Foundation Analysis and Design Information

Contents

5.1 SHALLOW FOUNDATIONS FOR A SEVEN-STORY OFFICE BUILDING, LOS
ANGELES, CALIFORNIA …………………………………………………………………………………………….. 3
5.1.1 Basic Information …………………………………………………………………………………………………… 3
5.1.2 Design for Gravity Loads ………………………………………………………………………………………… 8
5.1.3 Design for Moment-Resisting Frame System ……………………………………………………………. 11
5.1.4 Design for Concentrically Braced Frame System ……………………………………………………… 16
5.1.5 Cost Comparison ………………………………………………………………………………………………….. 24
5.2 DEEP FOUNDATIONS FOR A 12-STORY BUILDING, SEISMIC DESIGN CATEGORY D
………………………………………………………………………………………………………………………………….. 25
5.2.1 Basic Information …………………………………………………………………………………………………. 25
5.2.2 Pile Analysis, Design and Detailing ………………………………………………………………………… 33
5.2.3 Other Considerations …………………………………………………………………………………………….. 47

FEMA P-751, NEHRP Recommended Provisions: Design Examples
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This chapter illustrates application of the 2009 Edition of the NEHRP Recommended Provisions to the
design of foundation elements. Example 5.1 completes the analysis and design of shallow foundations for
two of the alternative framing arrangements considered for the building featured in Example 6.2.
Example 5.2 illustrates the analysis and design of deep foundations for a building similar to the one
highlighted in Chapter 7 of this volume of design examples. In both cases, only those portions of the
designs necessary to illustrate specific points are included.

The force-displacement response of soil to loading is highly nonlinear and strongly time dependent.
Control of settlement is generally the most important aspect of soil response to gravity loads. However,
the strength of the soil may control foundation design where large amplitude transient loads, such as those
occurring during an earthquake, are anticipated.

Foundation elements are most commonly constructed of reinforced concrete. As compared to design of
concrete elements that form the superstructure of a building, additional consideration must be given to
concrete foundation elements due to permanent exposure to potentially deleterious materials, less precise
construction tolerances and even the possibility of unintentional mixing with soil.

Although the application of advanced analysis techniques to foundation design is becoming increasingly
common (and is illustrated in this chapter), analysis should not be the primary focus of foundation design.
Good foundation design for seismic resistance requires familiarity with basic soil behavior and common
geotechnical parameters, the ability to proportion concrete elements correctly, an understanding of how
such elements should be detailed to produce ductile response and careful attention to practical
considerations of construction.

In addition to the Standard and the Provisions and Commentary, the following documents are either
referenced directly or provide useful information for the analysis and design of foundations for seismic
resistance:

ACI 318 American Concrete Institute. 2008. Building Code Requirements and
Commentary for Structural Concrete.

Bowles Bowles, J. E. 1988. Foundation Analysis and Design. McGraw-Hill.

CRSI Concrete Reinforcing Steel Institute. 2008. CRSI Design Handbook. Concrete
Reinforcing Steel Institute.

ASCE 41 ASCE. 2006. Seismic Rehabilitation of Existing Buildings.

Kramer Kramer, S. L. 1996. Geotechnical Earthquake Engineering. Prentice Hall.

LPILE Reese, L. C. and S. T. Wang. 2009. Technical Manual for LPILE Plus 5.0 for
Windows. Ensoft.

Rollins et al. (a) Rollins, K. M., Olsen, R. J., Egbert, J. J., Jensen, D. H., Olsen, K. G.and Garrett,
B. H. (2006). “Pile Spacing Effects on Lateral Pile Group Behavior: Load Tests.”
Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 132,
No. 10, p. 1262-1271.

Rollins et al. (b) Rollins, K. M., Olsen, K. G., Jensen, D. H, Garrett, B. H., Olsen, R. J.and Egbert,
J. J. (2006). “Pile Spacing Effects on Lateral Pile Group Behavior: Analysis.”

Chapter 5: Foundation Analysis and Design
5-3
Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 132,
No. 10, p. 1272-1283.

Wang & Salmon Wang, C.-K. and C. G. Salmon. 1992. Reinforced Concrete Design .
HarperCollins.

Several commercially available programs were used to perform the calculations described in this chapter.
SAP2000 is used to determine the shears and moments in a concrete mat foundation; LPILE, in the
analysis of laterally loaded single piles; and spColumn, to determine concrete pile section capacities.

