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Genaro Contreras Geotechnical Master Plan Company Sponsor: CVL Group 7 3/20/2015 Spring 2015 JOY RANCH HOUSING COMMUNITY

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Page 1: Team #7 Geotechnical Report (2)

Genaro Contreras

Geotechnical Master Plan

Company Sponsor: CVL

Group 7

3/20/2015

Spring 2015

JOY RANCH HOUSING COMMUNITY

Page 2: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 1

JOY RANCH HOUSING COMMUNITY

Table of Contents 1.0 EXECUTIVE SUMMARY .................................................................................................................2

2.0 INTRODUCTION ...........................................................................................................................2

2.1 Proposed Project.......................................................................................................................2

2.2 Site Conditions..........................................................................................................................2

3.0 SITE EXPLORATION ......................................................................................................................3

3.1 Exploratory Borings ..................................................................................................................3

32 Groundwater Table....................................................................................................................3

4.0 SOIL CHARACTERISTICS .................................................................................................................4

4.1 Test Results ..............................................................................................................................4

4.2 Strength and Capacity...............................................................................................................6

5.0 SOIL ISSUES ..................................................................................................................................7

5.1 Collapse....................................................................................................................................8

5.2 Subsidence ...............................................................................................................................8

5.3 Fissures ....................................................................................................................................8

5.4 Sulfate......................................................................................................................................8

6.0 DESIGN RECOMMENDATIONS ......................................................................................................8

6.1 Footings ...................................................................................................................................8

6.2 Earth Retaining Walls ...............................................................................................................8

6.3 Earthwork ................................................................................................................................8

7.0 SUSTAINABILITY ...........................................................................................................................8

8.0 CONCLUSION ................................................................................................................................9

APPENDIX A: SCHMERTMANN ANALYSIS ..................................................................................... 10-12

APPENDIX B: RETAINING WALL CALCULATIONS............................................................................ 13-15

APPENDIX C: BORING LOG DATA ................................................................................................. 16-37

APPENDIX D: PROJECT VALIDATION FORM ....................................................................................... 38

Page 3: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 2

JOY RANCH HOUSING COMMUNITY

Figure 1: Land Use Plan

1.0 Executive Summary

An apparently square, undeveloped area is proposed as the site for a small residential

community, titled Joy Ranch Housing. This land is intended to be divided into 5 main uses:

housing, recreational, commercial, water treatment and educational. Shown below in figure 1 are

the types of land use each parcel in this site is devoted to. Due to the scarcity of information

available concerning the earth conditions thereof, a geotechnical investigation was performed to

properly analyze and evaluate the challenges that could potentially arise from land development

on this site. General site topography and groundwater depth were provided by site visitation and

the Groundwater Site Inventory of the Arizona Department of Water Resources.

Exploratory borings were performed to obtain at least 1 soil sample from each of the 14

parcels. The soil characteristics determined or extrapolated from these samplings were used to

assign or affirm effective use of each subdivision. The incorporation of numerous assumptions

became necessary, as some crucial factors would require further laboratory testing for total

accuracy. Design recommendations for structure footings and earth retaining walls were

provided according to the soil properties and the loads of the planned structures (3,101,400 lb.

for an elementary school building and 157,784 lb. for a pedestrian bridge).

2.0 Introduction:

2.1 Proposed Project: Joy Ranch Housing is a small residential community, spanning

approximately 622.86 acres and divided into 14 parcels of land. The majority of these parcels are

devoted to housing, with both high and low dwelling unit densities, with the remaining ones set

aside for the purposes of wastewater treatment, education, recreation and commercial activity.

Two collector roads intersect at a roundabout towards the northeastern quadrant of the site,

providing access to the rest of the parcels.

The performance of a geotechnical investigation fulfills the requirement of ascertaining

the suitability of the soil concerning land development.

2.2 Site Conditions: The site for Joy Ranch Housing is bound by North 7th Avenue, North

7th Street, West Joy Ranch Road and West Cloud Road, all of which are arterials. No previous

development is evident or recorded. Surrounding establishments include, located to the south,

Page 4: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 3

JOY RANCH HOUSING COMMUNITY

Deer Mountain Elementary and Dove Valley Ranch, approximately two miles to the East. A

smaller fraction of the land surrounding the planned site is developed, with one story homes

lining the roads.

The topography is flat in general, with no apparent hills or earth depreciations, nor

apparent evidence of boulders or cobbles. Elevation slowly decreases from the northern to

southern half, which dictates the flow of the washes. Two major ones flow directly through the

site, one of which is the West Fork Desert Lake Wash and traverses the eastern half of the site.

