Page 1 1. 1. Introduction The trend in civil engineering today more than ever before is to provide 1. economical or robust design at certain levels of safety, 2. use new materials in construction. When newer materials are being used in civil engineering design, there is a need to understand to what extent the structure is safe, and 3. consider uncertainties in design. One has to recognize that there are many processes such as data collection, analysis and design in civil engineering systems which are random in nature. Design of many facilities such as: buildings, foundations, bridges, dams, highways, airports, seaports, offshore structures, tunnels, sanitary landfills, excavation etc. need to address the design issues rationally. The loading in civil engineering systems are completely unknown. Only some of the features of the loading are known. Some of the examples of loading are frequency and occurrence of earthquakes, movement of ground water, rainfall pattern, wind and ice loadings etc. All these loading are random in nature, and at times they create overloading situation. What we have been doing so far can be schematically shown as follows: Sampling Testing Formula Experience What is the extent of sampling ? What is the extent methods represent the actual field condition ? Assumption ? Build with confidence Sampling Testing Formula Experience What is the extent of sampling ? What is the extent methods represent the actual field condition ? Assumption ? Build with confidence At all stages indicated above, there is an element of uncertainty with regard to the suitability of the site in terms of soils, construction materials, which we transfer to a different level using a set of expressions to obtain the desired quantities such as the floor capacity, allowable loads in buildings etc. 1 Page 2 1. 1. Introduction The trend in civil engineering today more than ever before is to provide 1. economical or robust design at certain levels of safety, 2. use new materials in construction. When newer materials are being used in civil engineering design, there is a need to understand to what extent the structure is safe, and 3. consider uncertainties in design. One has to recognize that there are many processes such as data collection, analysis and design in civil engineering systems which are random in nature. Design of many facilities such as: buildings, foundations, bridges, dams, highways, airports, seaports, offshore structures, tunnels, sanitary landfills, excavation etc. need to address the design issues rationally. The loading in civil engineering systems are completely unknown. Only some of the features of the loading are known. Some of the examples of loading are frequency and occurrence of earthquakes, movement of ground water, rainfall pattern, wind and ice loadings etc. All these loading are random in nature, and at times they create overloading situation. What we have been doing so far can be schematically shown as follows: Sampling Testing Formula Experience What is the extent of sampling ? What is the extent methods represent the actual field condition ? Assumption ? Build with confidence Sampling Testing Formula Experience What is the extent of sampling ? What is the extent methods represent the actual field condition ? Assumption ? Build with confidence At all stages indicated above, there is an element of uncertainty with regard to the suitability of the site in terms of soils, construction materials, which we transfer to a different level using a set of expressions to obtain the desired quantities such as the floor capacity, allowable loads in buildings etc. 1 1.2. Probability of failure and reliability The failure of civil engineering systems is a consequence of decisions making under uncertain conditions and different type of failures such as temporary failures, maintenance failures, failures in design, failure due to natural hazards need to be addressed. For example, a bridge collapses which is a permanent failure, if there is a traffic jam on the bridge, it is a temporary failure. If there is overflow in a filter or a pipe due to heavy rainfall, it is a temporary failure. Thus definition of failure is important. It is expressed in terms of probability of failure and is assessed by its inability to perform its intended function adequately on demand for a period of time under specific conditions. The converse of probability of failure is called reliability and is defined in terms of the success of a system or reliability of a system is the probability of a system performing its required function adequately for specified period of time under stated conditions. 1. Reliability is expressed as a probability 2. A quality of performance is expected 3. It is expected over a period of time 4. It s expected to perform under specified conditions 1.2.1 Uncertainties in Civil engineering In dealing with design, uncertainties are unavoidable. Uncertainties are classified into two broad types. Those associated with natural randomness and those associated with inaccuracies in our prediction and estimation of reality. The former type is called aleatory type where as the latter is called epistemic type. Irrespective of the classification understanding the nature of randomness is necessary. The nature of the first type arising out of nature (for example, earthquake and rainfall effects) needs to be handled rationally in design as it can not altered and the second one needs to be reduced using appropriate prediction models and sampling techniques. The response of materials such as concrete, soil and rock to loading and unloading is of primary concern to the civil engineer. In all types of problems, the engineer is often dealing with incomplete information or uncertain conditions. It is necessary for the 2 Page 3 1. 