This example features the analysis and design of shallow foundations for two of the three framing
arrangements for the seven-story steel office building described in Section 6.2 of this volume of design
examples. Refer to that example for more detailed building information and for the design of the
superstructure.

5.1.1 Basic
Information

5.1.1.1 Description. The framing plan in Figure 5.1-1 shows the gravity load-resisting system for a
representative level of the building. The site soils, consisting of medium dense sands, are suitable for
shallow foundations. Table 5.1-1 shows the design parameters provided by a geotechnical consultant.
Note the distinction made between bearing pressure and bearing capacity. If the long-term, service-level
loads applied to foundations do not exceed the noted bearing pressure, differential and total settlements
are expected to be within acceptable limits. Settlements are more pronounced where large areas are
loaded, so the bearing pressure limits are a function of the size of the loaded area. The values identified
as bearing capacity are related to gross failure of the soil mass in the vicinity of loading. Where loads are
applied over smaller areas, punching into the soil is more likely.

FEMA P-751, NEHRP Recommended Provisions: Design Examples
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Figure 5.1-1 Typical framing plan

Because bearing capacities are generally expressed as a function of the minimum dimension of the loaded
area and are applied as limits on the maximum pressure, foundations with significantly non-square loaded
areas (tending toward strip footings) and those with significant differences between average pressure and
maximum pressure (as for eccentrically loaded footings) have higher calculated bearing capacities. The
recommended values are consistent with these expectations

Table 5.1-1 Geotechnical Parameters
Parameter Value
Net bearing pressure (to control
settlement due to sustained loads)
≤ 4,000 psf for B ≤ 20 feet

≤ 2,000 psf for B ≥ 40 feet

(may interpolate for intermediate dimensions)
Bearing capacity (for plastic
equilibrium strength checks with
factored loads)
2,000B psf for concentrically loaded square footings

3,000B’ psf for eccentrically loaded footings

where B and B’ are in feet, B is the footing width and B’ is
an average width for the compressed area.

Resistance factor, φ = 0.7

[This φ factor for cohesionless soil is specified in
Provisions Part 3 Resource Paper 4; the value is set at 0.7
for vertical, lateral and rocking resistance.]
Lateral properties
Earth pressure coefficients:

§§ Active, KA = 0.3
§§ At-rest, K0 = 0.46
§§ Passive, KP = 3.3

“Ultimate” friction coefficient at base of footing = 0.65
Resistance factor, φ = 0.7

The structural material properties assumed for this example are as follows:

§§ f’c = 4,000 psi

§§ fy = 60,000 psi

5.1.1.2 Seismic Parameters. The complete set of parameters used in applying the Provisions to design of
the superstructure is described in Section 6.2.2.1 of this volume of design examples. The following
parameters, which are used during foundation design, are duplicated here.

§§ Site Class = D

§§ SDS = 1.0

§§ Seismic Design Category = D
FEMA P-751, NEHRP Recommended Provisions: Design Examples
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5.1.1.3 Design Approach.

5.1.1.3.1 Selecting Footing Size and Reinforcement. Most foundation failures are related to excessive
movement rather than loss of load-carrying capacity. In recognition of this fact, settlement control should
be the first issue addressed. Once service loads have been calculated, foundation plan dimensions should
be selected to limit bearing pressures to those that are expected to provide adequate settlement
performance. Maintaining a reasonably consistent level of service load-bearing pressures for all of the
individual footings is encouraged since it will tend to reduce differential settlements, which are usually of
more concern than are total settlements.

Once a preliminary footing size that satisfies serviceability criteria has been selected, bearing capacity can
be checked. It would be rare for bearing capacity to govern the size of footings subjected to sustained
loads. However, where large transient loads are anticipated, consideration of bearing capacity may
become important.

The thickness of footings is selected for ease of construction and to provide adequate shear capacity for
the concrete section. The common design approach is to increase footing thickness as necessary to avoid
the need for shear reinforcement, which is uncommon in shallow foundations.

Design requirements for concrete footings are found in Chapters 15 and 21 of ACI 318. Chapter 15
provides direction for the calculation of demands and includes detailing requirements. Section capacities
are calculated in accordance with Chapters 10 (for flexure) and 11 (for shear). Figure 5.1-2 illustrates the
critical sections (dashed lines) and areas (hatched) over which loads are tributary to the critical sections.
For elements that are very thick with respect to the plan dimensions (as at pile caps), these critical section
definitions become less meaningful and other approaches (such as strut-and-tie modeling) should be
employed. Chapter 21 provides the minimum requirements for concrete foundations in Seismic Design
Categories D, E and F, which are similar to those provided in prior editions of the Provisions.

