Mathcad - Trinity Bearing Capacity - MDK [PDF]

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Bearing Capacity PROJECT: Trinity River Corridor Project 352010 PROJECT #: CREATED BY: Mark Kacmarcik/CVO REVIEWED BY: ________________________

Given: Find: Assumptions: References:

DATE: 03/23/2009__ DATE: ___________

MODIFIED: ___________

Soil strength data from geotechnical investigation and laboratory analyses. Allowable Bearing Capacity for design of shallow footings. Noted below in calculation. Bowles, J. Foundation Analysis and Design. 5th ed. McGraw Hill. San Francisco, 1996. pp. 263-266. Cernica, J. Geotechnical Engineering: Soil Mechanics. Wiley. New York, 1995. pp. 418-420.

Material Properties: Assume that foundations are constructed in the Upper Clay Unit or Flaggy Zone. ϕ := 24deg

Effective stress friction angle from results of ICU triaxial tests..

c := 0psf

Effective stress cohesion. Conservatively assumed to be 0 psf..

γm := 120pcf

Moist unit weight..

γsat := 125pcf

Saturated unit weight.

γwater := 62.4pcf

Unit weight of water.

γbuoy := γsat − γwater

Trinity Bearing Capacity_mdk.xmcd

γbuoy = 62.6⋅ pcf

1/5

Buoyant unit weight.

Print Date: 7/9/2009

Footing Geometry: Dftg := 12ft

Footing depth.

σzD := Dftg⋅ γbuoy

Effective stress at footing depth, assumed GWT at ground surface.σzD = 751.2⋅ psf

Bftg := 10ft

Footing width

Lftg := 100000ft

Footing length, (extremely large for strip footings, set equal to B.ftg for square footings).

β := 0deg

β = 0 ⋅ deg

Assume horizontal ground surface.

Vesic's Bearing Capacity Formula: qult = c⋅ Nc⋅ sc⋅ dc⋅ ic⋅ b c⋅ gc + σzD⋅ Nq⋅ sq⋅ d q ⋅ iq ⋅ bq ⋅ gq + 0.5⋅ γ⋅ B ⋅ Nγ⋅ sγ⋅ d γ⋅ iγ⋅ b γ⋅ gγ where:

sc, sq , sγ = shape factors dc, dq , dγ = depth factors ic, iq , iγ

= load inclination factors

bc, bq , bγ = base inclination factors gc, gq , gγ = ground inclination factors Bearing Capacity Factors:

Nq := e

π tan ( ϕ)

tan 45⋅ deg +

Trinity Bearing Capacity_mdk.xmcd



ϕ

2



Nq = 9.603

2

2/5

Print Date: 7/9/2009

5.14 if ϕ = 0

Nc :=

Nq − 1

otherwise

tan( ϕ)

(

Nc = 19.324

)

Nγ := 2 Nq + 1 tan( ϕ)

Nγ = 9.442

Footing Shape Factors sc := 1.0 +

 Nq   Bftg      Nc   Lftg 

sc = 1

sq := 1.0 +

 Bftg    ⋅ tan( ϕ) Lftg  

sq = 1

 Bftg  sγ := 1.0 − 0.4⋅    Lftg 

sγ = 1

Depth Factors: Dftg Bftg

k :=

= 1.2

Dftg Bftg

if

Dftg Bftg

≤ 1.0

k = 0.876

 Dftg   otherwise  Bftg 

atan

dc := 1 + 0.4⋅ k

dc = 1.35 2

dq := 1 + 2⋅ tan( ϕ) ⋅ ( 1 − sin( ϕ) ) ⋅ k dγ := 1.00

dq = 1.275

for all φ

dγ = 1

Inclination Factors: P := 0kip

Component of load that acts perpendicular to bottom of footing.

V := 0kip

Component of load that acts parallel to bottom of footing.

A := Bftg⋅ Lftg

Base area of footing

Trinity Bearing Capacity_mdk.xmcd

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Indicate direction of load Inclination by enabling appropriate scenario: Loads inclined in B direction. Bftg

2+

2+

Lftg

m :=

m :=

Bftg

1+

ic := 1 −

Loads inclined in L direction

1+

Lftg

m⋅ V

Lftg Bftg Lftg Bftg

ic = 1

A⋅ c⋅ Nc

V  iq :=  1 − A⋅ c  P+   tan( ϕ)  

m

iq = 1

m+ 1 V   iγ :=  1 − A⋅ c  P+   tan( ϕ)  

iγ = 1

Ground Factors: β gc := 1 − 147deg

gc = 1

gq := ( 1 − tan( β) )

2

gq = 1

gγ := gq

gγ = 1

Base Factors: Angle of inclination of base of footing.

α := 0deg

bc := 1 −

α

bq :=  1 −



bc := 1

147deg α⋅ tan( ϕ)  57deg

2

 

bq := 1

bγ := b q

Trinity Bearing Capacity_mdk.xmcd

bγ := 1

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qult := c⋅ Nc⋅ sc⋅ dc⋅ ic⋅ b c⋅ gc + σzD⋅ Nq⋅ sq⋅ d q ⋅ iq ⋅ bq ⋅ gq + 0.5⋅ γbuoy⋅ Bftg⋅ Nγ⋅ sγ⋅ d γ⋅ iγ⋅ b γ⋅ gγ qult = 12.15⋅ ksf

qallow :=

q ult 3

qallow = 4.05⋅ ksf

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Print Date: 7/9/2009