1 Foundation Analysis and Desing
2 FOUNDATION DESIGN
Proportioning Elements for:
• Transfer of Seismic Forces
• Strength and Stiffness
• Shallow and Deep Foundations
• Elastic and Plastic Analysis
3 Load Path and Transfer of Seismic Forces
soil pressure
4 Load Path and Transfer of Seismic Forces
foundation force transfer
5 Load Path and Transfer of Seismic Forces
soil to foundation force transfer
6 Load Path and Transfer of Seismic Forces
vertical pressures - shallow
7 Load Path and Transfer of Seismic Forces
vertical pressures - deep
8 Reinforced Concrete Footings: Basic Design Criteria (concentrically loaded)
9 Footing Subject to Compression and Moment: Uplift
Nonlinear
10 Example
7-story building:
shallow foundations designed for perimeter frame and core bracing
11 Shallow Footing Examples
1 Soil parameters:
• Medium dense sand
• (SPT) N = 20
• Density = 120 pcf
• Friction angle = 33o
2 Gravity load allowables
• 4000 psf, B < 20 ft
• 2000 psf, B > 40 ft
Bearing capacity (EQ)
• 2000B concentric sq.
• 3000B eccentric
• f = 0.7
12 Footings proportioned for gravity loads alone
13 Design of footings for perimeter moment frame
14 7 Story Frame, Deformed
15 Combining Loads
• Maximum downward load:
1.2D + 0.5L + E
• Minimum downward load:
0.9D + E
• Definition of seismic load effect E:
E = r1QE1 + 0.3 r2QE2 +/- 0.2 SDSD
rx = 1.0 ry = 1.0 and SDS = 1.0
16 Reactions
17 Reduction of Overturning Moment
• NEHRP Provisions allow base overturning moment to be reduced by 25% at the soil- foundation interface
• For a moment frame, the column vertical loads are the resultants of base overturning moment, whereas column moments are resultants of story shear
• Thus, use 75% of seismic vertical reactions
18 Additive Load w/ Largest eccentricity
• Combining loads on footings A-5 and A-6, applying the 0.75 multiplier for overturning effects to the axial loads, and neglecting the weight of the foundation and overlying soil,
• P = 256 kips
• Mxx = -6,717 ft-kips
• Myy = -126 ft-kips (which is negligible)
19 Counteracting Load w/ Largest e
• Again combining loads on footings A-5 and A-6, including the overturning factor, and neglecting the weight of the footing and overlying soil,
• P = 8 kips
• Mxx = -5,712 ft-kips
• Myy = -126 ft-kips (negligible)
20 Elastic Response
• Objective is to set L and W to satisfy equilibrium and avoid overloading soil
• Successive trials usually necessary
21 Additive Combination
Given P = 256 k, M =6717 k-ft
Try 4.5 foot around, thus L = 34 ft, B = 9 ft
• Minimum W = M/(L/2) – P = 139 k = 455 psf
Try 2 foot soil cover & 3 foot thick footing
• W = 214 k; for additive combo use 1.2W
• Qmax = (P + 1.2W)/(3(L/2 – e)B/2) = 9.74 ksf
• fQn = 0.7(3)Bmin = 18.9 ksf, OK by Elastic
22 Plastic Response
• Same objective as for elastic response
• Smaller footings can be shown OK thus
23 Counteracting Case
Given P = 8 k; M = 5712
Check prior trial; W = 214 k (use 0.9W)
• e = 5712/(214 + 8) = 25.7 > 34/2 NG
New trial: L = 40 ft, 5 ft thick, 2 ft soil cover
• W = 360 k; e = 17.2 ft; plastic Qmax= 8.78 ksf
• fQn = 0.7(3)4.1 = 8.6 ksf, close
• Try plastic solution, L’ = 4.2 ft, fQn = 8.82 ksf
• MR = (0.9(360)+8)(40/2-4.2/2) = 5943 > 5712
24 Additional Checks
• Moments and shears for reinforcement should be checked for the overturning case
• Plastic soil stress gives upper bound on moments and shears in concrete
• Horizontal equilibrium: Hmax< fm(P+W)
in this case friction exceeds demand; passive could also be used
25 Results for all Seismic Resistant System Footings
26 Design of footings for core-braced 7 story building
27 Solution for Central Mat
Very high uplifts at individual columns; mat is only practical shallow foundation
28 Bearing Pressure Solution
Plastic solution is satisfactory; elastic is not
29 Pile/Pier Foundations
