Geotechnichal engineering formulas.pdf
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Transcript of Geotechnichal engineering formulas.pdf
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GEOTECHNICAL ENGINEERING FORMULAS
A handy reference for use in geotechnical analysis and design
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TABLE OF CONTENTS Page
1. SOIL CLASSIFICATION ...............................................................................3
1.1 USCS: Unified Soil Classification System..........................................3 1.1.1 Relative Density of Cohesionless Soils: .....................................4 1.1.2 Fine Grained(Cohesive) Soil Charts using the USCS System:..4 1.1.3 Consistency of Fine Grained Soils: .............................................5
1.2 USDA Soil Classification System ........................................................5 1.3 AASHTO Soil Classification System:..................................................6
2. PHASE RELATIONSHIP EQUATIONS: .......................................................7 2.1 Shear Strength of Soils ........................................................................7 2.2 Bearing Capacity of Soils ....................................................................7
3. STRESSES IN SOILS ...................................................................................9 3.1 Various Loading Conditions:...............................................................9 ..........................................................................................................................9 ..........................................................................................................................9
4. SHALLOW FOUNDATIONS .......................................................................10 4.1 Conventional Footings.......................................................................10
4.11Geotechnical Analysis........................................................................10 4.12 Structural Design:..............................................................................10
4.2 Strap or Cantilever Footings: .................................................................11 4.3 Trapezoidal Footings: .............................................................................12
5. SOIL CONSOLIDATION EQUATIONS .......................................................14 5.1 Instant Settlement of footings: ..........................................................14 5.2 Primary Consolidation: ......................................................................14 5.3 Overconsolidated Soils ..........................................................................14 5.4 Time rate of settlement ..........................................................................15
5.41 Coefficient of consolidation..............................................................15 6. RETAINING STRUCTURES: ......................................................................16
6.1 Horizontal Stresses: Active, At Rest and Passive ................................16 6.2 Basement Wall with surcharge: .............................................................17 6.3 Braced Excavations: ...............................................................................17 6.4 Forces on Struts:.....................................................................................18 6.5 Cantilever Sheetpiles in Sand ................................................................20 6.6 Cantilever Sheetpiles in Clay .................................................................21 6.6 Anchored Sheetpiles in Sand (Also called Bulkheads) .......................22 6.7 Anchored Sheetpiles in Clay (Also called Bulkheads).........................24
7. PILE FOUNDATIONS .................................................................................25 8. Post Tensioned Slabs: ..............................................................................28 9. Asphalt Mix Design: ..................................................................................30 10. Concrete Mix Design:.............................................................................33
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1. SOIL CLASSIFICATION
1.1 USCS: Unified Soil Classification System
Coarse Grained soils have less than 50% passing the # 200 sieve:
Symbol Passing the #200
Cu=
30
60
D
D
Cc =
6010
2
30)(
DD
D
×
Soil Description
GW < 5% 4 or higher 1 to 3 Well graded gravel
GP < 5% Less than 4 1 to 3 Poorly graded gravel
GW-GM 5 to12% 4 or higher 1 to 3 but with <15% sand
Well graded gravel with silt
GW-GM 5 to12% 4 or higher 1 to 3 but with
≥15% sand
Well graded gravel with silt and sand
GW-GC 5 to12% 4 or higher 1 to 3 but with <15% sand
Well graded gravel with clay or silty clay
GW-GC 5 to12% 4 or higher 1 to 3 but with
≥15% sand
Well graded gravel with clay and sand
GC >12% N/A N/A,<15%sand Clayey Gravel
GC > 12% N/A N/A,>15%sand Clayey Gravel with sand
GM-GC >12% N/A N/A,<15%sand Clayey Silt with gravel
GM-GC >12% N/A N/A,≥15%sand Clayey Silt with sand
SW < 5% 6 or higher 1 to 3 Well graded sand
SP < 5% Less than 6 1 to 3 Poorly graded sand
SM >12% N/A N/A Silty Sand or Sandy Silt
SC >12% N/A N/A Clayey Sand or Sandy Clay
SC-SM >12% N/A N/A Silty Clay with Sand
Where:
Cu = Uniformity Coefficient; gives the range of grain sizes in a given sample. Higher Cu means well graded.
Cz = Coefficient of Curvature is a measure of the smoothness of the gradation curve. Usually less than 3.
D10, D3, & D60 are the grain size diameter corresponding to 10%, 30% and 60% passing screen.
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1.1.1 Relative Density of Cohesionless Soils:
SPT or N value Relative Density % Relative Density
0 – 3 Very loose 0 – 15
4 – 10 Loose 15 – 35
11 – 30 Medium dense 35 – 65
31 – 50 Dense 65 -85
> 50 Very dense 85 - 100
1.1.2 Fine Grained(Cohesive) Soil Charts using the USCS System:
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1.1.3 Consistency of Fine Grained Soils:
SPT or N value Cohesion, C or Su Consistency
< 2 < 500 psf Very soft
2 – 4 500 – 1000 psf Soft
5 – 8 1000 – 2000 psf Firm
9 – 15 2000 – 4000 psf Stiff
16-30 4000 – 8000 psf Very stiff
>30 > 8000 psf Hard
1.2 USDA Soil Classification System
The percent SAND,SILT,and CLAY lines are drawn and their intersection gives the
soil classification.
