- Email: [email protected]
Limit states design in geotechnical engineering
Structural Safety, 1 (1982) 67-71 Elsevier ScientificPublishing Company, Amsterdam - Printed in The Netherlands
67
LIMIT STATES DESIGN IN GEOTECHNICAL ENGINEERING G.G. Meyerhof Technical University of Nova Scotia, Halifax, N.S. (Canada)
(Received February 16, 1982; acceptedMarch 28, 1982)
Keywords: Earthworks, factor of safety, failure, foundations, limit states probability, retaining walls, safety, serviceability, settlement, stability.
ABSTRACT The paper outlines the ultimate and serviceability limit states in geotechnical engineering practice. The magnitude of conventional partial and total safety factors in earthworks, earth retaining structures and foundations are discussed in terms of the reliability of the subsoil and loading conditions and the probability and
seriousness of failure of the structure during its service life. The serviceability of structures and foundations are treated on the basis of empirical damage criteria related to relative rotation and deflection ratios of foundations supporting different types of buildings and engineering structures.
INTRODUCTION In two earlier papers [1,2] the author reviewed the safety factors in soil mechanics and foundation engineering. It was shown that estimates of the performance of earth structures and foundations should include adequate safety factors against both the ultimate limit state (mainly instability against sliding, bearing capacity, overturning, uplift, seepage and erosion) and the serviceability limit state (mainly total and differential movements, cracking and vibration). The inevitable uncertainties in problems of geotechnical design 0167-4730/82/0000-0000/$02.75
and construction may be either objective (such as loads, soil resistance and deformation) or subjective (such as analysis, judgement, experience and human errors).
ULTIMATE LIMIT STATE The magnitude of partial and total safety factors is governed by the reliability of information (mainly loads and load effects, resistance, deformation, design and construction),
© 1982 Elsevier ScientificPublishing Company
68 the economy of construction and maintenance, the probability and seriousness of failure during service life. The safety margin is influenced by the loads and load effects for dead, live and environmental (water. wind, ice and earthquake) loads, the soil resistance and deformation (including effects of sampling disturbance, specimen size, rate and variation of loading, anisotropy, plane strain, local and progressive failure, pore pressures and drainage), analysis (method, accuracy, assumed failure mechanism, simplified soil profile and weak zones) and construction (geometry, quality and control of materials and workmanship, maintenance during service life). The factors of safety (ratio of resistance of structure to applied load effects for freedom of danger, loss or unacceptable risk) are usually based on characteristic loads including uncertainties of the analysis, and characteristic resistance or deformation including uncertainties of construction. Typical values of the partial coefficient of variation of loads, soil properties, geotechnical analysis and construction are given in Table 1, and they have
TABLE 2 Values of minimum partial safet'~ fac~,w~ Category
Item
Safety Factor
Loads
Dead loads Live loads Static water pressure Environmental loads
0.9-- 1.2 1.0- 1.5 1.0 t.2 I 2 1.4
Soil strength
Cohesion ( c ) Friction (tan q,) Cohesion plus friction
1.5- 2 1.2 i 3 1.3-1.5
been used to estimate the corresponding partial safety factors for a 90% reliability. The range of these partial safety factors is supported by customary values of minimum partial safety factors on loads and soil strength [3] shown in Table 2. Similarly, typical values of the total coefficient of variation of the stability and settlement of earth structures and foundations are given in Table3. and they have been used to estimate total stability safety factors for a 99% reliability and total
TABLE 1 Partial variability and partial safety factors Variability Coefficient Very low <0.1 Low 0.1-0.2 Medium 0.2-0.3 High 0.3-0.4
Loads
Soil properues
Analysis & Construction
Safet3, Factor {90% Reliability)
Dead loads
Unit weight
Earthworks Earth retaining structures
<1.1 <1.!
