Foundation Analysis and Design

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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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