Lecture 9: Foundation Design using Load Factor Design

I. Introduction

The Load Factor Design (Ultimate Strength Design) is an alternate method for design of

simple and continuous beam and girder structures of moderate length. It is a method of

proportioning structural members for multiples of the design loads. To ensure serviceability

and durability, consideration is given to the control of permanent deformations under

overloads, to the fatigue characteristics under service loadings, and to the control of live

load deflections under service loadings. (NSCP Vol. 2, 2nd edition, 10.42)

II. Types of Foundation

Figure 1: Types of Foundations

a. Spread Footing A foundation which derives its support by transferring load directly

to the soil or rock at shallow depth. If a single slab covers the supporting

stratum beneath the entire area of the superstructure, the foundation is known

as a combined footing. If various parts of the structure are supported

individually, the individual supports are known as spread footings and the

foundation is called a footing foundation.

b. Deep Foundation (Piles) A foundation which derives its support by transferring loads

to soil or rock at some depth below the structure by end bearing, by

adhesion or friction or both.

i. Driven Piles

1. Batter Pile A pile driven at an angle inclined to the vertical to

provide higher resistance to lateral loads.

2. Combination of End-Bearing and Friction Pile Pile that derives its

capacity from the contributions of both end bearing

developed at the pile tip and resistance mobilized along the

embedded shaft.

3. End-Bearing Pile A pile whose support capacity is derived

principally from the resistance of the foundation material on

which the pile tip rests.

4. Friction Pile A pile whose support capacity is derived principally

from soil resistance mobilized along the side of the

embedded pile.

ii. Drilled Shaft or Bored Pile A deep foundation unit, wholly or partly

embedded in the ground constructed by placing fresh

concrete in a drilled hole with or without steel reinforcements.

Drilled shafts derive their capacities from the surrounding soil

and/or from the soil or rock strata below their tips. Drilled

shafts are also commonly referred to as caissons, drilled

caissons, bored piles or drilled piers.

III. Shear and Flexural Behavior of Footings

To simplify foundation design, footings are assumed to be rigid and the supporting soil

layers elastic. Consequently, uniform or uniformly varying soil distribution can be assumed.

The net soil pressure is used in the calculation of bending moments and shears by

subtracting the footing weight intensity and the surcharge from the total soil pressure. If a

column footing is considered as an inverted floor segment where the intensity of net soil

pressure is considered to be acting as a column supported cantilever slab, the slab would

be subjected to both bending and shear in a similar manner to a floor slab subjected to

gravity loads.

The mechanism of shear failure in footing slabs is similar to that in supported floor slabs.

However, the shear capacity is considerably higher than that of beams. Since the footing in

most cases bends in double curvature, shear and bending about both principal axes of the

footing plan have to be considered.

Figure 2: Punching shear failure of footing slab.

Figure 3: Punching shear failure in footing slabs is comparable to shearing failure in floor slabs and columns.

IV. Loads and Load Combinations

Foundations shall be proportioned to withstand safely all load combinations stipulated in

AASHTO Standard Specifications for Highway Bridges 17th edition (2002) Article 3.22

which are applicable to the particular site or foundation type. With the exception of the

portions of concrete or steel piles that are above the ground line and are rigidly

connected to the superstructure as in rigid frame or continuous structures, impact forces

shall not be considered in foundation design.

a. Service Loads the combined unfactored loads transmitted from columns to spread

footings or piles should be less than the bearing capacity of the soil.

An abutment generally receives unsymmetrical earth pressure. When

designing for such structure, the safe loaded condition differs for the

front footing and for the rear footing.

Toe or Front footing:

The backfill earth on the footing is not necessarily present for a long

period of time and ordinary variations in vertical loads and bending

moment are very small even if the influence of the backfill earth is

taken into consideration. Therefore, the footing should be designed by

neglecting the overburden, but considering the footings own weight,

subgrade reaction and pile reaction, and presence of buoyancy.

There is a possibility that the abutment may tilt backward, top tension

reinforcements should be placed.

Heel or Rear footing:

The influence of overburden is large and its fluctuations are small. In

general, the footing must be designed by including the influence of

the overburden load in the design load.

b. Lateral Loads

Modified Design Forces for Foundations Seismic design forces for

foundations, including footings, pile caps, and piles shall be the elastic

seismic forces obtained from Load Case 1 (DL + 1.0 LONGIT. EQK +

0.3 TRANS. EQK) and Load Case 2 (DL + 0.3 LONGIT. EQK + 1.0

TRANS. EQK) divided by the Response Modification Factor (R). These

modified seismic forces shall then be combined independently with

forces from other loads as specified in the following group loading

combination to determine two alternate load combinations for the

foundations.

c. Load Combinations

See Lecture 4 on Loads and Load Combinations.

V. Design of Foundation

a. Spread Footing footings shall be designed to keep the soil pressure as nearly

uniform as practicable. The distribution of soil pressure shall be

consistent with properties of the soil and the structure and with

established principles of soil mechanics. Determine the footing

dimensions using the reactions (axial, bending and shear) from service

loads.

Figure 4: Uniform subgrade reaction

Figure 5: Trapezoidal subgrade reaction due to eccentric loading.

