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Probabilistic Methods in Geotechnical Engineering 3 The Role of Probability in Codes and Regulations INTRODUCTION This chapter addresses Question 3 as defined in Chapter 1, namely: “What is the appropriate role of probabilistic methods in codes and regulations that govern geotechnical engineering practice?” Question 3 is implicitly addressed herein by an assessment of recent code and regulation developments in foundation design and environmental engineering. Although the application of probabilistic methods in engineering may still be in the formative stages, in the geotechnics areas of foundation design and environmental engineering efforts have been initiated (to varying degrees) to introduce the methods into practice. In considering the following developments, it is helpful to realize that probabilistic methods have a wide range of formats. At one extreme, detailed probabilistic methods are applied with the intention of calculating the probability of failure of a system. This is rarely done, in part because the required data related to properties are usually not available, and also because the data needed to establish appropriate “target” probabilities of failure are not available. It is highly desirable that information for defining target probabilities of failure for civil engineering structures be assembled and analyzed. In recognition of the fact that the actuarial data on large civil engineering systems is rarely adequate for calibrating such precise methods, developers of codes and standards have usually opted for a less rigorous or “nominal” approach. For example, the use of partial safety factors is one popular method, in which the largest conservatism (safety factors) is applied to the elements of the design that are most uncertain. The determination of the partial safety factors may be done using probabilistic methods, but these are transparent to the designer, because the designer may not necessarily be aware of the probabilistic basis underlying those partial safety factors that are recommended in the design code. Another approach that has a probabilistic flavor is risk analysis. This type of analysis takes many forms, but it is generally a formal approach to identifying the risks in an enterprise. An assessment is made (using probability, judgment, or perhaps codes or standards) of their likelihood and consequences, which then form the basis for decisions.
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Probabilistic Methods in Geotechnical Engineering BACKGROUND Probabilistic methods are gaining status in design codes for foundations. Probabilistic analysis has been transplanted from structural to geotechnical practice in the form of “load and resistance factor design” (LRFD). In LRFD, partial safety factors are applied to the components of both load and resistance, depending on the bias and uncertainty of the respective components. The loading components are multiplied by factors, usually greater than 1.0, to add conservatism to the design loads. The resistance components are divided by factors, also usually greater than 1.0, for the same purpose. A safe equilibrium state must then exist using these factored components. Probabilistic analysis is the basis for selection of these partial factors, thus allowing the largest conservatism to be placed where the uncertainty is most significant. This approach tends to result in a more consistent level of risk than the use of a single global safety factor. In the United States, efforts have been made for several years to develop resistance factors for the foundation designs of offshore structures (Hamilton and Murff, 1992; Tang, 1988) and for the foundation design of highway facilities (Barker et al., 1991). Reliability-based procedure also has been applied to the foundation design of transmission-line structures (Kulhawy et al., 1988–1994). Risk considerations are well entrenched in regulations for environmental geotechnics. In the first instance, the U.S. Environmental Protection Agency (EPA) commonly performs health risk analyses for various engineering options and relates its technological requirements to risk-based standards. These standards have been treated mostly in a deterministic sense, as described further in this chapter. However, EPA has begun to acknowledge uncertainty in the risk calculation; hence, probabilistic methods are expected to take on a major role. APPLICATION OF LOAD- AND RESISTANCE-FACTOR DESIGN The impetus for using load factors in civil engineering design comes from structural engineering, where material properties typically have modest uncertainty (compared with soils, for example), and loading conditions are the key uncertainties. Logically, the use of partial factors (i.e., load and resistance coefficients) is appropriate and helpful where the uncertainty in the design load is large. Structures such as offshore platforms, transmission towers, bridges, and buildings in active seismic zones are examples in which extreme or transient loads infrequently applied can control choice of structural section. The LRFD may not be as useful in those geotechnical engineering problems where design is largely controlled by uncertainty in material properties, such as in stability analysis of embankments and excavations where loading is chiefly from soil and water, and live loads are small compared with the earth loading. The difficulty with the geotechnical portion of this process lies in interpreting site conditions, predicting soil behavior, and assessing the interdependence between design and construction. Basically, the geotechnical design environment is more uncertain than that in structural engineering