For shallow foundations, reinforcement is designed to satisfy flexural demands. ACI 318 Section 15.4
defines how flexural reinforcement is to be distributed for footings of various shapes.

Section 10.5 of ACI 318 prescribes the minimum reinforcement for flexural members where tensile
reinforcement is required by analysis. Provision of the minimum reinforcement assures that the strength
of the cracked section is not less than that of the corresponding unreinforced concrete section, thus
preventing sudden, brittle failures. Less reinforcement may be used as long as “the area of tensile
reinforcement provided is at least one-third greater than that required by analysis.” Section 10.5.4 relaxes
the minimum reinforcement requirement for footings of uniform thickness. Such elements need only
satisfy the shrinkage reinforcement requirements of Section 7.12. Section 10.5.4 also imposes limits on
the maximum spacing of bars.

5.1.1.3.2 Additional Considerations for Eccentric Loads. The design of eccentrically loaded footings
follows the approach outlined above with one significant addition: consideration of overturning stability.
Stability calculations are sensitive to the characterization of soil behavior. For sustained eccentric loads,
a linear distribution of elastic soil stresses is generally assumed and uplift is usually avoided. If the
structure is expected to remain elastic when subjected to short-term eccentric loads (as for wind loading),
uplift over a portion of the footing is acceptable to most designers. Where foundations will be subjected
to short-term loads and inelastic response is acceptable (as for earthquake loading), plastic soil stresses
may be considered. It is most common to consider stability effects on the basis of statically applied loads
even where the loading is actually dynamic; that approach simplifies the calculations at the expense of
increased conservatism. Figure 5.1-3 illustrates the distribution of soil stresses for the various
assumptions. Most textbooks on foundation design provide simple equations to describe the conditions

FEMA P-751, NEHRP Recommended Provisions: Design Examples
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5.1.2 Design
for
Gravity
Loads

Although most of the examples in this volume do not provide detailed design for gravity loads, it is
provided in this section for two reasons. First, most of the calculation procedures used in designing
shallow foundations for seismic loads are identical to those used for gravity design. Second, a complete
gravity design is needed to make the cost comparisons shown in Section 5.1.5 below meaningful.

Detailed calculations are shown for a typical interior footing. The results for all three footing types are
summarized in Section 5.1.2.5.

5.1.2.1 Demands. Dead and live load reactions are determined as part of the three-dimensional analysis
described in Section 6.2 of this volume of design examples. Although there are slight variations in the
calculated reactions, the foundations are lumped into three groups (interior, perimeter and corner) for
gravity load design and the maximum computed reactions are applied to all members of the group, as
follows:

§§ Interior: D = 387 kips
L = 98 kips

§§ Perimeter: D = 206 kips
L = 45 kips

§§ Corner: D = 104 kips
L = 23 kips

The service load combination for consideration of settlement is D + L. Considering the load
combinations for strength design defined in Section 2.3.2 of the Standard, the controlling gravity load
combination is 1.2D + 1.6L.

5.1.2.2 Footing Size. The preliminary size of the footing is determined considering settlement. The
service load on a typical interior footing is calculated as:

P = D + L = 387 kips + 98 kips = 485 kips

Since the footing dimensions will be less than 20 feet, the allowable bearing pressure (see Table 5.1-1) is
4,000 psf. Therefore, the required footing area is 487,000 lb/4,000 psf = 121.25 ft2
.

Check a footing that is 11′-0″ by 11′-0″:

Pallow = 11 ft(11 ft)(4,000 psf) = 484,000 lb = 484 kips ≈ 485 kips (demand) OK

The strength demand is:

Pu = 1.2(387 kips) + 1.6(98 kips) = 621 kips

As indicated in Table 5.1-1, the bearing capacity (qc) is 2,000B = 2,000 × 11 = 22,000 psf = 22 ksf.

The design capacity for the foundation is:

φPn = φqcB2
= 0.7(22 ksf)(11 ft)2
= 1,863 kips > 621 kips OK

Chapter 5: Foundation Analysis and Design
5-9
For use in subsequent calculations, the factored bearing pressure qu = 621 kips/(11 ft)2
= 5.13 ksf.