1. Introduction The trend in civil engineering today more than ever before is to provide 1. economical or robust design at certain levels of safety, 2. use new materials in construction. When newer materials are being used in civil engineering design, there is a need to understand to what extent the structure is safe, and 3. consider uncertainties in design. One has to recognize that there are many processes such as data collection, analysis and design in civil engineering systems which are random in nature. Design of many facilities such as: buildings, foundations, bridges, dams, highways, airports, seaports, offshore structures, tunnels, sanitary landfills, excavation etc. need to address the design issues rationally. The loading in civil engineering systems are completely unknown. Only some of the features of the loading are known. Some of the examples of loading are frequency and occurrence of earthquakes, movement of ground water, rainfall pattern, wind and ice loadings etc. All these loading are random in nature, and at times they create overloading situation. What we have been doing so far can be schematically shown as follows: Sampling Testing Formula Experience What is the extent of sampling ? What is the extent methods represent the actual field condition ? Assumption ? Build with confidence Sampling Testing Formula Experience What is the extent of sampling ? What is the extent methods represent the actual field condition ? Assumption ? Build with confidence At all stages indicated above, there is an element of uncertainty with regard to the suitability of the site in terms of soils, construction materials, which we transfer to a different level using a set of expressions to obtain the desired quantities such as the floor capacity, allowable loads in buildings etc. 1 1.2. Probability of failure and reliability The failure of civil engineering systems is a consequence of decisions making under uncertain conditions and different type of failures such as temporary failures, maintenance failures, failures in design, failure due to natural hazards need to be addressed. For example, a bridge collapses which is a permanent failure, if there is a traffic jam on the bridge, it is a temporary failure. If there is overflow in a filter or a pipe due to heavy rainfall, it is a temporary failure. Thus definition of failure is important. It is expressed in terms of probability of failure and is assessed by its inability to perform its intended function adequately on demand for a period of time under specific conditions. The converse of probability of failure is called reliability and is defined in terms of the success of a system or reliability of a system is the probability of a system performing its required function adequately for specified period of time under stated conditions. 1. Reliability is expressed as a probability 2. A quality of performance is expected 3. It is expected over a period of time 4. It s expected to perform under specified conditions 1.2.1 Uncertainties in Civil engineering In dealing with design, uncertainties are unavoidable. Uncertainties are classified into two broad types. Those associated with natural randomness and those associated with inaccuracies in our prediction and estimation of reality. The former type is called aleatory type where as the latter is called epistemic type. Irrespective of the classification understanding the nature of randomness is necessary. The nature of the first type arising out of nature (for example, earthquake and rainfall effects) needs to be handled rationally in design as it can not altered and the second one needs to be reduced using appropriate prediction models and sampling techniques. The response of materials such as concrete, soil and rock to loading and unloading is of primary concern to the civil engineer. In all types of problems, the engineer is often dealing with incomplete information or uncertain conditions. It is necessary for the 2 engineer to be aware of many assumptions and idealizations on which methods of analysis and design are based. The use of analytical tools must be combined with sound engineering judgment based on experience and observation. In the last two decades the need for solving complex problems has led to the development and use of advanced quantitative methods of modeling and analysis. For example, the versatile finite element method has proved to be valuable in problems of stability, deformation, earthquake response analysis etc. The rapid development of computers and computing methods has facilitated the use of such methods. However, it is well known that the information derived from sophisticated methods of analysis will be useful only if comprehensive inputs data are available and only if the data are reliable. Thus, the question of uncertainty and randomness of data is central to design and analysis in civil engineering. Decisions have to be made on the basis of information which is limited or incomplete. It is, therefore, desirable to use methods and concepts in engineering planning and design which facilitate the evaluation and analysis of uncertainty. Traditional deterministic methods of analysis must be supplemented by methods which use the principles of statistics and probability. These latter methods, often called probabilistic methods, enable a logical analysis of uncertainty to be made and provide a quantitative basis for assessing the reliability of foundations and structures. Consequently, these methods provide a sound basis for the development and exercise of engineering judgment. Practical experience is always important and the observational approach can prove to be valuable; yet, the capacity to benefit from these is greatly enhanced by rational analysis of uncertainty. 1.2.2 Types of uncertainty There are many uncertainties in civil geotechnical engineering and these may be classified into three main groups as follows: (a) The first group consists of uncertainties in material parameters such as modulus of concrete, steel stability of concrete and steel in different condition such as tension and 3 Page 4 1. 