View of cap with column above and piles below
30 Pile/Pier Foundations
1 Pile Stiffness:
• Short (Rigid)
• Intermediate
• Long
Cap Influence
Group Action
2 Soil Stiffness
• Linear springs – nomographs e.g. NAVFAC DM7.2
• Nonlinear springs – LPILE or similar analysis
31 Sample p-y Curves
32 Passive Pressure
33 Group Effect
34 Pile Shear: Two Soil
Stiffnesses
35 Pile Moment vs Depth
36 Pile Reinforcement
•Site Class C
•Larger amounts where moments and shears are high
•Minimum amounts must extend beyond theoretical cutoff points
•“Half” spiral for 3D
37 Pile Design
•Site Class E
•Substantially more reinforcement
•“Full” spiral for 7D
•Confinement at boundary of soft and firm soils (7D up and 3D down)
38 Other Topics for Pile Foundations
• Foundation Ties: F = PG(SDS/10)
• Pile Caps: high shears, rules of thumb; look for 3D strut and tie methods in future
• Liquefaction: another topic
• Kinematic interaction of soil layers
39 Tie between pile caps
•Designed for axial force (+/-)
•Pile cap axial load times SDS/10
•Oftentimes use grade beams or thickened slabs on grade
40 Questions
Title Slide
Foundation Design -1
The subtitles are effectively a table of contents, although the topics are not really
treated in that specific order. This unit is primarily aimed at the structural
engineering of foundations, not at the geotechnical engineering.
This presentation relates to example computations in Chapter 5 of the FEMA P752,
NEHRP Recommended Provisions: Design Examples.
Foundation Design -2
First model: soil pressures in unmoving soil caused by force at top of deep pile;
most of stress resisted at top of pile; only small stresses below about twice the
characteristic length of pile. Second model: unloaded pile subject to earthquake
ground motion; small stresses induced by upper levels of soil lagging behind deep
motion. Note opposing directions of “push”. Third model: both types of force act
on pile. The lag of structure induces inertial forces at top of pile similar to static
force in first model; net force shape similar to static situation.
Foundation Design -3
As building lags behind ground motion, induced inertial forces must be transferred
between footing and soil. Design may consider that inertial forces are transferred as
passive earth pressure on face of footing, friction on bottom of footing, or both.
Foundation Design -4
Same single story structure; now on deep pile foundation. One leg shows pile
displacements; other shows resulting earth pressures; third diagram shows bending
moment in pile. One reference that has long been used for laterally loaded piles is
the Navy Design Manual 7.2, Foundations and Earth Structures. However, it and
most other older methods are based upon assumptions of linear behavior in soil.
Over the past two decades considerable progress has been made in developing
design tools rooted in the strongly nonlinear behavior of soil. “LPILE” is one
widely used example that allows the user to specify soil parameters that model
resistance of soil to lateral movement of piles.
Foundation Design -5
As aspect ratio of building height to width increases, overturning moment becomes
significant; induced vertical forces must be transferred in addition to horizontal
pressures. (Similar vertical forces in footing result from column moments not
specifically related to overturning.) Slide shows overturning moment being resisted
below basement of medium sized building; horizontal pressures are transferred at
the basement walls.
Foundation Design -6
This example of tall building with shear wall continuing through deep basement
shows that the horizontal and vertical forces can be resisted by different portions of
foundation structure. Basement wall resists horizontal forces near ground surface;
vertical forces resisted by piles at base of wall.