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Probabilistic Methods in Geotechnical Engineering because of complex geological variations, limited information of uncertain quality, poorer understanding of material behavior, and less controlled construction procedures and workmanship. The uncertainty of site conditions and soil properties depends on the scope of site exploration, sampling/testing programs, and the experience of the engineer with the local geology and with the performance of foundations in similar soil conditions. In short, the degree of uncertainty of the pertinent geotechnical parameters can vary significantly from project to project. Current applications of probability theory in foundation design codes focus primarily on uncertainties arising from loads and, to a lesser extent, from material strengths. Considerably more work is needed to include those other factors that are specific to geotechnical design into the LRFD procedure. With further research, the geotechnical profession should be able to realize greater benefit from the LRFD approach—a design approach that provides a more consistent level of performance reliability than the current practice of using conventional factors of safety. Although the next generation of design codes will be based on probabilistic considerations, geotechnical engineers will likely find the design procedure similar to the current deterministic format. Like those structural engineers using LRFD-based codes, most geotechnical engineers will not have to use probability theory themselves. However, having a knowledge of the underlying probabilistic basis is always desirable. EUROCODE NO. 7, GEOTECHNICS As part of the efforts launched by the European Committee for Standardization to develop a reliability-based design code, work on “Eurocode No. 7, Geotechnics,” has been under way for the last several years by a committee chaired by N. K. Ovesen. Working drafts are now available (CEN-European Committee for Standardization, 1990). This code will point the way to the future form of geotechnical codes for design and will serve as an important first step toward greater rationality in foundation engineering. It may also be more advanced in form than any of the other attempts to draw in reliability and probability as load and resistance factors. A key element in the new Eurocode deals with “characteristic value.” The code does not encourage obtaining that value by relying solely on conventional statistical analysis of geotechnical data. In section 2.2.5 of the code, “Material Properties,” a design value is either assessed directly or is derived from the characteristic value by dividing the value by a partial safety factor, described as follows: Characteristic values shall be selected with the intention that the probability of a more unfavorable value governing the occurrence of a limit state is not greater than 5 percent. For parameters for which the values governing the field behavior are well established with little uncertainty, the characteristic value may be taken as the best estimate of the value in the field. Where there is greater uncertainty, the characteristic value is more
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Probabilistic Methods in Geotechnical Engineering conservative. . . . It might sometimes be helpful to use statistical methods. However, it is emphasized that this will rarely lead directly to characteristic values since these depend on an assessment of the field situation. . . . (CEN-European Committee for Standardization, 1990, p. 12) The reason for discouraging the use of percentile value of measured data to obtain characteristic values is the presence of systematic uncertainties (i.e., bias) resulting from the discrepancy between measured and in situ property values, as described in Appendix C of this report. A comprehensive probabilistic analysis of the pertinent uncertainties will provide a better basis for obtaining a characteristic value that meets the 5 percent probability level required by the Eurocode No. 7. According to the new Eurocode, the partial safety factors to be applied to the characteristic value for the frictional parameter tan φ are 1.2 to 1.25 and for cohesion, either drained or undrained, are equal to 1.5 to 1.8. The Eurocode describes further the possible variations of these partial factors that can be chosen depending on the design situation. For example, the following exception is stated: For structures under construction for which failure will not involve risk to life or great social consequences, partial factors corresponding to the square root of the values (quoted above) for conventional design situations may be used. (CEN-European Committee for Standardization, 1990, p. 12) The selection of the design safety factor should reflect the consequences in the event of failure. For instance, a smaller safety factor may be used when the consequence is relatively small. This concept is included, though in a somewhat crude manner, in the proposed Eurocode. Professor J. Michael Duncan stated in the 1992 workshop that in his four-year effort to apply probability methods to the design of bridge foundations, “It was found to be necessary and desirable to base the values of the resistance factors largely on judgment and common sense.” This is what the Eurocode tries to do. A particularly good example of this concept is found in the Eurocode section 188.8.131.52, (CEN-European Committee for Standardization, 1991) which describes how partial resistance factors for pile design are selected based on a pile-load test program and on the pile type adopted in design. The following example of resistance factors for pile design may be illuminating. Section 184.108.40.206 of the Eurocode describes a procedure for using the measured value of the ultimate bearing resistance from a pile load test, Rm, to determine a design value of the ultimate bearing resistance, Rc. To account for the variability that is inevitably encountered in pile load testing, the characteristic value of the ultimate bearing resistance, Rck, is taken to be Rck = Rm / ξ
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Probabilistic Methods in Geotechnical Engineering where ξ is given in Table 3-1 for several different conditions. Note that both calculations (a) and (b) are made, and the characteristic value is the minimum of the two. This process weighs both the mean value and the minimum value measured and offers incentives (lower safety factors) for doing more tests. To determine the design value of the ultimate bearing resistance, the characteristic value obtained above is divided into components of base resistance, Rbk, and shaft resistance, Rsk. The determination of the ratio of these components is made directly from field measurements or estimated using analytical methods, if this can be reasonably done. The characteristic value of the ultimate bearing resistance can then be written as Rck = Rbk + Rsk The characteristic components are then divided by factors γb and γs which reflect their relative uncertainties (based on the judgment of the code writers), to obtain the design value of the ultimate bearing resistance as follows, Rc = Rbk / γ + Rsk / γs where the resistance values, γs, are prescribed in Table 3-2. Where the ratio of the components cannot be reasonably estimated, the characteristic value of the total ultimate bearing resistance is divided by γt. The factors given in Table 3-2 are clearly chosen to reflect the physical nature of the pile installation and the ensuing uncertainty of the respective components of resistance. The code then notes rules for modifying the component bearing-capacity factors. The essence of these rules is simply to make the best use of load-test results, first by assessing the reliability of the array of load tests and then by evaluating the degree of predictability of the respective resistance components. The reduction factors (Table 3-1) and the partial safety factors (Table 3-2) are based on probability concepts, incorporating clearly the significant role of judgment in their selection. This somewhat subjective approach reflects the general lack of robust data sources from which a more objective set of factors can be derived. Realistically, because Table 3-1 Factors for Obtaining Characteristic Value of Ultimate Bearing Resistance as Function of the Number of Load Tests Number of Load Tests Calculations 1 2 > 2 a) Factor ξ on mean Rm 1.5 1.35 1.3 b) Factor ξ on lowest Rm 1.5 1.25 1.1