Index properties (sand) Friction Index properties (clay) Cohesion Compressibility Consolidation Penetration
Onshore foundations
Static water pressure
Pore water pressure Live loads Environmental loads
Offshore foundations
1.1~-1.3 1.1 1.3 1.3-1.6 1.3-1.6
> 1.6-2 1.6-2 1.6-2
Resistance
Very High
> 0.4
Permeability
>2
69 TABLE 3 Total variability and total safety factors Variability Coefficient
Stability
Stability Safety Factor
Settlement
Settlement Factor (90% Reliability)
(99% Reliability) Low 0.1-0.2
Slopes (sand)
Medium 0.2-0.3
Earth retaining structures Slopes and foundations (clay) Foundations (sand)
High 0.3-0.4 Very High >0.4
1.3-1.9 Foundations (clay)
Foundations (sand)
>3.3
1.3 1.6
> 1.6
Piles (dynamic analyses)
settlement factors for a 90% reliability. The range of these total stability safety factors is in reasonable agreement with conventional values of the corresponding minimum total safety factors in stability estimates [4] shown in Table 4. The upper values of the above mentioned partial and total safety factors apply to normal loads, service or operation, while the lower values can be used for maximum loads and worst environmental conditions and also with performance observations, large field tests, analyses of similar failures at the end of the service life and for temporary works. The conventional total safety factors are associated with nominal life-time stability failure TABLE 4 Values of minimum total safety factors Failure Type
Item
Safety Factor
Shearing
Earthworks Earth retaining structures Offshore foundations Onshore foundations Uplift, heave Piping, exit gradient
1.3-1.5 1.5-2 1.5-2 2 -3 1.5-2.5 3 -5
Seepage
1.9-3.3 1.9-3.3
probabilities of the order of 10 -2 for earthworks, 10-3 for earth retaining structures and offshore foundations, and 10 4 for onshore foundations, and these values appear to be acceptable in practice [1,2]. In the new Ontario Highway Bridge Design Code [5], which is based on limit states design principles, the following soil strength safety factors are recommended for the design of substructures and retaining walls: stability and earth pressure, cohesion = 1.5 and friction = 1.25; footings and piles, cohesion = 2.0 and f r i c t i o n = 1.25. These safety factors, which have to be used in conjunction with the factored loads stipulated in the Code, are similar to the partial safety factors given in Table2. For preliminary design of substructures an overall dead and live load, a factor of 1.25 has been obtained on the basis of calibration studies. A load factor of 1.2 is recommended in the Code for water pressures.
SERVICEABILITY LIMIT STATE Allowable movements of foundations and structures depend on soil-structure interaction, desired serviceability, harmful cracking and distortion, restricting the safety or use of
70
the particular structure. Empirical damage criteria are generally related to relative rotation or angular distortion, deflection ratio or tilt of the structure. These criteria differ for frame buildings (bare or cladded), load-bearing walls (sagging or hogging) and other structures, depending on the relative settlement ratios after the end of the construction. While the allowable movements of structures can only be determined in each particular case, this is especially true for bridges, which are usually designed to include the effects of anticipated foundation movements. For common types of buildings, however. some early conservative suggestions [6] are confirmed by comprehensive surveys [7,8]. Similarly, for some other types of engineering structures tentative safe limits may be suggested as a guide. Accordingly, the author has recently reviewed published data on the failure of earth retaining structures and steel storage tanks. It is found that retaining walls and sheet pile walls may fail if the relative rotation exceeds about 1% and about one-half of this value for bridge abutments. Similarly, for steel storage tanks the limiting relative rotation is found to be about 0.7% along the
perimeter of the tank. Using a nlmimum safety factor of about 1.5 to cover inevitable unce~tainties and limited field data, the tentative limits of relative rotation glvet~ in Table5 may be suggested as a guide fo~ usual types of structures, In general, the design of foundations and structures should include provisions for reducing or accommodating nlovemenls without damage, and suitable constructioa precautions should be taken to prevent excessive yield and movement of the g o u n d
CONCLUSIONS The margin of safety in earthwork and foundation engineering depends mainly on the uncertainties and variability of the soil conditions, the approximations in the stability analyses and to a smaller extent on the variability of the loads, except for the dynamic environmental loads on offshore structures. At the ultimate limit state customary minim u m partial safety factors on the loads and soil strength compare fairly well w i t h a 90% reliability of the loads, soil properties, geotechnical analysis and construction. More-
TABLE 5 Tentative rotation limits for structures Relative Rotation
Type of limit and structure
(~//) l/lO0 1/150 1/150 1/250 1/250 1/500 1/500 1/1000 1/lO00
1/2ooo
Danger limit for statically determinate structures and retaining walls Safe limit for statically determinate structures and retaining walls Danger limit for open steel and reinforced concrete frames, steel storage tanks and tilt of high, rigid structures Safe limit for open steel and reinforced concrete frames, steel storage tanks and tilt of high, rigid structures Danger limit for panel walls of frame buildings and tilt of bridge abutments Safe limit for panel walls of frame buildings and tilt of bridge abutments Danger limit for sagging of unreinforced toad-bearing walls Safe limit for sagging of unreinforced load-bearing walls Danger limit for hogging of unreinforced load-bearing walls Safe limit for hogging of unreinforced load-bearing walls
71
over, corresponding minimum total safety factors on the stability of slopes, earth retaining structures and foundations require about 99% reliability of the data. This value corresponds to nominal life-time stability failure probabilities of the order of 10 - 2 for earthworks, 10 -3 for earth retaining structures and offshore foundations, and 10 - 4 for onshore foundations. Allowable movements of foundations and structures at the serviceability limit state depend mainly on soil-structure interaction, harmful cracking and distortion. Empirical damage criteria based on relative rotation or angular distortion for different types of structures have been summarized to suggest tentative design limits as a guide for usual types of structures on a basis of about 90% reliability to cover inevitable uncertainties and limited field data. It is hoped that performance observations on different structures and foundations be actively continued to obtain further quantitative information on their actual safety and reliability for comparison with estimates.