5.1.2.3 Footing Thickness. Once the plan dimensions of the footing are selected, the thickness is
determined such that the section satisfies the one-way and two-way shear demands without the addition of
shear reinforcement. Demands are calculated at critical sections, shown in Figure 5.1-2, which depend on
the footing thickness.

Check a footing that is 26 inches thick:

For the W14 columns used in this building, the side dimensions of the loaded area (taken halfway
between the face of the column and the edge of the base plate) are approximately 16 inches.
Accounting for cover and expected bar sizes, d = 26 – (3 + 1.5(1)) = 21.5 in.

One-way shear:

( )
16
12 11 21.5 11 5.13
2 12
Vu
⎛ ⎞ − = ⎜ ⎟ −
⎝ ⎠
= 172 kips

( ) ( )( )( ) 1
1,000 0.75 2 4,000 11 12 21.5 φ φ V V n c = = × = 269 kips > 172 kips OK

Two-way shear:

( ) ( ) 2 16 21.5
12 621 5.13 Vu + = − = 571 kips

( ) ( ) ( )( ) 1
1,000 0.75 4 4,000 4 16 21.5 21.5 φ φ V V n c = = ⎡ ⎤ × + ⎣ ⎦ = 612 kips > 571 kips OK

5.1.2.4 Footing Reinforcement. Footing reinforcement is selected considering both flexural demands
and minimum reinforcement requirements. The following calculations treat flexure first because it
usually controls:

( ) ( )
2 16
12 1 11
11 5.13 659 ft-kips 2 2
Mu
⎛ ⎞ − = = ⎜ ⎟
⎝ ⎠

Try nine #8 bars each way. The distance from the extreme compression fiber to the center of the top layer
of reinforcement, d = t – cover – 1.5db = 26 – 3 – 1.5(1) = 21.5 in.

T = As fy = 9(0.79)(60) = 427 kips

Noting that C = T and solving the expression C = 0.85 f’c b a for a produces a = 0.951 in.

( ) ( )( )( ) 0.951 1
2 2 12 0.90 427 21.5 a φ φ M Td n = − = − = 673 ft-kips > 659 ft-kips OK

The ratio of reinforcement provided is ρ = 9(0.79)/[(11)(12)(26)] = 0.00207. The distance between bars
spaced uniformly across the width of the footing is s = [(11)(12)-2(3+0.5)]/(9-1) = 15.6 in.

According to ACI 318 Section 7.12, the minimum reinforcement ratio = 0.0018 < 0.00207 OK

FEMA P-751, NEHRP Recommended Provisions: Design Examples
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and the maximum spacing is the lesser of 5 × 26 in. and 18 = 18 in. > 15.6 in. OK

5.1.2.5 Design Results. The calculations performed in Sections 5.1.2.2 through 5.1.2.4 are repeated for
typical perimeter and corner footings. The footing design for gravity loads is summarized in Table 5.1-2;
Figure 5.1-4 depicts the resulting foundation plan.

Table 5.1-2 Footing Design for Gravity Loads
Location Loads Footing Size and Reinforcement;
Soil Capacity
Critical Section Demands and
Design Strengths
Interior
D = 387 kip
L = 98 kip

P = 485 kip
Pu = 621 kip
11′-0″ × 11′-0″ × 2′-2″ deep
9-#8 bars each way

Pallow = 484 kip
φPn = 1863 kip
One-way shear: Vu = 172 kip
φVn = 269 kip
Two-way shear: Vu = 571 kip
φVn = 612 kip
Flexure: Mu = 659 ft-kip
φMn = 673 ft-kip
Perimeter
D = 206 kip
L = 45 kip

P = 251 kip
Pu = 319 kip
8′-0″ × 8′-0″ × 1′-6″ deep
9-#6 bars each way

Pallow = 256 kip
φPn = 716 kip
One-way shear: Vu = 88.1 kip
φVn = 123 kip
Two-way shear: Vu = 289 kip
φVn = 302 kip
Flexure: Mu = 222 ft-kip
φMn = 234 ft-kip
Corner
D = 104 kip
L = 23 kip

P = 127 kip
Pu = 162 kip
6′-0″ × 6′-0″ × 1′-2″ deep
6-#5 bars each way

Pallow = 144 kip
φPn = 302 kip
One-way shear: Vu = 41.5 kip
φVn = 64.9 kip
Two-way shear: Vu = 141 kip
φVn = 184 kip
Flexure: Mu = 73.3 ft-kip
φMn = 75.2 ft-kip

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