computer analyses of foundation design · 2018. 9. 6. · computer analyses of foundation design...

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


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


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


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.


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


List of Appendices

A. Appendix A – References ...................................................................................................... 31

B. Appendix B – Spreadsheet Program Output ............................................................... 32

C. Appendix C – Foundation Design Program Script .................................................... 33


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

Foundation Design 5 Fall 2012

Graduate Final Paper

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.




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.




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.




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.




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)


(Continuous Foundations)


(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.




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.




∑

(

)

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.




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




ii. Table 2- Typical Values for Soil Properties (Part 2 of 3)

USCS Description


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


GC Clayey gravel - Not


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


1981) 0.2739 Table 8.3 (Holtz &


Relationship

CL Low plasticity clay 0.3125


1981) 0.1927 Table 8.3 (Holtz &


Relationship

CH High plasticity clay 0.5000


1981) 0.2801 Table 8.3 (Holtz &


Relationship *Unless otherwise noted, the table and figure references are in reference to Coduto Foundation Design




iii. Table 3- Typical Values for Soil Properties (Part 3 of 3)

USCS Description


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




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




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




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




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




Desired:

Ultimate consolidation settlement due to the weight of this fill



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

)




b. Layer 2

i. Input layer height: 2

ii. Select analysis for soil type: Normally Consolidated (NC)




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




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)


The total settlement for the given scenario is: 0.442025 m

An excel file containing a summary of the results (Please see Appendix B)




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



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




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.


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.




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



a. Select the length inputs units: ft

b. Select the force input units: lbs


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





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)


Based on the inputs, the design load for analysis is: 270000 lbs

The minimum footing width for the given scenario is: 6.25 feet




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



a. Select the length inputs units: m

b. Select the force input units: kN


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





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


The maximum allowable load for the given scenario is: 1771.83 kN




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.




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.




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.




8. List of Appendices

A.) Appendix A – References

B.) Appendix B – Spreadsheet Program Output

C.) Appendix C – Spacing Program Script




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.

http://www.geotechnicalinfo.com/cohesion.html




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




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');


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');


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

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