REFERENCES 1 G.G. Meyerhof, Safety factors in soil mechanics, Can. Geotech. J., 7 (1970) 349-355. 2 G.G. Meyerhof, "Factors of safety in foundation engineering ashore and offshore, Proc. First Int. Conf. Behaviour of Offshore Structures, Trondheim, 1 (1976) 901-911. 3 J. Brinch Hansen, The philosophy of foundation design: design criteria, safety factors and settlement limits, Symp. Bearing Capacity Settlement Foundations, Duke Univ., Durham, N.C., 1965, pp. 9-13. 4 K. Terzaghi and R.B. Peck, Soil Mechanics in Engineering Practice, Wiley, New York, 1967. 5 Ontario Highway Bridge Design Code, Ministry of Transportation and Communication, Toronto, Ont., 1982. 6 G.G. Meyerhof, Some recent foundation research and its application to design, Struct. Eng., 31 (1953) 151167. 7 A.W. Skempton and D.H. MacDonald, Allowable settlement of buildings, Proc, Inst. Civ. Eng. London, 5 (part 3) (1956) 727-784. 8 J.B. Burland and C.P. Wroth, Allowable and differential settlements of structures, Proc. Conf. Settlements of Structures, Cambridge, 1974, pp. 611-654.
67
LIMIT STATES DESIGN IN GEOTECHNICAL ENGINEERING G.G. Meyerhof Technical University of Nova Scotia, Halifax, N.S. (Canada)
(Received February 16, 1982; acceptedMarch 28, 1982)
Keywords: Earthworks, factor of safety, failure, foundations, limit states probability, retaining walls, safety, serviceability, settlement, stability.
ABSTRACT The paper outlines the ultimate and serviceability limit states in geotechnical engineering practice. The magnitude of conventional partial and total safety factors in earthworks, earth retaining structures and foundations are discussed in terms of the reliability of the subsoil and loading conditions and the probability and
seriousness of failure of the structure during its service life. The serviceability of structures and foundations are treated on the basis of empirical damage criteria related to relative rotation and deflection ratios of foundations supporting different types of buildings and engineering structures.
INTRODUCTION In two earlier papers [1,2] the author reviewed the safety factors in soil mechanics and foundation engineering. It was shown that estimates of the performance of earth structures and foundations should include adequate safety factors against both the ultimate limit state (mainly instability against sliding, bearing capacity, overturning, uplift, seepage and erosion) and the serviceability limit state (mainly total and differential movements, cracking and vibration). The inevitable uncertainties in problems of geotechnical design 0167-4730/82/0000-0000/$02.75
and construction may be either objective (such as loads, soil resistance and deformation) or subjective (such as analysis, judgement, experience and human errors).