The depth of embedment of footings shall be determined with respect

to the character of the foundation materials and the possibility of

undermining. Footings at stream crossings shall be founded at depth

below the maximum anticipated depth of scour.

Thickness of footings

According to NSCP Vol 1 415.8, the minimum footing depth should not be less

than 150mm for footings on soil or not less than 300mm for footings on piles.

Check for toppling

Maam Ellen, upon checking, both AASHTO and NSCP Vol.2 dont

have a specified thickness. They only gave the minimum depth of

embedment which is below the scour level.

A resultant acting point of loads which work on a spread footing shall have o be

located within 1/6 of the bottom width from the center during normal time and

within 1/3 of the same during an earthquake.

Design procedure

Gather reactions from the column (Axial, Bending, Shear)

Check if reactions do not exceed allowable bearing capacity of soil as

recommended by the Geotechnical Engineer.

Plan View of a spread footing

Where P = Axial reaction

A = Area of the spread footing

M = Bending moment reaction

c = distance of the outer most element to the neutral axis

I = Moment of Inertia of the spread footing

x

y

Check for punching shear and one way shear. Adjust the thickness of the footing to

satisfy the shear requirements.

Vu Vn

Vn = Vc+Vs

Figure 6: Punching shear failure mechanism

Punching shear or two-way shear critical at a distance d/2 from face of column

:Ultimate shear at d/2 from face of column

(

) (Eqn. 1) Shear capacity of concrete

Where c=a/b : a>b

bo = perimeter of critical section

= 2(a+d)+2(b+d)

(Eqn.2) Shear capacity of concrete

Equate: Vup = Vcp

Solve for d.

Beam shear or one-way shear critical at a distance d from the face of the

column

Figure 7: Beam shear failure mechanism

(

) (x direction)

(

) (y direction)

Fh=0:

Vu-Vc=0

Solve for d.

When d is acquired, add bar diameter + concrete cover to determine footing

thickness.

Determine the governing design bending moment for both directions which is most

critical at face of column.

Figure 8: Maximum moment at face of column

Ultimate moment to be resisted by footing:

(

)

Allowable Moment capacity of concrete:

*

+

Strength reduction factor of concrete for bending stress:

Equate Mu with Mucap.

Solve for .

Solve for area of steel require, As.

Determine spacing.

b. Driven Piles and Bored Piles

Figure 9: Elevation and Plan view of Pile Foundation

Determine number of piles.

Gather allowable pile capacity from Geotechnical Engineer.

Determine maximum vertical reaction from service load condition.

Divide Reaction by Pile Capacity (round up to the nearest whole number).

Determine load carried by a unit pile.

The pile is subjected to bending due to the lateral force of seismic base shear.

A pile behaves like an ordinary column and should be designed as such.

Maximum area of steel reinforcement,

As < 0.08Ag NSCP Vol. 2 8.18.1.1

Minimum area of steel reinforcement,

As > 0.01Ag NSCP Vol. 2 8.18.1.2

The group of piles with pile cap must be modeled in engineering software

such as STAAD.Pro to determine the maximum bending moment carried by

each pile.

Figure 10: Pile cap with four (4) driven piles as modeled in STAAD.Pro with soil acting as spring.

With the maximum bending moment in hand and using Structure Point

SPColumn, assume a pile section, assign a rebar area, load the axial and

bending forces. The software will generate a column-interaction diagram

showing that the loads are within the allowable capacity of the member. If in

case the loads exceed the capacity, revise the pile section or add

reinforcements or do adjust both.

Figure 11: The SPColumn interface.

Figure 12: All necessary data/parameters are systematically inputted.

Figure 13: The General Information dialog box.

Figure 14: The Material Properties dialogue box. Input the correct parameters for the materials.

Figure 15: Section dialogue box for rectangular piles.

Figure 16: Section dialogue box for circular section.

Figure 17: Dialogue box for assigning longitudinal reinforcements.

Figure 18: Dialogue box for assigning shear reinforcements.

Figure 19: Factored Loads dialogue box where forces derived from

STAAD.Pro is inputted.

Figure 20: The column interaction diagram generated using the parameters inputted by the design engineer. The encircled point is the coordinate of the Axial and Bending forces. If it is within the capacity of the column, the assumed dimension and reinforcements are safe to use.

Design pile cap.

Design Bottom Reinforcement.

Determine maximum moment of the pile cap at face of column.

Figure 21: Free Body Diagram for Longitudinal Reinforcement.

Figure 22: Free Body Diagram for Longitudinal Reinforcement.

Ultimate moment to be resisted by footing:

Longitudinal:

Or

Allowable Moment capacity of concrete:

*

+

Transverse:

Or

Allowable Moment capacity of concrete:

*

+

Strength reduction factor of concrete for bending stress:

Equate Mu with Mucap.

Solve for .

Solve for area of steel require, As.

Determine spacing.

VI. Miscellaneous Design

Protection from Scouring

Footings supported on soil or degradable rock strata shall be embedded below the

maximum computed scour depth or protected with a scour counter-measure.

Figure 23: Exposed group of piles due to scouring of soil.

Figure 24: Concrete armors placed around columns as scour protection.

Figure 25: Variety of shapes of concrete armor.

Figure 26: Workers place concrete armor around a pier support.

Figure 27: Hydrocast armor unit, an alternative to concrete armor units.