Design Procedures

3.2 Design Procedures

Over the years, design procedures have been developed by engineers to provide satisfactory margins of safety. These procedures were based on the engineer's confidence in predicting the magnitude of the load and the effect of the load on the strength of the materials being provided. In the next section, the existing procedure for design of foundations is discussed.

3.2.1 Allowable Stress Design (ASD)

The design of foundations has traditionally been based on ASD. ASD is different for the Service Limit State and the Strength Limit State. For the Strength Limit State, safety is achieved in the foundation element by restricting the estimated loads (or stresses) to values less than the ultimate resistance divided by a factor of safety, FS using the relationship:

Q i (Eq. 3-2) FS

where: R n =

Nominal resistance (e.g., ultimate bearing resistance of foundation soils) ∑ Q i =Q n = Nominal load effect (e.g., moment produced by design vehicle)

Load effects consist of dead, live and environmental load components. Environmental loads include wind, water and earthquake forces, for example. In ASD all of these loads are assumed to have the

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The factor of safety is a number greater than unity. The FS provides reserve strength in the event that an unusually high load occurs or in the event that the resistance is less than expected.

For the Service Limit State, unfactored loads are used to calculate deformations, and these deformations are compared to the maximum tolerable values.

The advantage of ASD is its simplicity; however, there are shortcomings of ASD.

3.2.2 Shortcomings of ASD

In ASD, no consideration is given to the fact that various types of loads have different levels of uncertainty. For example, the dead load of a bridge can be estimated with a high degree of accuracy.

However, earthquake loads acting on bridge abutments and piers cannot be estimated with the same degree of accuracy and confidence. Nevertheless, dead, live, and environmental loads are all treated equally in ASD. In ASD, fixed values of design loads are selected, usually from a specification or design code. The factor of safety is applied to the resistance side of the design inequality, and the load side of the inequality is not factored.

Factors of safety in geotechnical engineering vary considerably depending on the type of problem.

y Slope Stability: 1.3 ≤ FS ≤ 1.5 y

Foundation Bearing Capacity: 2 ≤ FS ≤ 3 y

Foundation Sliding: FS ≥ 1.5 y

Foundation Overturning: FS ≥ 2.0

Because the factor of safety chosen is based on experience and judgment, quantitative measures of risk cannot be determined for ASD.

Limitations of ASD:

Does not adequately account for variability of loads and resistances. The FS is applied only to resistance. Loads are considered to be without variation (i.e., deterministic).

Does not embody a reasonable measure of strength, which is a more fundamental measure of resistance than is allowable stress.

Selection of a FS is subjective, and does not provide a measure of reliability in terms of probability of failure.

What is needed to overcome these deficiencies is a method that:

y Considers variability not only in the resistance, but also in the effect of loads y

Uses the strength of the material (e.g., soil and rock) as a basis of resistance y

Provides a measure of safety related to probability of failure

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Such a method is incorporated in load and resistance factor design, LRFD.

3.2.3 Load and Resistance Factor Design (LRFD)

The American Concrete Institute (ACI) introduced a limit state design code in an appendix to the 1956 ACI building code. Initially, the code did not include any resistance factors, only load factors, so the code was known as load factor design (LFD). The load factors (and resistance factors when they were introduced) were not based on the reliability concepts used in developing the AASHTO LRFD Specification, but rather on matching with the then existing ASD ACI code. The fact that reliability theory was not used in the selection of load and resistance factors represents the greatest difference between LFD and LRFD.

In LRFD, the resistance side of Eq. 3-1 is multiplied by a statistically-based resistance factor, φ, whose value is usually less than one. As applied to the geotechnical design of substructures, φ accounts for factors such as weaker foundation soils than expected, poor construction of the foundations, and foundation materials such as concrete, steel or wood that may not completely satisfy the requirements in the specifications.

