PE Refresher Course

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PE Refresher Course Geotechnical Component Class 2
Notes available at www.ce.washington.edu/geotech
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• Organization
• Lecture No. 1
• Basics (Chapter 35)
• Soil classification
• Phase diagrams
• Soil properties
• Compaction
• Permeability
• Consolidation
• Shear strength
• Applications (Chapter 35, 40)
• Settlement problems
• Magnitude of settlement
• Rate of settlement

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• Organization
• Lecture No. 2
• Applications ( Chapters 36, 37, 38, 39, 40)
• Seepage problems
• Slope stability problems
• Foundations
• Shallow Foundation
• Deep foundations
• Retaining structures
• Retaining walls
• Braced excavations

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Seepage
ht hp he
he elevation head relative to datum hp u/rw
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Solution
Pressure head
12
8
4
Total head
Head (cm of water)
0
Elevation head
-4
B
D
E
C
-8
A
0
4
9
14
17
All points same elevation
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Flow Nets

• Easiest way to solve 2-D flow problems
• Graphical solution to Laplace equation
• Based on concept of flow and equipotential lines
• Flow line path followed by a single water
  molecule. No water can cross a flow line
• Equipotential line line of constant total head
• Flow lines must intersect equipotential lines at
  right angles
• Elements must be square (except for partial
  drop)

(vol/time per unit length)
Number of flow channels
Number of equipotential drops
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Seepage Problems

• Seepage is driven by the hydraulic gradient, i.

• The rate of flow is proportional to the hydraulic
  gradient

• where ?h is the change in total head that
• occurs over a distance ?l
• Total head is the sum of pressure head and
  elevation head.
• Pressure head u/?w ( water pressure)
• Elevation head elevation relative to datum
  (any datum can be used)

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Slope Stability

• 2 primary failure mechanisms

?
?
Toe Failure Common for ? gt 0
Base Failure Common for ?0

• Stability usually expressed in terms of FS

• Slope stability charts are very useful for rapid
  
• evaluation of factor of safety
• For permanent slopes, min. FS of 1.5 is usually
  required
• For temporary slopes, lower value (1.2) may be
  appropriate

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Charts for uniform strength and ?0 (circular
failure surface expected)

• Calculate depth factor, d D/H
• Determine x0 and y0 from charts at bottom of Fig.
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• (toe circle if ? gt 53) (Establishes Center of
  Circle)
• Estimate average value of c over length of
  failure surface.
• Calculate Pd using

• From chart at top of Fig. 6, calculate stability
  number, No.
• Calculate factor of safety from
• Typical for undrained failure conditions
  (usually clays)

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Example
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Charts for uniform soils with ? gt 0 (Fig. 9) cgt0,
?gt0

• Estimate the location of the critical failure
  surface
• Estimate average values of c and tan? for the
  critical failure surface
• Calculate the stress

• Using average values of the strength parameters
• calculate the dimensionless parameter.

• If ?c? gt 3 or 4, the critical failure surface
  will pass through
• the toe of the slope. Double-check failure
  surface
• from Step 1 using chart on the right side of Fig.
  9.

• Calculate

• From chart on left side of Fig. 9, determine
  stability number, Ncf.
• Using ?c? and slope angle.

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• Calculate factor of safety using

Often used for drained (c0) conditions (common
for sands)
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Example
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Shallow Foundations

• Depth usually less than 3-4 times width
• Types
• Footings
• Spread (isolated)
• Strip (length gtgt width)
• Grid (grade beams)
• Mat (raft)

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Ultimate Bearing Capacity, qult
qult the stress or pressure applied at the
contact between the footing and underlying soil
that will just initiate failure in the soil.
Called Pult in your notes.
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Note how rapidly the B.C. factors increase as ?
increases
N
Nc
Ng
Nq
?
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Example
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Example
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• General form of bearing capacity equation was
  developed for
• Strip footing (L/B inf)
• Footing on ground surface
• Vertical footing load
• Deviations from these conditions are common and
  are accounted for by the use of Bearing capacity
  correction factors. With correction factors, the
  bearing capacity equation becomes

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Need to assume one or the other then check
accuracy of assumption at end
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Net Bearing Capacity

• qnet the net pressure that can be applied to
  the footing
• by external loads that will just initiate failure
  in the underlying soil.
• Equal to ultimate bearing capacity minus the
  stress due to the weight of the footing and any
  soil or surcharge directly above it.

Assuming the density of the footing (concrete)
and soil are close enough to be considered
equal, then
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Allowable Bearing Pressure

• Both ultimate bearing capacity and net bearing
  capacity determine loads that will bring footing
  to point of incipient failure. Due to uncertainty
  regarding loads, soil properties, soil and
  foundation geometries, and bearing capacity
  theory, lower loads must be used for design.
  Design is usually specified in terms of an
  allowable bearing pressure.
• Reduction depends on amount of uncertainty and
  potential effects of failure. Bearing capacity
  failures often have catastrophic effect on
  structure, so allowable bearing pressure is
  usually considerably smaller than bearing
  capacity.