Surface indicators of the location of these washes include clear lines of trees, which will

necessitate clearing and possible grubbing to make further use of the washes. Other vegetation

includes abundant shrubbery in the southwestern corner. The surrounding area is mountainous.

3.0 Site Exploration:

3.1 Borings: For the purpose of exploring various subsurface conditions throughout the

site, exploratory borings were performed by use of a 6 5/8” hollow stem auger. The locations for

these borings were selected according to the planned parcels. One boring was performed in each

smaller parcel, with two performed in larger ones, such as parcels 5 and 10, to obtain more

reliable averages for the soil characteristics pertaining to a given area. Because the depths of the

logs are approximately 6 feet, they are preliminary. Deeper ones that fall within the range of 10-

15 feet will be required to make reliable foundation recommendations for larger loads.

4.2 Groundwater: Though some moisture was present in the majority of the samples, the

groundwater table is evidently located far below the depth of any exploratory boring for the

pertinent project. Researching of the records kept by the Arizona Department of Water

4 2 1

5

7

6

10

3

11 9

14

8

13

12

Legend

= Boring Location

= Parcel Number

Figure 2: Boring Map

Page 5: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 4

JOY RANCH HOUSING COMMUNITY

Resources revealed no existing data specifically regarding the pertinent land, affirming that no

previous development has been completed nor attempted. Data from wells at various adjacent

points, monitored as recent as 2010, indicates the depth of the groundwater table to be far below

the range of the infrastructure for Joy Ranch Housing, ranging from 301.2 to 511.6 feet.

Considering this, it is highly unlikely that the groundwater table will pose any difficulties that

need to be figured into the calculations.

4.0 Soil Characteristics

4.1 Test Results: In accordance with the standards of ASTM D2937, the drive-cylinder

test was performed on samples from the boring sites. The simple measurement of sample

cylindrical masses before and after drying enabled the computation of the dry unit weights and

water contents. On the field, visual classification was performed by ASTM D2487 and ASTM

D2488 specifics, producing the descriptions included in the boring logs. Weak cementation was

an abundant characteristic, noted from most of the samples. ASTM C136 standards were

followed for the sieve analysis, showing a predominance of clayey sands, particularly within the

surface strata.

Plasticity was required to determine the quality of strength for each boring location.

ASTM D4318 procedure was followed in identifying the liquid and plastic limits, both of which

are required for the plasticity indices. The results to these are shown in tables 1 and 2. The

separation into 2 tables of data was necessitated by the availability of data for the multiple depths

at which exploratory borings were performed.

Figure 3: Map of Sample Wells

Legend

= Site Border

= Well Location

Top Number = Well Elevation

Bottom Number = Date of Data

Collection

Page 6: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 5

JOY RANCH HOUSING COMMUNITY

Table 1: Laboratory Test Results

Table 2: Soil Classification and Consistency

Page 7: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 6

JOY RANCH HOUSING COMMUNITY

4.2 Strength and Bearing Capacity: In determining strength and capacity characteristics

for the soils within the site, it must be acknowledged that insufficient data has been gathered

from laboratory tests to produce truly accurate quantities. This necessitates assumptions

regarding certain vital factors, based on previously established correlations and standards.

Laboratory results for soil classification were utilized when available, with visual classification

accepted as reasonable approximation for all other cases. The angle of internal friction required

already established value ranges assigned to each soil type. The value used for calculation was

selected in relation to the dry density of the soil. Cohesion was also determined using previous

data based on soil types. The bearing capacity factors were obtained from a chart constructed for

use in conjunction with two common methods for ultimate bearing pressure, and are listed below

in table 3. Furthermore, due to the extensive depth of the groundwater table and the presence of

moisture within the soil samples from the exploratory borings, soil conditions were assumed to

be unsaturated, drained and normally consolidated. The latter two conditions are acceptable for

this preliminary analysis, partially due to the lack of previous land development.

Terzhagi’s method for computing soil bearing capacity was utilized with the footing

dimensions for the different planned structures, applying the standard factor of safety of 2.5. The

results are shown in table 4.

Table 3: Bearing Capacity Factors

Page 8: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 7

JOY RANCH HOUSING COMMUNITY

5.0 Soil Issues 5.1 Subsidence: While data from the site itself is currently unavailable, studies on the

greater Maricopa area from the Hydrology Division of the ADWR reveal that the site does not

fall within the areas of major subsidence, which are outlined below in figure 3.

