive calculations,
which could be easily added to the Matlab script. While this is just one example,
there are many similar possibilities for additions in common foundation design
calculations that could further increase the value of the program to engineering
firms. Another investigation that could increase the value to some firms is
establishing default values for soils specific to the firm’s region. While the current
default values are still accurate for most general design purposes, testing in a
specific region would be a more accurate way to model soil properties.
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The final recommendation is focused on enhancing the consolidation settlement
analysis. Specifically, it is recommended that research into the implementation of
the overconsolidation margin of a sample be incorporated into the consolidation
settlement analysis. While this did not have an effect on the example explaining the
consolidation settlement section of the Foundation Design Program (Example 2),
the analysis has the capability to analyze different sub-layers of the same overall
layer as a different consolidation type. Depending on the depth of the layer, this may
be desirable in some cases. However, the accuracy of the analysis would be
enhanced if the overconsolidation margin was used at each sub-layer to estimate the
preconsolidation stress at that layer. This would require implementing typical
ranges of overconsolidation margins, such as those listed in Table 3.6 (Coduto, 2001,
p. 69). This enhancement could prove particularly useful if settlement of shallow
foundations is also incorporated into the Matlab script.
Overall, it was determined that the Foundation Design Program was a success and
had many applications. It is recommended for implementation in engineering firms
that do not own a computer program with similar capabilities.
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8. List of Appendices
A.) Appendix A – References
B.) Appendix B – Spreadsheet Program Output
C.) Appendix C – Spacing Program Script
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A. Appendix A – References
Coduto, Donald P. (2001). Foundation Design Principles and Practices (2nd ed.).
Upper Saddle River, NJ: Prentice Hall.
Geotechdata.info.com (2011, April 29). Angle of Friction. Retrieved November 1,
2012, from the Geotechdata.info Web site: http://www.geotechnicalinfo.com
/cohesion.html
Geotechnicalinfo.com. (n.d.). Cohesion of Soil. Retrieved November 1, 2012, from the
Geotechnicalinfo Web site: http://www.geotechnicalinfo.com/cohesion.html
Holtz, R., & William, K. (1981). An Introduction to Geotechnical Engineering.
Englewood Cliffs, NJ: Prentice Hall.
National Cooperative Highway Research Program, Transportation Research Board,
& National Research Council. (2001). Guide for Mechanistic-Empirical Design
of New and Rehabilitated Pavement Structures. Champaign, IL: ARA, Inc., ERES
Division.
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B. Appendix B – Spreadsheet Program Output
Appendix B contains the spreadsheet program output for the consolidation
settlement analysis performed by the Foundation Design Program. This output was
referenced in Example 2 contained in the User’s Guide section of the report. For
multiple settlement analyses, the user is advised to copy the spreadsheet out of the
Matlab folder and rename the file by appending an appropriate description onto the
file name. Then, the user should open the SettlementResults.xlsx Excel spreadsheet
in the Matlab folder and highlight the two cells corresponding to the unit selection
from the Matlab inputs, right-click, and select “Clear Contents”. The user should
repeat this step after highlighting the appropriate number of rows from the Results
table underneath the Height column (starting at cell G12).
Settlement Results
Units
Length: m
Force: kN
Results
At Midpoint of Layer
He
igh
t (m
)
z (m
)
σ_z
0'
(kN
/m^2
)
Δσ
_z
(kN
/m^2
)
σ_z
f'
(kN
/m^2
)
σ_c
' (k
N/m
^2)
Cc/
(1+e
0)
Cr/
(1+e
0)
(δc)
ult
(m
) (δc)tot
1.50 0.75 13875.0 57600.0 71475.0 0.0 0.008 0.002 0.0085 0.442 m
2.00 2.50 37440.0 57600.0 95040.0 0.0 0.008 0.002 0.0065
3.33 5.17 57446.7 57600.0 115046.7 70000.0 0.190 0.038 0.1479
3.33 8.50 78080.0 57600.0 135680.0 70000.0 0.190 0.038 0.1524
3.33 11.83 98713.3 57600.0 156313.3 70000.0 0.190 0.038 0.1267
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C. Appendix C – Foundation Design Program Script
Appendix C contains an excerpt from the Foundation Design Program script
referenced in the report. Because of the limitations of the report, it was determined
that the inclusion of the entire script, and additional function scripts, was not
necessary. A digital copy will be provided in addition to this excerpt of the Matlab
script.
clear all
clc
%This Matlab Code is a project completed per the requirements of CEE598
%Create a menu for the choice of units (length) type
Units_Length_Type = menu('What type of input units (length) would you like to use for
analysis?', ...
'feet','inches','m','cm','mm');
%Ensure a choice selected
while Units_Length_Type == 0
clc
disp('Please choose an appropriate response for the units (length) type')
Units_Length_Type = menu('What type of input units (length) would you like to use for
analysis?', ...
'feet','inches','m','cm','mm');
end
clc
EffectiveLengthConversionFactor=[0.3048,0.0254,1,0.01,0.001];
LengthUnits={'feet','inches','m','cm','mm'};
%Create a menu for the choice of units (force) type
Units_Force_Type = menu('What type of input units (force) would you like to use for
analysis?', ...
'kips','lbs','kN','N');
%Ensure a choice selected
while Units_Force_Type == 0
clc
disp('Please choose an appropriate response for the units (force) type')
Units_Force_Type = menu('What type of input units (force) would you like to use for
analysis?', ...
'kips','lbs','kN','N');
end
clc
EffectiveForceConversionFactor=[4448.2216,4.4482216,1000,1];
ForceUnits={'kips','lbs','kN','N'};
%Create a menu for the choice of anlaysis type
Analysis_Type = menu('What type of analysis do you wish to perform?', ...
'Bearing Capacity Analysis','Allowable Serviceability Requirements','Consolidation
Settlement');
%Ensure a choice selected
while Analysis_Type == 0
clc
disp('Please choose an appropriate response for the analysis type')
Analysis_Type = menu('What type of analysis do you wish to perform?', ...
'Bearing Capacity Analysis','Allowable Serviceability Requirements','Consolidation
Settlement');
end
clc