1. Introduction The trend in civil engineering today more than ever before is to provide 1. economical or robust design at certain levels of safety, 2. use new materials in construction. When newer materials are being used in civil engineering design, there is a need to understand to what extent the structure is safe, and 3. consider uncertainties in design. One has to recognize that there are many processes such as data collection, analysis and design in civil engineering systems which are random in nature. Design of many facilities such as: buildings, foundations, bridges, dams, highways, airports, seaports, offshore structures, tunnels, sanitary landfills, excavation etc. need to address the design issues rationally. The loading in civil engineering systems are completely unknown. Only some of the features of the loading are known. Some of the examples of loading are frequency and occurrence of earthquakes, movement of ground water, rainfall pattern, wind and ice loadings etc. All these loading are random in nature, and at times they create overloading situation. What we have been doing so far can be schematically shown as follows: Sampling Testing Formula Experience What is the extent of sampling ? What is the extent methods represent the actual field condition ? Assumption ? Build with confidence Sampling Testing Formula Experience What is the extent of sampling ? What is the extent methods represent the actual field condition ? Assumption ? Build with confidence At all stages indicated above, there is an element of uncertainty with regard to the suitability of the site in terms of soils, construction materials, which we transfer to a different level using a set of expressions to obtain the desired quantities such as the floor capacity, allowable loads in buildings etc. 1 1.2. Probability of failure and reliability The failure of civil engineering systems is a consequence of decisions making under uncertain conditions and different type of failures such as temporary failures, maintenance failures, failures in design, failure due to natural hazards need to be addressed. For example, a bridge collapses which is a permanent failure, if there is a traffic jam on the bridge, it is a temporary failure. If there is overflow in a filter or a pipe due to heavy rainfall, it is a temporary failure. Thus definition of failure is important. It is expressed in terms of probability of failure and is assessed by its inability to perform its intended function adequately on demand for a period of time under specific conditions. The converse of probability of failure is called reliability and is defined in terms of the success of a system or reliability of a system is the probability of a system performing its required function adequately for specified period of time under stated conditions. 1. Reliability is expressed as a probability 2. A quality of performance is expected 3. It is expected over a period of time 4. It s expected to perform under specified conditions 1.2.1 Uncertainties in Civil engineering In dealing with design, uncertainties are unavoidable. Uncertainties are classified into two broad types. Those associated with natural randomness and those associated with inaccuracies in our prediction and estimation of reality. The former type is called aleatory type where as the latter is called epistemic type. Irrespective of the classification understanding the nature of randomness is necessary. The nature of the first type arising out of nature (for example, earthquake and rainfall effects) needs to be handled rationally in design as it can not altered and the second one needs to be reduced using appropriate prediction models and sampling techniques. The response of materials such as concrete, soil and rock to loading and unloading is of primary concern to the civil engineer. In all types of problems, the engineer is often dealing with incomplete information or uncertain conditions. It is necessary for the 2 engineer to be aware of many assumptions and idealizations on which methods of analysis and design are based. The use of analytical tools must be combined with sound engineering judgment based on experience and observation. In the last two decades the need for solving complex problems has led to the development and use of advanced quantitative methods of modeling and analysis. For example, the versatile finite element method has proved to be valuable in problems of stability, deformation, earthquake response analysis etc. The rapid development of computers and computing methods has facilitated the use of such methods. However, it is well known that the information derived from sophisticated methods of analysis will be useful only if comprehensive inputs data are available and only if the data are reliable. Thus, the question of uncertainty and randomness of data is central to design and analysis in civil engineering. Decisions have to be made on the basis of information which is limited or incomplete. It is, therefore, desirable to use methods and concepts in engineering planning and design which facilitate the evaluation and analysis of uncertainty. Traditional deterministic methods of analysis must be supplemented by methods which use the principles of statistics and probability. These latter methods, often called probabilistic methods, enable a logical analysis of uncertainty to be made and provide a quantitative basis for assessing the reliability of foundations and structures. Consequently, these methods provide a sound basis for the development and exercise of engineering judgment. Practical experience is always important and the observational approach can prove to be valuable; yet, the capacity to benefit from these is greatly enhanced by rational analysis of uncertainty. 