The load components on the right side of Eq. 3-1 are multiplied by their respective statistically based load factors, γ i , whose values are usually greater than one. Because the load effect at a particular limit state involves a combination of different load types, Q i , each of which has different degrees of predictability, the load factors differ in magnitude for the various load types. Therefore, the load effects can be represented by a summation of γ i Q i products. If the nominal resistance is given by R n , then the safety criterion can be written as:

R r = φ R n ≥ ∑ η i γ i Q i (Eq. 3-3) (A1.3.2.1-1)

where:

φ= Statistically-based resistance factor (dim) R n = Nominal resistance

η i = Load modifier to account for effects of ductility, redundancy and operational

importance (dim) γ i = Statistically-based load factor (dim)

Q i = Load effect

Because Eq. 3-3 involves both load factors and resistance factors, the design method is called Load and Resistance Factor Design (LRFD). For a satisfactory design, the factored nominal resistance should equal or exceed the sum of the factored load effects for a particular limit state. Load and resistance factors are chosen so that in the highly improbable event that the nominal resistance of the foundation material is overestimated, and at the same time the loads are underestimated, there is a reasonably high probability that the actual resistance of the foundation material should still be large to support the loads.

The value of φ chosen for a particular limit state can take into account the:

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Reliability of the equations used for predicting resistance y

Quality of the construction workmanship and quality control programs y

Extent of soil exploration (little versus extensive) y

Consequence(s) of a failure

In the AASHTO LRFD Specifications (1997a), not all of these features have been implemented. However, they all can be included in the LRFD format once research has been completed and the experience base has been established. The LRFD Specifications will continue to improve and the resistance factors will be adjusted as more field performance measurements are evaluated. It is important that the experience of geotechnical engineers with LRFD be shared and that the quality of the geotechnical data base be improved (e.g., load-deformation response of spread footing foundations) through the use of well planned and instrumented testing programs. As a result, our understanding of design methods and the safety margins needed for their effective and economic use in reducing the risk of failure can be improved.

Some methods of predicting the nominal resistance are empirical whereas others are based on classical theories of mechanics. Also, different methods of predicting resistances employ the use of different soil parameters [e.g., friction angle of cohesionless soils based on Standard Penetration Test (SPT) blow counts or Cone Penetration Test (CPT) tip resistance, and undrained shear strength of cohesive soils based on CPT sleeve friction]. It is generally true in ASD that a higher FS is used for empirically-based methods (e.g., bearing resistance estimated using SPT blow counts), as opposed to methods based on classical bearing resistance theories. Because different methods of predicting resistance have different degrees of reliability, different values of resistance factors are required for each method.

The load factor, γ i , chosen for a particular load type must consider the uncertainties in the:

y Magnitude and direction of loads y

Location of application of loads y

Possible combinations of loads (i.e., dead load + live load to dead load + environmental load)

Loads and load combinations are addressed in Chapter 4.

3.2.4 Advantages and Limitations of LRFD

Before 1970 in the United States, design of both the superstructure and substructure components of highway bridges was accomplished using ASD. In the 1971 and 1972 Interims, AASHTO introduced load factor design (LFD) for the design of bridge superstructures. Design of steel and concrete structures has switched from ASD to LFD to LRFD over the years. Limit state concepts are currently used in the LFD American Concrete Institute (ACI, 1995) design code, the LRFD American Institute of Steel Construction (AISC, 1989) specifications for design of steel buildings, and the LFD AASHTO Standard Specifications (AASHTO, 1997b) for design of concrete, wood, and metal bridge superstructures. Several countries have adopted the limit states design code format for design of substructures including the Canadian Foundation Engineering Manual (1985), Ontario Highway Bridge Design Code (1991) and the Danish Code of Practice for Foundation Engineering

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(1985). Limit states concepts for foundation design are also being considered in Japan and other countries in Europe. Some of the advantages and limitations of the LRFD method are:

Advantages of LRFD:

Accounts for variability in both resistance and load.

Achieves relatively uniform levels of safety based on the strength of soil and rock for different limit states and foundation types.

Provides more consistent levels of safety in the superstructure and substructure as both are designed using the same loads for predicted or target probabilities of failure.

Limitations of LRFD:

The most rigorous method for developing and adjusting resistance factors to meet individual situations requires availability of statistical data and probabilistic design algorithms.

Resistance factors vary with design methods and are not constant.

Implementation requires a change in design procedures for engineers accustomed to ASD.

Due to the advantages of LRFD and the prospect that the method will eventually supersede ASD in geotechnical engineering, a discussion on the basis for the derivation of resistance factors is presented in Section 3.3. This derivation is presented for background information and for understanding the process. In using the AASHTO LRFD Specifications, resistance factors are provided and no probability or statistical analysis is required.