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1.3 AASHTO Soil Classification System:
CLASSIFICATION OF HIGHWAY SUBGRADE MATERIALS
(With suggested subgroups)
General Classification
Group Classification
Sieve Analysis,
Percent Passing:
No. 10
No. 40
No. 200
Characteristics of
fraction passing # 40:
Liquid Limit
Plasticity Index
Group Index
Usual Types of
Significicant Constituent
Materials
General Rating as
Subgrade
A-2
A-1-a A-1-b A-2-4 A-2-5 A-2-6 A-2-7
0-6
0
Stone Fragments,
Gravel and Sand
A-3
51-100
0-10
N.P.
0
Fine
Sand
0-50
Granular Materials (35% or less passing No. 200)
0-35 0-35 0-35 0-35
0-30
0-15
0-50
0-25
A-1
0-10
0-40 41+
0-10
0-40
11+
41+
11+
0 0-4
Silty or Clayey Gravel and Sand
Excellent to Good
Silt-Clay Materials (More than 35%
passing #200)
A-4 A-5 A-6
A-7
A-7-5
A-7-6
36-100 36-100 36-100 36-100
0-40
0-10
41+
0-10
0-40
11+
41+
11+
Silty Soils Clayey Soils
Fair to Poor
0-8 0-12 0-16 0-20
Cohesive soils classification in AASHTO System:
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2. PHASE RELATIONSHIP EQUATIONS: Dry Unit
Weight, γd
Bulk or Wet or Total
Unit Weight, γm or
γw or γt or γ
Saturated Unit
Weight, γs or γsat
2.1 Shear Strength of Soils
2.2 Bearing Capacity of Soils
Hansen B.C. Factors:
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Terzaghi B.C. Factors
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Note:If Df/B > 1, terzaghi’s B.C. factors do not apply. Use Hansen’s B.C. factors.
For example, if depth of footing (Df) is 3 ft but footing width (B) is 2.75 ft.
3. STRESSES IN SOILS
3.1 Various Loading Conditions:
Strip
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4. SHALLOW FOUNDATIONS
4.1 Conventional Footings
4.11Geotechnical Analysis qall = Q / Bx1 for Continuous Footings qall = Q / BxL for Rectangular Footings qall = Q / BxB for Square Footings qall < qu / 3 from Bearing Capacity Calculations e < B/6, where e=eccentricity Df > 1.0 ft minimum Df > frost depth Df > setback distance for footings on slope Df > scour depth Df > high moisture variations depth(expansive soils)
4.12 Structural Design: Given: A Continuous footing with γm = 100 pcf, Df = 5 ft, qall = 4,000 psf, D.L=22 k/ft, L.L.=12 k/ft, f’c=3 ksi, fy= 60 ksi. Design the footings using the ACI code:
Layer 1
Layer 2
Layer 33B
2B
1B
BDf
q all
GWT
2
1 Cc___1+Eo
C=
Q
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4.2 Strap or Cantilever Footings: Strap Footing with varying beam thickness
Strap Footings with constant beam thickness
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4.3 Trapezoidal Footings:
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5. SOIL CONSOLIDATION EQUATIONS
5.1 Instant Settlement of footings:
or
5.2 Primary Consolidation:
or
5.3 Overconsolidated Soils
or
or
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5.4 Time rate of settlement (i=immediate, c=consolidation, & s=secondary)
5.41 Coefficient of consolidation, Cv:
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6. RETAINING STRUCTURES:
6.1 Horizontal Stresses: Active, At Rest and Passive
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6.2 Basement Wall with surcharge:
6.3 Braced Excavations:
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6.4 Forces on Struts:
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Bottom Heave Calculations:
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6.5 Cantilever Sheetpiles in Sand
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6.6 Cantilever Sheetpiles in Clay
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6.6 Anchored Sheetpiles in Sand (Also called Bulkheads)
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6.7 Anchored Sheetpiles in Clay (Also called Bulkheads)
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7. PILE FOUNDATIONS 7.1 Single Piles Equations:
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7.2 Group capacity of piles:
Example:
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7.3 Settlement of Group Piles:
8. Post Tensioned Slabs: Edge Lift:
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Center Lift:
The Structural Engineer also needs Kv (given in immediate settlement section), effective PI(pp 138 of Geotechnical DVD book) and other climatic constants that are from building codes(given).
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9. Asphalt Mix Design:
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AC Mix design Formulas:
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When weighing in Water:
When weighing in Air:
Open Graded Mixtures:
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10. Concrete Mix Design:
Fineness modulus:
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Yield:
Relative Yield:
Modulus of Rupture: = (7.5√f’c) or