1.2.2 Types of uncertainty There are many uncertainties in civil geotechnical engineering and these may be classified into three main groups as follows: (a) The first group consists of uncertainties in material parameters such as modulus of concrete, steel stability of concrete and steel in different condition such as tension and 3 flexure, soil unit weight, cohesion, angle of internal friction, pore water pressure, compressibility and permeability. For example in a so-called homogeneous soil, each parameter may vary significantly. Moreover, natural media, i.e. earth masses are often heterogeneous and an isotropic and the soil profile is complex due to discontinuities and minor geological details. (b) The second group consists of uncertainties in loads. Under static loading conditions, one is concerned with dead and live load and there are usually more uncertainties in relation to live loads. Structures and soil masses may also be subjected to dynamic loads from earthquakes, wind and waves. Significant uncertainties are associated with such random loads. Often the uncertainties associated with static loads may be negligible in comparison to those associated with material parameters. On the other hand, uncertainties associated with dynamic loads may be of the same order of magnitude or even greater than those associated with material parameters. It should also be noted that under dynamic loads, the magnitude of material parameters may change significantly. For example, the shear strength of a soil decreases during cyclic loading and, as such, there are additional uncertainties concerning geotechnical performance. (c) The third group consists of uncertainties in mathematical modeling and methods of analysis. Each model of soil behavior is based on some idealization of real situations. Each method of analysis or design is based on simplifying assumptions and arbitrary factors of safetyâ€™s are often used. 1.3 Deterministic and probabilistic approaches 1.3.1. Deterministic approach An approach based on the premise that a given problem can be stated in the form of a question or a set of questions to which there is an explicit and unique answer is a deterministic approach. For example, the concept that unique mathematical relationships govern mechanical behavior of soil mass or a soil structure system. 4 Page 5 1. 1. Introduction The trend in civil engineering today more than ever before is to provide 1. economical or robust design at certain levels of safety, 2. use new materials in construction. When newer materials are being used in civil engineering design, there is a need to understand to what extent the structure is safe, and 3. consider uncertainties in design. One has to recognize that there are many processes such as data collection, analysis and design in civil engineering systems which are random in nature. Design of many facilities such as: buildings, foundations, bridges, dams, highways, airports, seaports, offshore structures, tunnels, sanitary landfills, excavation etc. need to address the design issues rationally. The loading in civil engineering systems are completely unknown. Only some of the features of the loading are known. Some of the examples of loading are frequency and occurrence of earthquakes, movement of ground water, rainfall pattern, wind and ice loadings etc. All these loading are random in nature, and at times they create overloading situation. What we have been doing so far can be schematically shown as follows: Sampling Testing Formula Experience What is the extent of sampling ? What is the extent methods represent the actual field condition ? Assumption ? Build with confidence Sampling Testing Formula Experience What is the extent of sampling ? What is the extent methods represent the actual field condition ? Assumption ? Build with confidence At all stages indicated above, there is an element of uncertainty with regard to the suitability of the site in terms of soils, construction materials, which we transfer to a different level using a set of expressions to obtain the desired quantities such as the floor capacity, allowable loads in buildings etc. 1 1.2. Probability of failure and reliability The failure of civil engineering systems is a consequence of decisions making under uncertain conditions and different type of failures such as temporary failures, maintenance failures, failures in design, failure due to natural hazards need to be addressed. For example, a bridge collapses which is a permanent failure, if there is a traffic jam on the bridge, it is a temporary failure. If there is overflow in a filter or a pipe due to heavy rainfall, it is a temporary failure. Thus definition of failure is important. It is expressed in terms of probability of failure and is assessed by its inability to perform its intended function adequately on demand for a period of time under specific conditions. The converse of probability of failure is called reliability and is defined in terms of the success of a system or reliability of a system is the probability of a system performing its required function adequately for specified period of time under stated conditions. 1. Reliability is expressed as a probability 2. A quality of performance is expected 3. It is expected over a period of time 4. It s expected to perform under specified conditions 1.2.1 Uncertainties in Civil engineering In dealing with design, uncertainties are unavoidable. Uncertainties are classified into two broad types. Those associated with natural randomness and those associated with inaccuracies in our prediction and estimation of reality. The former type is called aleatory type where as the latter is called epistemic type. Irrespective of the classification understanding the nature of randomness is necessary. The nature of the first type arising out of nature (for example, earthquake and rainfall effects) needs to be handled rationally in design as it can not altered and the second one needs to be reduced using appropriate prediction models and sampling techniques. The response of materials such as concrete, soil and rock to loading and unloading is of primary concern to the civil engineer. In all types of problems, the engineer is often dealing with incomplete information or uncertain conditions. It is necessary for the 2 engineer to be aware of many assumptions and idealizations on which methods of analysis and design are based. The use of analytical tools must be combined with sound engineering judgment based on experience and observation. In the last two decades the need for solving complex problems has led to the