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Probabilistic Methods in Geotechnical Engineering Table 3-2 Partial Factors for Various Pile Types Component Factors γb γs γt Driven Piles 1.3 1.3 1.3 Bored Piles 1.6 1.3 1.5 Continuous Flight Auger 1.45 1.3 1.4 of the tremendous range of property values and site conditions that one may encounter, it is unlikely that completely objective factors can be developed in the foreseeable future. In summary, the proposed Eurocode has made a significant step toward implementation of probability concepts in geotechnical design. In the committee's view, this has resulted in a more rational approach than the conventional procedure of using a single, purely deterministic safety factor. This seems to be an appropriate goal for the next generation of design codes for foundation engineering. On the other hand, this approach neglects the larger issues in traditional geotechnical practice, which emphasize the importance of interpreting site conditions based on a sound knowledge of local geology. It does not fully account for the vagaries of soil behavior, such as the significance of progressive failure, nor for the strong interrelationship between design and construction. CODES RELATED TO ENVIRONMENTAL GEOTECHNICS Risk-assessment procedures have been used broadly in federal and state codes and regulations that deal with environmental geotechnics. Three examples are discussed below: The use of risk analysis to support rule-making decisions. The EPA commonly performs health-risk analyses for various engineering options and bases its technological requirements upon risk-based standards. An example is EPA's rules for municipal solid-waste landfills (MSWLFs), promulgated October 9, 1991 (EPA, 1991). The EPA considered four options: (1) the limited approach option, which, rather than focusing on limiting contamination by landfill design standards, would rely almost exclusively on monitoring and cleanup; (2) the hazardous waste option, which would apply standards for hazardous waste disposal to MSWLFs; (3) the hybrid option, which is a compromise between the first two options; and (4) a categorical approach, which would establish MSWLF design criteria based on factors such as rainfall and hydrogeology at a site. In evaluating these options, EPA's primary criterion was to meet statutory requirements for protection of human health and the environment. The EPA evaluated the mitigation of human health risks (e.g., cancer risk) and resource damage (e.g., contamination of groundwater supply) of each option. The EPA found that options 1 and 3 are superior in terms of balancing cost with reduction of cancer risks. In fact, these options would reduce
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Probabilistic Methods in Geotechnical Engineering the probable number of cancer cases from six (current baseline) to three over a 300-year period for one set of 3,000 replacement landfills. Option 3 was ultimately selected. The use of risk analysis to evaluate Superfund site cleanup. The EPA requires a risk analysis for all potential cleanup options at Superfund sites. The parameter used to measure and judge the severity of a health hazard due to a contaminated site is individual health risk. Current EPA guidance documents (e.g., EPA, 1985) for risk assessment at Superfund sites require determination of the reasonable maximum exposure (RME) at a site, which is then compared with the compliance standards given in the regulations. The approach for ascertaining reasonable maximum exposure has been essentially deterministic in nature, assuming the definite occurrence of many conditional factors, even though the likelihood of each of these factors occurring is considerably less than 1.0. Because of the compounding of the conservatism at various stages of the determination of reasonable maximum exposure, the calculated risk will likely be an overestimate of the real risk, often by several orders of magnitude, thus inflating the estimated cost of cleanup unnecessarily. Recent developments at EPA, however, have begun to include uncertainty in the risk calculations. A performance-based approach to risk assessment has been introduced (e.g., Freeze et al., 1990). This represents a more realistic method for predicting human health impacts at contaminated sites. The derivation of the exposure risk is in terms of the actual frequency of occurrence of a carcinogenic health problem. The acceptable RME can be decided at the end of the calculations from the probability distribution of the risk exposure such that the acceptable RME will meet a desired probability of performance. By following a performance-based approach, the site owners can easily take into account their own risk and liability exposure and can even factor exposed population sizes into the decision on a treatment strategy. In short, site remediation decisions can be facilitated by an open acknowledgment of uncertainty and of the tradeoff between the cost of cleanup and the estimated chance of not reaching the performance goal. The use of statistical methods for interpretation of groundwater monitoring data. When groundwater samples are analyzed for monitoring purposes, the data are analyzed for statistical variability between samples collected from wells that are up-gradient from a facility and samples collected from down-gradient wells. Statistical and probabilistic methods are used to determine whether the data suggest a significant degree of contamination coming from the facility. The reliability of such predictions depends on the number and locations of monitoring wells, together with the uncertainties in the flow direction.