Table 4: Bearing Capacity

Legend

= Subsidence Zone

= Major Highway

Figure 3: Subsidence Map

Page 9: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 8

JOY RANCH HOUSING COMMUNITY

Because the majority of the area is composed of clayey sands, a considerable amount of

immediate settlement is expected, but consolidation is not anticipated due to the depth of the

groundwater table and overall scarcity of clays.

5.2 Collapse: Parcels 6 and 8, which are intended to serve as the locations for low density

housing and a grocery store respectably, were shown to have collapsible soil. In addition to

potentially exacerbating differential settlement, this issue may be compounded be compounded

by the area’s comparatively high flood rate, as an influx of water is one of the triggers for soil

collapse. Methods for combating this problem are explained under the design recommendations

for footings.

5.3 Fissures: Fissuring is often the result of subsidence. Because the site is not located

within any of the major subsidence zones in Maricopa County, fissuring is not a major concern.

Furthermore, data maps from the ADWR did not identify any nearby areas with a high risk of

fissuring. Though this geological hazard does not pose a problem for this particular case, it is a

common concern for geotechnical engineers. Thus, the reasons for disregarding it are

noteworthy.

5.4 Sulfate: The soil of parcel 2 was shown to have a significantly high sulfate

concentration, at 299 ppm. According to the standards from the Portland Cement Association,

this level of soluble sulfates constitutes a moderate hazard, capable of causing cracks and

disintegration on concrete constructs, including footings.

6.0 Design Recommendations

6.1 Footings: The spread footings for the homes in both low and high density

housing developments will be square and 3 feet in width, although the soil conditions of parcel 2

necessitate a width of 4 feet to meet, or exceed, an acceptable bearing capacity of 5,000 𝑙𝑏/𝑓𝑡2 .

For parcel 6, the high concentration of soluble sulfates necessitates that any concrete slab

footings be composed of type II concrete, which is resistant to sulfate attack. A 3 foot width is

sufficient for most of the other land use types, except for the two story elementary school

building and the bridges.

A 10 foot wide continuous footing was assumed for the pedestrian bridge, which passes

the design criteria for this type of foundation, including the bearing capacity. The predicted

immediate settlement following construction is well below the allowable total settlement for

bridges, according to table 2.1 of Coduto’s text on foundations. The building from the

elementary school requires 16 spread footings, each 5 feet in width.

6.2 Earth Retaining Walls: Concrete cut-off walls will be constructed below the

pedestrian bridge along the wash between the housing development in parcel 12 and the

recreational park in parcel 10. This is primarily to prevent the issue of scour on the bridge

footings, which could prove severe in the long run, and without a deep foundation. At the least in

the short term, the level of flooding in this wash is not predicted to be high enough to pose an

issue for the adjacent housing development. Parcels 6 and 8 will also require cut-off walls along

the adjacent wash, primarily to prevent soil collapse. These walls will also be composed of type

II concrete to combat damage from soluble sulfates. The other walls will be composed of type I

concrete.

Page 10: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 9

JOY RANCH HOUSING COMMUNITY

The walls themselves will be a total of 16 feet in height, with a toe of 3 feet, a stem of 1.5

feet and a heel of 7 feet. These dimensions are acceptable for the soil conditions of all the walls

due to the common backfill, which will be high quality granular soil. The soil properties will

include a unit weight of 120 𝑙𝑏/𝑓𝑡2 , a friction angle of 30 degrees and no cohesion.

6.3 Earthwork: In addition to the excavation required for the footings of the residential,

commercial and educational structures, the soil at the edge of the washes adjacent to parcels 12,

10, 6 and 8 will be removed as part of the construction of the retaining walls. This will be done

with typical excavators. Scrapers will be used to transport the removed soil, as a different

backfill will be placed behind the walls. Prior to any compaction, the soils will be moisture

conditioned to within 3% of the optimum moisture content, identified during the Proctor tests.

Compaction will increase the density of the soil to approximately 95% of the proctor test results.

7.0 Sustainability

Cells are installed underground, designed to provide additional nutrients to the surrounding soil

to sustain the health of the vegetation. These are located near the pedestrian and vehicle bridges,

and can be particularly beneficial to the recreational park and the washes, which may eventually

develop vegetation that can be maintained and increase the aesthetic appeal of the area. The cells

are provided power, at least in part, by specialized batteries that convert the vibrations of the

bridges, from passing pedestrians and vehicles, to electricity.