development and use of advanced quantitative methods of modeling and analysis. For example, the versatile finite element method has proved to be valuable in problems of stability, deformation, earthquake response analysis etc. The rapid development of computers and computing methods has facilitated the use of such methods. However, it is well known that the information derived from sophisticated methods of analysis will be useful only if comprehensive inputs data are available and only if the data are reliable. Thus, the question of uncertainty and randomness of data is central to design and analysis in civil engineering. Decisions have to be made on the basis of information which is limited or incomplete. It is, therefore, desirable to use methods and concepts in engineering planning and design which facilitate the evaluation and analysis of uncertainty. Traditional deterministic methods of analysis must be supplemented by methods which use the principles of statistics and probability. These latter methods, often called probabilistic methods, enable a logical analysis of uncertainty to be made and provide a quantitative basis for assessing the reliability of foundations and structures. Consequently, these methods provide a sound basis for the development and exercise of engineering judgment. Practical experience is always important and the observational approach can prove to be valuable; yet, the capacity to benefit from these is greatly enhanced by rational analysis of uncertainty. 1.2.2 Types of uncertainty There are many uncertainties in civil geotechnical engineering and these may be classified into three main groups as follows: (a) The first group consists of uncertainties in material parameters such as modulus of concrete, steel stability of concrete and steel in different condition such as tension and 3 flexure, soil unit weight, cohesion, angle of internal friction, pore water pressure, compressibility and permeability. For example in a so-called homogeneous soil, each parameter may vary significantly. Moreover, natural media, i.e. earth masses are often heterogeneous and an isotropic and the soil profile is complex due to discontinuities and minor geological details. (b) The second group consists of uncertainties in loads. Under static loading conditions, one is concerned with dead and live load and there are usually more uncertainties in relation to live loads. Structures and soil masses may also be subjected to dynamic loads from earthquakes, wind and waves. Significant uncertainties are associated with such random loads. Often the uncertainties associated with static loads may be negligible in comparison to those associated with material parameters. On the other hand, uncertainties associated with dynamic loads may be of the same order of magnitude or even greater than those associated with material parameters. It should also be noted that under dynamic loads, the magnitude of material parameters may change significantly. For example, the shear strength of a soil decreases during cyclic loading and, as such, there are additional uncertainties concerning geotechnical performance. (c) The third group consists of uncertainties in mathematical modeling and methods of analysis. Each model of soil behavior is based on some idealization of real situations. Each method of analysis or design is based on simplifying assumptions and arbitrary factors of safetyâ€™s are often used. 1.3 Deterministic and probabilistic approaches 1.3.1. Deterministic approach An approach based on the premise that a given problem can be stated in the form of a question or a set of questions to which there is an explicit and unique answer is a deterministic approach. For example, the concept that unique mathematical relationships govern mechanical behavior of soil mass or a soil structure system. 4 In this method of analysis or design one is concerned with relatively simple cause and effect relationship. For each situation it is assumed that there is a single outcome; for each problem a single and unique solution. Of course, one may not be able to arrive at the exact solution and also unique solution may not exist. In such circumstances a deterministic approach aims at obtaining approximate solution. Empirical and semi- empirical methods have always been used in civil engineering although with varying degrees of success. Finally, in deterministic method of analysis, uncertainty is not formally recognized or accounted for one is not concerned with the probabilistic outcome but with well defined outcomes which may or may not occur, that is, either a 100% probability of occurrence or 0% without intermediate value. For example, one may arrive at the conclusion that a foundation will be safe on the basis that the safety factor, F, has a magnitude greater than one. On the other hand, one may conclude that a foundation or a slope is not safe on the basis that the magnitude of the factor of safety F is less than one. A given magnitude of F. e.g. F = 2.5 represents a unique answer to a problem posed in specific terms with certain unique values of loads and of shear strength parameters. In conventional analysis one is not concerned with the reliability associated with this unique value. 1.3.2. Probabilistic approach A probabilistic approach is based on the concept that several or varied outcomes of a situation are possible to this approach uncertainty is recognized and yes/no type of answer to a question concerning geotechnical performance is considered to be simplistic. Probabilistic modeling aims at study of a range of outcomes given input data. Accordingly the description of a physical situation or system includes randomness of data and other uncertainties. The selected data for a deterministic approach would, in general not be sufficient for a probabilistic study of the same problem. The raw data would have to be organized in a more logical way. Often additional data would be for meaningful probabilistic analysis. A probabilistic approach aims determining the probability p, of an outcome, one of many 5Read More