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Probabilistic Methods in Geotechnical Engineering CONCLUSIONS Probabilistic methods provide a systematic treatment of the uncertainties and a means to evaluate the implication of these uncertainties on the likelihood of satisfactory performance for an engineering system. In this role, a probability-based design code promotes consistency in the level of performance between various design environments. In the case of foundation engineering, the impetus comes from structural engineers, and the impact is not greatly different from that of systematized common sense. The initial versions of the probability-based foundation design codes represent a step toward a more systematic and rational approach. However, they still has ample room for further revisions as additional data become available and, more importantly, for incorporation of factors such as site-specific information. For environmental geotechnics, it is laudable that risk assessment is included as a basis for meeting regulations to reflect the potential hazards that can arise. However, by working with unquantified conservatism as in most of the current risk evaluations, one could easily become overly conservative. To avoid this, one needs a more objective assessment of the likelihoods of the respective events, so that the level of risk specified for different applications can better represent the expected potential consequences. Moreover, the environmental risk analyses arising from human health-risk statistics have been largely imposed by outside sources. There has been relatively little input from geotechnical engineers, considering the scope of the geotechnical aspects of the problem. In both foundation and environmental geotechnics areas, geotechnical engineers should strive to reach an understanding of the mechanics of risk analysis to allow their expertise to be effectively communicated and incorporated, or they will concede the control of the codes and regulations to others.
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Probabilistic Methods in Geotechnical Engineering REFERENCES Barker, R.M., J.M. Duncan, K.B. Rojiani, P.S.K. Ooi, C.K. Tan, and S.G. Kim. 1991. Load Factor Design Criteria for Highway Structure Foundations. Final Report prepared for the National Cooperative Highway Research Program, Vrginia Polytechnic Institute and State University. Blacksburg, Virginia: VPISU. CEN-European Committee for Standardization. 1990. Eurocode No. 7 Geotechnics, Chapters 1–6, 9, 10. Prepared for the Commission of the European Communities (draft). Brussels, Belgium: CEN. CEN-European Committee for Standardization. 1991. Eurocode No. 7 Geotechnics, Chapter 7 Pile Foundations. Prepared by the Commission of the European Communities (draft). Brussels, Belgium: CEN. EPA. 1985. The Endangerment Assessment Handbooks. U.S. Environmental Protection Agency, Office of Waste Programs Enforcement . Washington, D.C.: U.S. EPA. EPA. 1991. Solid Waste Disposal Facility Criteria. EPA/OSW-FR-91-004, U.S. Environmental Protection Agency, Office of Solid Waste. Washington, D.C.: U.S. EPA. Freeze, R.A., J.W. Massmann, L. Smith, T. Sperling, and B. James. 1990. Hydrological decision analysis: I. A framework. Ground Water 28(5): 738–766. Hamilton, J.M., and J.D. Murff. 1992. Selection of LRFD Resistance Factors for Pile Foundation Design. Pp. 788–795 in Structures Congress '92, American Society of Civil Engineers, San Antonio, Texas. New York: ASCE. Kulhawy, F.H., B. Birgisson, O.B. Filippaz, M.D. Grigoriu, C.J. Orchant, M.J. Spry, and C.H. Trautmann. 1988–1994. Reliability-Based Foundation Design for Transmission Line Structures . Report EL-5507, Electric Power Research Institute, series of reports released over period. Palo Alto, California, EPRI. Tang, W.H. 1988. Offshore Axial Pile Design Reliability. Final Report for Project PRAC 86-29B sponsored by the American Petroleum Institute. Copies of this report may be obtained from the American Petroleum Institute, Washington, D.C.
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