Foundation Design -7
Reinforced concrete footings are proportioned according the provisions of ACI 318,
Building Code Requirements for Structural Concrete. It is often opined that
foundations should not yield, due to the high cost of foundation repair. However,
nonlinear soil behavior is common in strong ground shaking, and it is traditional to
design foundations for the reduced forces computed with the response modification
factor, R, used for the superstructure. Neither the NEHRP Recommended
Provisions nor earlier model building codes required the use of amplified forces for
foundation design.
Foundation Design -8
ASCE 41 has a good discussion of the plastic behavior of soil beneath eccentrically
loaded footings. Just as for analysis of structural members, plastic analysis of a
footing is simple “by hand”, but not so with a computer.
Both uplift and nonlinear behavior introduce complications in conventional
analysis. Many commercially available software packages for structural analysis
now handle the uplift case; a smaller set can also handle nonlinear behavior.
Foundation Design -9
Title slide for 7-story building showing plan of steel building.
Foundation Design -10
The gravity load allowables are set to control settlements. The values between 20
and 40 feet should be interpolated. The bearing capacity is the classic value from
theoretical soil mechanics (normal gravity loads are checked). The subject of
strength design in soils is in its infancy, and many geotechnical professionals are not
yet comfortable with strength design concepts.
Note that the term phi is Resistance Factor for bearing capacity. B is the footing
width.
Foundation Design -11
The size of the square footing is controlled by the allowable bearing pressure at total
loads, and the thickness is controlled by two-way shear at the critical section
(“punching shear”).
The point of this information is primarily for later comparison with footings
designed for seismic loads.
Foundation Design -12
The only portion of the steel frame that resists lateral forces is at the perimeter, thus,
the only footings that will be affected by the seismic load are at the perimeter.
Foundation Design -13
The image is taken from the RAM Frame analysis used to design the steel moment
resisting frame for seismic loads.
Foundation Design -14
Load combinations for strength-based design, which is the fundamental method for
earthquake resistant design.
Greek rho is the redundancy factor. Q is the effect of horizontal seismic motions.
The 0.2SdsD is an approximation for the effect of vertical earthquake motions.
For the footings, the horizontal motions produce vertical and horizontal forces, as
well as bending moments, at the base of each column. Dead and Live loads are
taken to produce only vertical forces in this example.
Foundation Design -15
Grid A-6 is at the lower left corner of the plan, and A-5 is adjacent. (Go back three
slides to show the location on the plan.) Recall that the seismic reactions can be
positive or negative; what is given here is for motion in the positive x and y
directions. Carefully note that subscripts x and y on the load effect E refer to the
global north-south and east-west, respectively, but the subscripts x and y on the
moments at the column bases refer to the local strong and weak axes, respectively,
which is just the opposite as the global directions, unfortunately.
The most significant point of this slide is that seismic uplift at A-6 exceeds the dead
load by a considerable margin. It is possible to place a footing with sufficient size
to resist the uplift and the overturning moment, but it is much more economical to
combine one footing for the two locations. These reactions include the effects of
horizontal torsion on the system. Also recall that the footing must resist horizontal
forces.
Foundation Design -16
The Provisions allow an overturning moment reduction of 25% at the soil-foundation
interface.
Foundation Design -17
None of these loads include the weight of the footing.
P is positive in compression. M is positive by the local right hand rule.
This is not the maximum downward load; it is the maximum ratio of moment to
axial load for the additive combos.
Foundation Design -18
Note that the net vertical load is upward without the weight of the footing. It so
happens that this combo also gives the maximum eccentricity, when combined with
the weight of footing and soil.
Foundation Design -19
Slide is drawn for the case with substantial moment, such that uplift will occur at
the heel. Note that eccentricity e changes as W changes.
For our footing, L will exceed 25 feet by some margin, given that the two columns
are 25 feet apart.
Foundation Design -20
Initial approximation of W is simply to keep the resultant of earth pressure within
the footing. It must be somewhat larger in order to control the bearing pressures.