8.0 Conclusion

Due to a number of assumptions, limitations to this preliminary analysis include a lack of

conclusive shear strength values, the margin of error for bearing capacity and the preliminary

nature of the exploratory borings. The depth of the borings is of particular note, as it only

increases the uncertainty of the conditions under which substructures are constructed. However,

the error for the ultimate bearing capacity calculations is not significant because of the adherence

to typical soil factor values, making the computed bearing capacities reasonably accurate for the

purposes of this report. Earth conditions for the site of the proposed Joy Ranch Housing

community are concluded to be manageable for the purposes of land development, although

further testing is still required to refine the design recommendations and improve safety.

Page 11: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 10

JOY RANCH HOUSING COMMUNITY

Appendix A: Schmertmann Analysis

Footings (Elementary School Building)

o 𝑞 = 8000𝑙𝑏

𝑓𝑡2 , 𝐵 = 5 𝑓𝑡, 𝐻 = 1.5 𝑓𝑡, 𝐷 = 3.5 𝑓𝑡,𝑃 = 194,375 𝑙𝑏

o Important Geostatic Stresses

𝜎𝑧𝐷′ = (114.38

𝑙𝑏

𝑓𝑡3 ) (3.5 𝑓𝑡) = 400.33𝑙𝑏

𝑓𝑡2

𝜎𝑧𝑝′ = (114.38

𝑙𝑏

𝑓𝑡3 ) (3.5𝑓𝑡 +5

2𝑓𝑡) = 686.28

𝑙𝑏

𝑓 𝑡2

o Equivalent Modulus: 𝐸𝑠 = (50,000𝑙𝑏

𝑓𝑡2 ) √1 + 12,000 (25𝑙𝑏

𝑓𝑡2 ) = 350,000𝑙𝑏

𝑓𝑡2

o Peak Influence Factor: 𝐼𝜖𝑝 = 0.5 + 0.1√(8,000

𝑙𝑏

𝑓𝑡2−343.14𝑙𝑏

𝑓𝑡2)

629 .09𝑙𝑏

𝑓𝑡2

= 0.849

o Depth, Creep and Shape Factors

𝐶1 = 1 − 0.5 ((343 .14

𝑙𝑏

𝑓𝑡2 )

8,000𝑙𝑏

𝑓𝑡2−343.14𝑙𝑏

𝑓𝑡2

) = 0.974

𝐶2 = 1 + log (0.1

0.1) = 1

𝐶3 = 1 (value for square footings)

o Settlement: 𝛿 =((0.978) (1)(1)(8,000

𝑙𝑏

𝑓𝑡2−343.14𝑙𝑏

𝑓𝑡2)(0.849 +0.025) (5 𝑓𝑡))

350,000𝑙𝑏

𝑓𝑡2

= 0.091 𝑓𝑡 =

1.09 𝑖𝑛

o Immediate settlement falls within the acceptable range of 0.5 to 2 inches.

Footing (Pedestrian Bridge, Parcel 10)

o 𝑞 = 1,014𝑙𝑏

𝑓𝑡2 , 𝐵 = 10 𝑓𝑡, 𝐻 = 1.5 𝑓𝑡, 𝐷 = 3.5 𝑓𝑡,𝑃 = 78,892 𝑙𝑏

5’

3.5’

2.5’

P

2’

Page 12: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 11

JOY RANCH HOUSING COMMUNITY

o Important Geostatic Stresses

𝜎𝑧𝐷′ = (108.4

𝑙𝑏

𝑓𝑡3 ) (3.5 𝑓𝑡) = 379.4𝑙𝑏

𝑓𝑡2

𝜎𝑧𝑝′ = (108.4

𝑙𝑏

𝑓𝑡3 ) (3.5 𝑓𝑡) = 1,463.4𝑙𝑏

𝑓𝑡2

o Equivalent Modulus: 𝐸𝑠 = (50,000𝑙𝑏

𝑓𝑡2 ) √1 + (12,000𝑙𝑏

𝑓𝑡2 ) (33) = 446,000𝑙𝑏

𝑓𝑡2

o Peak Influence Factor: 𝐼𝜖𝑝 = 0.5 + 0.1√(1,255

𝑙𝑏

𝑓𝑡2−379.4𝑙𝑏

𝑓𝑡2)

1,463 .4𝑙𝑏

𝑓𝑡2

= 0.566

o Depth, Creep and Shape Factors

𝐶1 = 1 − 0.5 ((379 .4

𝑙𝑏

𝑓𝑡2 )

1,255𝑙𝑏

𝑓𝑡2−379.4𝑙𝑏

𝑓𝑡2

) = 0.783

𝐶2 = 1

𝐶3 = 1.03 − 0.3(10) = 0.73

o Settlement: 𝛿 =(0.783) (1)(0.73)(1,255

𝑙𝑏

𝑓𝑡2 −379.4𝑙𝑏

𝑓𝑡2)(2∗0.566+0.1) (10)

446 ,000𝑙𝑏

𝑓𝑡2

= 0.012 𝑓𝑡 =

0.15 𝑖𝑛

o Immediate settlement falls below the acceptable limit of 2 inches for bridges.