ULTIMATE LIMIT STATE The magnitude of partial and total safety factors is governed by the reliability of information (mainly loads and load effects, resistance, deformation, design and construction),
© 1982 Elsevier ScientificPublishing Company
68 the economy of construction and maintenance, the probability and seriousness of failure during service life. The safety margin is influenced by the loads and load effects for dead, live and environmental (water. wind, ice and earthquake) loads, the soil resistance and deformation (including effects of sampling disturbance, specimen size, rate and variation of loading, anisotropy, plane strain, local and progressive failure, pore pressures and drainage), analysis (method, accuracy, assumed failure mechanism, simplified soil profile and weak zones) and construction (geometry, quality and control of materials and workmanship, maintenance during service life). The factors of safety (ratio of resistance of structure to applied load effects for freedom of danger, loss or unacceptable risk) are usually based on characteristic loads including uncertainties of the analysis, and characteristic resistance or deformation including uncertainties of construction. Typical values of the partial coefficient of variation of loads, soil properties, geotechnical analysis and construction are given in Table 1, and they have
TABLE 2 Values of minimum partial safet'~ fac~,w~ Category
Item
Safety Factor
Loads
Dead loads Live loads Static water pressure Environmental loads
0.9-- 1.2 1.0- 1.5 1.0 t.2 I 2 1.4
Soil strength
Cohesion ( c ) Friction (tan q,) Cohesion plus friction
1.5- 2 1.2 i 3 1.3-1.5
been used to estimate the corresponding partial safety factors for a 90% reliability. The range of these partial safety factors is supported by customary values of minimum partial safety factors on loads and soil strength [3] shown in Table 2. Similarly, typical values of the total coefficient of variation of the stability and settlement of earth structures and foundations are given in Table3. and they have been used to estimate total stability safety factors for a 99% reliability and total
TABLE 1 Partial variability and partial safety factors Variability Coefficient Very low <0.1 Low 0.1-0.2 Medium 0.2-0.3 High 0.3-0.4
Loads
Soil properues
Analysis & Construction
Safet3, Factor {90% Reliability)
Dead loads
Unit weight
Earthworks Earth retaining structures
<1.1 <1.!
Index properties (sand) Friction Index properties (clay) Cohesion Compressibility Consolidation Penetration
Onshore foundations
Static water pressure
Pore water pressure Live loads Environmental loads
Offshore foundations
1.1~-1.3 1.1 1.3 1.3-1.6 1.3-1.6
> 1.6-2 1.6-2 1.6-2
Resistance
Very High
> 0.4
Permeability
>2
69 TABLE 3 Total variability and total safety factors Variability Coefficient
Stability
Stability Safety Factor
Settlement
Settlement Factor (90% Reliability)
(99% Reliability) Low 0.1-0.2
Slopes (sand)
Medium 0.2-0.3
Earth retaining structures Slopes and foundations (clay) Foundations (sand)
High 0.3-0.4 Very High >0.4
1.3-1.9 Foundations (clay)
Foundations (sand)
>3.3
1.3 1.6
> 1.6
Piles (dynamic analyses)
settlement factors for a 90% reliability. The range of these total stability safety factors is in reasonable agreement with conventional values of the corresponding minimum total safety factors in stability estimates [4] shown in Table 4. The upper values of the above mentioned partial and total safety factors apply to normal loads, service or operation, while the lower values can be used for maximum loads and worst environmental conditions and also with performance observations, large field tests, analyses of similar failures at the end of the service life and for temporary works. The conventional total safety factors are associated with nominal life-time stability failure TABLE 4 Values of minimum total safety factors Failure Type
Item
Safety Factor
Shearing
Earthworks Earth retaining structures Offshore foundations Onshore foundations Uplift, heave Piping, exit gradient
1.3-1.5 1.5-2 1.5-2 2 -3 1.5-2.5 3 -5
Seepage
1.9-3.3 1.9-3.3
probabilities of the order of 10 -2 for earthworks, 10-3 for earth retaining structures and offshore foundations, and 10 4 for onshore foundations, and these values appear to be acceptable in practice [1,2]. In the new Ontario Highway Bridge Design Code [5], which is based on limit states design principles, the following soil strength safety factors are recommended for the design of substructures and retaining walls: stability and earth pressure, cohesion = 1.5 and friction = 1.25; footings and piles, cohesion = 2.0 and f r i c t i o n = 1.25. These safety factors, which have to be used in conjunction with the factored loads stipulated in the Code, are similar to the partial safety factors given in Table2. For preliminary design of substructures an overall dead and live load, a factor of 1.25 has been obtained on the basis of calibration studies. A load factor of 1.2 is recommended in the Code for water pressures.