Note that the load factor on W does not include the amplifier for vertical seismic
acceleration; this is the author’s interpretation of the NEHRP Provisions.
The minimum B used to find the nominal bearing capacity is found by comparing
the width of the footing and the half length of the loaded area. The half length is
used because the soil pressure is not uniform.
Foundation Design -21
Slide shows basis of plastic design of foundation.
Foundation Design -22
Note how much larger the footing must be for the counteracting case. Also, it
would have been even larger if the elastic solution were used in lieu of the plastic
solution.
Foundation Design -23
Notes for additional checks for foundation design.
Foundation Design -24
Given the combined footing strategy, footing sizes are more strongly influenced by
the uplift on columns at the ends of frames than by the moments transmitted by the
columns. Note that a complete perimeter grade beam would be a very feasible
solution for this project, especially in cold climates where a continuous perimeter
wall for frost control is necessary. A 4 ft by 4 ft continuous grade beam would be
sufficient.
Foundation Design -25
The screen capture is from the RAM Frame analysis of the structure, and the small
plan is based on the same grids used for the 7 story moment frame. The braced
frames appear to be 8 stories high, because there is a small penthouse over the core.
Foundation Design -26
The fundamental method is the same as used in the previous example: Determine
the total applied vertical and horizontal loads and the moments. The complicating
factor here is that the bending is significant about two axes simultaneously. Elastic
solutions can be found from software that has the capacity for compression-only
springs; SAP2000 was used in this case. Plastic solutions typically need to be done
“by hand,” although spreadsheets are a great asset for the successive trial nature of
the solution.
Foundation Design -27
Slide shows the results from “hand” analysis for plastic distribution and for
SAP2000 elastic solution. See Chapter 5 of FEMA P-751 for more detail on the
solution, as well as the design of the footing cross section for moment and shear.
Foundation Design -28
Title slide for pier foundations.
Foundation Design -29
Most pile analysis for lateral loads is performed assuming linear response in the pile
itself, although it is now common to consider nonlinear soil response. Some “byhand”
plastic techniques do make use of the classic pile stiffness idealizations.
Foundation Design -30
Note the logarithmic scale on the vertical axis.
Foundation Design -31
This passive pressure mobilization is useful for inclusion of the pile cap. It is from
ASCE 41. Delta/H is the imposed displacement as a fraction of the minimum
dimension of the face being pushed into the soil mass.
Foundation Design -32
Plots of group effect factors computed based on Rollins et al., “Pile Spacing Effects
on Lateral Pile Group Behavior: Analysis,” Journal of Geotechnical and
Geoenvironmental Engineering, October 2006. The plot shows four curves, each
for a different spacing (in terms of pile diameter). The horizontal axis is the number
of rows of piles, and the vertical axis is the Group Effect Factor.
Foundation Design -33
Note that the shear forces in the pile (as well as deformations and bending
moments) carries to greater depths in soft soils than in firm soils. Pile (or pier)
foundations are often used in stiff soils to control settlement of heavy structures or
heave of expansive soils.
Foundation Design -34
See Chapter 5 of FEMA P-751.
Foundation Design -35
Diagram and notes indicate requirements for pile reinforcement. “D” is pile diameter.
Foundation Design -36
The drawing shows one of the piles with detail of reinforcement. “D” is pile
diameter.
See Chapter 5 of FEMA P-751.
Foundation Design -37
Additional considerations for Pile Foundations. The equation is from ASCE 7-10 Section
12.13.5.2, where F is the design tension/compression force in the foundation tie beam and
PG is the load in the pile.
Foundation Design -38
Required iin higher seismic design categories for softer soils. It is designed for
“pure” axial force. Fundamental objective is to prevent relative lateral displacement
between column bases. It “fixes” the column bases for translation, but it is not
intended to restrain rotation at the column bases.
Foundation Design -39
Slide to initiate questions from the participants.
Foundation Design -40