Footing( Pedestrian Bridge, Parcel 12)

o 𝑞 = 1,014𝑙𝑏

𝑓𝑡2 , 𝐵 = 10 𝑓𝑡, 𝐻 = 1.5 𝑓𝑡, 𝐷 = 3.5 𝑓𝑡,𝑃 = 78,892 𝑙𝑏

o Though the top soil stratum of this area is has different properties, the bottom of

the footing extends below this layer, making the simplified Schmertmann’s

analysis appropriate.

o Important Geostatic Stresses

𝜎𝑧𝐷′ = (132.24

𝑙𝑏

𝑓𝑡3 ) (3.5 𝑓𝑡) = 462.84𝑙𝑏

𝑓𝑡2

𝜎𝑧𝑝′ = (132.24

𝑙𝑏

𝑓𝑡3 ) (3.5𝑓𝑡 + 10𝑓𝑡) = 1,785.24𝑙𝑏

𝑓𝑡2

o Equivalent Modulus: 𝐸𝑠 = (50,000𝑙𝑏

𝑓𝑡2 ) √1 + (12,000𝑙𝑏

𝑓𝑡2 ) (53) = 686,000𝑙𝑏

𝑓𝑡2

o Peak Influence Factor: 𝐼𝜖𝑝 = 0.5 + 0.1√(1,014

𝑙𝑏

𝑓𝑡2−462.84𝑙𝑏

𝑓𝑡2)

1,785.24𝑙𝑏

𝑓𝑡2

= 0.556

o Depth, Creep and Shape Factors

𝐶1 = 1 − 0.5 ((462 .84

𝑙𝑏

𝑓𝑡2 )

1,014𝑙𝑏

𝑓𝑡2−462.84𝑙𝑏

𝑓𝑡2

) = 0.580

𝐶2 = 1

𝐶3 = 1.03 − 0.3(10) = 0.73

Page 13: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 12

JOY RANCH HOUSING COMMUNITY

o Settlement: 𝛿 =(0.580) (1)(0.73)(1,014

𝑙𝑏

𝑓𝑡2 −462 .84𝑙𝑏

𝑓𝑡2)(2∗0.556+0.1) (10 𝑓𝑡)

686 ,000𝑙𝑏

𝑓𝑡2

= 0.006 𝑓𝑡 =

0.068 𝑖𝑛

o Immediate settlement falls below the acceptable limit of 2 inches for bridges.

Page 14: Team #7 Geotechnical Report (2)

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JOY RANCH HOUSING COMMUNITY

Appendix B: Retaining Wall Calculations

Cantilever Cut-Off Wall

o The following calculations are applicable to all of the planned retaining walls.

o 𝐻𝑤 = 14 𝑓𝑡,𝐵ℎ𝑒𝑒𝑙 = 7 𝑓𝑡, 𝐵𝑡𝑜𝑒 = 3 𝑓𝑡, 𝐵𝑠𝑡𝑒𝑚 = 1.5 𝑓𝑡, 𝑒𝑚𝑏𝑒𝑑𝑚𝑒𝑛𝑡 =

0.5 𝑓𝑡, 𝐻 = 16 𝑓𝑡, 𝛾 = 120𝑙𝑏

𝑓𝑡3 , 𝑐 = 0𝑙𝑏

𝑓𝑡2 , 𝜙 = 30°,𝛽 = 3°, 𝜇 = 0.45

o Sliding

Coefficient of Lateral Earth Pressure: 𝐾𝑎 =(cos(3)−√cos2(3)−cos2(32) )

cos(3)+√cos2(3)−cos2(32)=

0.322

Soil Load on Wall (per unit length): 𝑃𝑎

𝑏=

((132 .24

𝑙𝑏

𝑓𝑡3 )(17𝑓𝑡) 2(0.322)