Allowable bearing pressure can be determined by
A factor of safety of 3 is commonly used for
foundation design purposes.
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inclination
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Effect of Water Level

• If groundwater level is above bottom of footing,
  (qq?Df) (surcharge) term in bearing capacity
  equation must reflect effective stress at level
  of bottom of footing.
• If groundwater level is more than one footing
  width below bottom of footing, it will not affect
  bearing capacity.
• If groundwater level is within one footing width
  of bottom of footing, replace ? in last term of
  bearing capacity equation by

where d is the distance between the bottom of the
footing and the groundwater level.
d
B
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Footings Subjected to Overturning Moments
Vertical load and moment replaced by
eccentrically applied vertical load
P
P
e
M
Bearing pressure varies across bottom of footing
P
B
qmin
qmax
Maximum and minimum pressures given by
Need to check qmax- should be less than qall
qmin- should try to keep gt0
(if not, recalculate pressures using B'
B - 2e)
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Allowable Settlement of Footings on Sand

• For moderately high ?, bearing capacity factors
  become quite large
• As a result, bearing capacities become very
  large
• For sands, however, vertical displacement
  required to mobilize bearing capacity may be
  excessive (several inches or more)
• Must also check allowable bearing pressure
  based on settlement considerations
• Criteria usually based on SPT and 1 allowable
  settlement

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Deep Foundations

• Capacity
• Comes from 2 sources
• Point resistance bearing capacity at bottom of
  foundation (usually high for sands, low for
  clays)
• Skin resistance result of shear stresses
  mobilized along sides of foundation

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Point Resistance

• Treat as deep bearing capacity problem.
• Bearing capacity equation for deep Foundations
  is

where q vertical effective stress at bottom of
foundation Nc Nq deep bearing capacity
factors qlim limiting value of bearing capacity
(qult at depth of 10B)
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Skin Resistance

• Based on shear strength on vertical interface
  between side of foundation and adjacent soil
• Like shear strength of soil, this interface has
  components that are independent of normal stress
  and proportional to normal stress
• Component that is independent of normal stress
  is called adhesion, Ca. adhesion is related to
  cohesive strength of surrounding soil by

where a varies with c as shown below
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• Component that is proportional to normal stress
  is given by

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So, the total skin resistance
Where pr perimeter of foundation (length) N
number of pile segments ?Lilength of ith pile
segment Adding Pskinto Ptipgives total ultimate
capacity
Pskin
Note Net capacities and allowable capacities are
determined in the same way as shallow
foundations.
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Example
A pile load test is to be conducted on the
18diameter closed-end pipe pile shown below.
The pile is filled with concrete after
installation. Predict the load that will cause
failure.
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Pile Group Capacities

• Piles are often driven in groups connected by a
  common pile cap to support heavy loads. Because
  of interaction of closely spaced piles, capacity
  of group may not equal sum of individual pile
  capacities.
• For pile groups in sand,

Where ? is the pile group efficiency which can be
Estimated from the Converse-Labarre formula
Where n1 of piles in one direction n2 of
piles in other direction D pile
diameter dcenter to center spacing And the
arctan is in degrees.
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• For clays, can take group capacity as lower of
• 1. Sum of individual pile capacities
• 2. Capacity of equivalent pier shown below

Skin Resistance
Boundary of Equivalent Pier
Tip Resistance Equivalent pier
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Lateral Earth Pressures and Retaining Structures
Three basic earth pressure conditions to consider
1. At-rest conditions zero lateral strain
2. Active earth pressure conditions- extensional
lateral strains
3. Passive earth pressure conditions-
compressive lateral strains
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• For retaining wall backfill, coarse-grained
  soils are invariably used
• Good drainage qualities prevents buildup of
  water behind wall
• No time-dependent behavior cohesive soils are
• subject to creep and stress relaxation
• For c 0 soils, all earth pressures are
  proportional to depth

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Loose sand e 0.6
Assume dry
5 feet
? 30
10 feet
Assume saturated
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Typical cantilever retaining wall

• 9 step procedure listed in txt (Section 37.11)
• Find Pa and its point of reaction
• Find Pp and its point of reaction
• Find total vertical force and its point of
  reaction
• Check FS against overturning about toe of wall
• (Note that this is only meaningful If it
  represents a realistic failure mechanism
  Probably only for walls founded on rock.
• Check footing against bearing failure
  (eccentrically loaded footing).
• Calculate FS against sliding

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• Sloped Backfill
• See charts of Appendix 37.A p A. 54
• Broken Backfill
• See charts of Appendix 37.B p A.55
• Surcharge Loading on Backfill
• Uniform surcharge, q leads to uniform pressure
• On back of wall of magnitude K?q
• Point loads and line loads
• Use elasticity-based solutions in Secs. 40.1
  A40A,B
• Effect of water in Backfill
• Must calculate soil pressures on basis of
  effective stresses,
• then add full hydrostatic water pressure
• Example 3
• Design of Retaining Walls
• Must consider

Heel
Toe
Key
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Anchored Bulkheads
Flexible wall with lateral support from anchor
Anchor may consist of deadman , pile, beam, etc
Failure mechanisms Base failure Tierod
failure Anchor pullout Kickout at
toe Structural failure of sheeting
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