SERVICEABILITY LIMIT STATE Allowable movements of foundations and structures depend on soil-structure interaction, desired serviceability, harmful cracking and distortion, restricting the safety or use of
70
the particular structure. Empirical damage criteria are generally related to relative rotation or angular distortion, deflection ratio or tilt of the structure. These criteria differ for frame buildings (bare or cladded), load-bearing walls (sagging or hogging) and other structures, depending on the relative settlement ratios after the end of the construction. While the allowable movements of structures can only be determined in each particular case, this is especially true for bridges, which are usually designed to include the effects of anticipated foundation movements. For common types of buildings, however. some early conservative suggestions [6] are confirmed by comprehensive surveys [7,8]. Similarly, for some other types of engineering structures tentative safe limits may be suggested as a guide. Accordingly, the author has recently reviewed published data on the failure of earth retaining structures and steel storage tanks. It is found that retaining walls and sheet pile walls may fail if the relative rotation exceeds about 1% and about one-half of this value for bridge abutments. Similarly, for steel storage tanks the limiting relative rotation is found to be about 0.7% along the
perimeter of the tank. Using a nlmimum safety factor of about 1.5 to cover inevitable unce~tainties and limited field data, the tentative limits of relative rotation glvet~ in Table5 may be suggested as a guide fo~ usual types of structures, In general, the design of foundations and structures should include provisions for reducing or accommodating nlovemenls without damage, and suitable constructioa precautions should be taken to prevent excessive yield and movement of the g o u n d
CONCLUSIONS The margin of safety in earthwork and foundation engineering depends mainly on the uncertainties and variability of the soil conditions, the approximations in the stability analyses and to a smaller extent on the variability of the loads, except for the dynamic environmental loads on offshore structures. At the ultimate limit state customary minim u m partial safety factors on the loads and soil strength compare fairly well w i t h a 90% reliability of the loads, soil properties, geotechnical analysis and construction. More-
TABLE 5 Tentative rotation limits for structures Relative Rotation
Type of limit and structure
(~//) l/lO0 1/150 1/150 1/250 1/250 1/500 1/500 1/1000 1/lO00
1/2ooo
Danger limit for statically determinate structures and retaining walls Safe limit for statically determinate structures and retaining walls Danger limit for open steel and reinforced concrete frames, steel storage tanks and tilt of high, rigid structures Safe limit for open steel and reinforced concrete frames, steel storage tanks and tilt of high, rigid structures Danger limit for panel walls of frame buildings and tilt of bridge abutments Safe limit for panel walls of frame buildings and tilt of bridge abutments Danger limit for sagging of unreinforced toad-bearing walls Safe limit for sagging of unreinforced load-bearing walls Danger limit for hogging of unreinforced load-bearing walls Safe limit for hogging of unreinforced load-bearing walls
71
over, corresponding minimum total safety factors on the stability of slopes, earth retaining structures and foundations require about 99% reliability of the data. This value corresponds to nominal life-time stability failure probabilities of the order of 10 - 2 for earthworks, 10 -3 for earth retaining structures and offshore foundations, and 10 - 4 for onshore foundations. Allowable movements of foundations and structures at the serviceability limit state depend mainly on soil-structure interaction, harmful cracking and distortion. Empirical damage criteria based on relative rotation or angular distortion for different types of structures have been summarized to suggest tentative design limits as a guide for usual types of structures on a basis of about 90% reliability to cover inevitable uncertainties and limited field data. It is hoped that performance observations on different structures and foundations be actively continued to obtain further quantitative information on their actual safety and reliability for comparison with estimates.
REFERENCES 1 G.G. Meyerhof, Safety factors in soil mechanics, Can. Geotech. J., 7 (1970) 349-355. 2 G.G. Meyerhof, "Factors of safety in foundation engineering ashore and offshore, Proc. First Int. Conf. Behaviour of Offshore Structures, Trondheim, 1 (1976) 901-911. 3 J. Brinch Hansen, The philosophy of foundation design: design criteria, safety factors and settlement limits, Symp. Bearing Capacity Settlement Foundations, Duke Univ., Durham, N.C., 1965, pp. 9-13. 4 K. Terzaghi and R.B. Peck, Soil Mechanics in Engineering Practice, Wiley, New York, 1967. 5 Ontario Highway Bridge Design Code, Ministry of Transportation and Communication, Toronto, Ont., 1982. 6 G.G. Meyerhof, Some recent foundation research and its application to design, Struct. Eng., 31 (1953) 151167. 7 A.W. Skempton and D.H. MacDonald, Allowable settlement of buildings, Proc, Inst. Civ. Eng. London, 5 (part 3) (1956) 727-784. 8 J.B. Burland and C.P. Wroth, Allowable and differential settlements of structures, Proc. Conf. Settlements of Structures, Cambridge, 1974, pp. 611-654.