2) cos(3) = 5,141

𝑙𝑏

𝑓𝑡

Soil Load (per unit length): 𝑃

𝑏= 0.5 ∗ (6𝑓𝑡)(1𝑓𝑡 + 2 ∗ 14𝑓𝑡 +

6 tan(3)𝑓𝑡) (120𝑙𝑏

𝑓𝑡3 ) = 12,334𝑙𝑏

𝑓𝑡2

Load from Wall Weight (per unit length): 𝑊𝑓

𝑏= (6𝑓𝑡 + 3𝑓𝑡 +

1.5𝑓𝑡)(1.5𝑓𝑡) (150𝑙𝑏

𝑓𝑡3 ) + (1.5𝑓𝑡)(14𝑓𝑡 + 0.5𝑓𝑡) (150𝑙𝑏

𝑓𝑡3 ) = 5,850𝑙𝑏

𝑓𝑡

Factor of Safety: 𝐹 =((12 ,334

𝑙𝑏

𝑓𝑡2+5,850𝑙𝑏

𝑓𝑡2)(0.45))

4,295𝑙𝑏

𝑓𝑡2

= 1.59

This is an acceptable factor of safety, as it falls within the range of

1.5 to 2.

7’ 3’

14’

1.5’

𝑃𝑎

𝑏

1.5’

Page 15: Team #7 Geotechnical Report (2)

TEAM 7: GEOTECHNICAL MASTER PLAN 14

JOY RANCH HOUSING COMMUNITY

o Overturning

𝜙𝑤 =2

3(30°) = 20°

Loads Contributing to Turning Moments (per unit length) and Arm

Lengths

𝑃𝑎sin (𝜙𝑤 )

𝑏= 1,758

𝑙𝑏

𝑓𝑡, 𝑏 = 𝐵𝑡𝑜𝑒 + 𝐵𝑠𝑡𝑒𝑚 = 4.5 𝑓𝑡

𝑃𝑎 cos(𝜙𝑤 )

𝑏= 4,830

𝑙𝑏

𝑓𝑡, 𝑐 =

(0.5𝑓𝑡+15𝑓𝑡+6 tan(3°) )

3= 4.96 𝑓𝑡

𝑊𝑓

𝑏= 2,588

𝑙𝑏

𝑓𝑡,𝑎 =

6𝑓𝑡+1.5𝑓𝑡+3𝑓𝑡

2= 5.75 𝑓𝑡

𝑃

𝑏= 12,334

𝑙𝑏

𝑓𝑡, 𝑒 = (3𝑓𝑡 + 1.5𝑓𝑡 +

6𝑓𝑡

2) = 8 𝑓𝑡

𝑊𝑠𝑡𝑒𝑚

𝑏= 3,263

𝑙𝑏

𝑓𝑡, 𝑑 = (3𝑓𝑡 +

1.5𝑓𝑡

2) = 3.75 𝑓𝑡

Factor of Safety: 𝐹 =((1,758 𝑙𝑏)(4.5𝑓𝑡) +(2,588 𝑙𝑏)(5.75 𝑓𝑡)+(12,334 𝑙𝑏)(8 𝑓𝑡)+(3,263 𝑙𝑏)(3.75𝑓𝑡) )

(4,830 𝑙𝑏)(4.96𝑓𝑡)= 5.58

This factor of safety is acceptable, well above the required value of

1.5.

Eccentricity

𝑃𝑎

𝑏

c

𝑊𝑠𝑡𝑒𝑚

𝑏

𝑊𝑓

𝑏

𝑃

𝑏

a

d

b

e

𝜙𝑤

Moment

Reference Point

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(((1,758 𝑙𝑏)(4.5𝑓𝑡)+(2,588 𝑙𝑏)(5.75 𝑓𝑡)+(12,334 𝑙𝑏)(8 𝑓𝑡)+(3,263 𝑙𝑏)(3.75𝑓𝑡) )−(4,830 𝑙𝑏)(4.96𝑓𝑡))

1,758𝑙𝑏

𝑓𝑡+2,588

𝑙𝑏

𝑓𝑡+12,334

𝑙𝑏

𝑓𝑡+3,263

𝑙𝑏

𝑓𝑡

=

4.77 𝑓𝑡 = 𝑥

𝑒𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦 =11.5 𝑓𝑡

2− 4.77 𝑓𝑡 = 0.981

𝐵

6= 1.92

𝐵

6> 𝑒𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦 => 𝑎𝑐𝑐𝑒𝑝𝑡𝑎𝑏𝑙𝑒

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Appendix C: Boring Logs

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