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Soil Parameters for Drained and Undrained Analysis Applied Theory Dr Minna Karstunen based on work by Dr H. Burd, University of Oxford

Introduction • The aim is to discuss the choice of parameters for the Mohr-Coulomb model. • More advanced soil models may have some advantages over the Mohr-Coulomb model (but require the specification of a larger number of parameters) • Typical experimental methods currently used to measure the soil parameters are briefly discussed. • It is also useful, however, to estimate values of soil properties based on previous experience, and on correlations with other soil parameters.

Undrained and Drained Loading • In carrying out any analysis in geotechnical engineering it is usually necessary to distinguish between drained and undrained loading. • The soil may also be partially drained which means that it lies between these two extremes.

Undrained and Drained Loading • drained analysis appropriate when – permeability is high – rate of loading is low – short term behavior is not of interest for problem considered

• undrained analysis appropriate when – permeability is low and rate of loading is high – short term behavior has to be assessed

Undrained and Drained Loading Suggestion by Vermeer & Meier (1998) T < 0.10 (U < 10%)

undrained analysis

T > 0.40 (U > 70%)

drained analysis

k E oed T= t 2 γw D

k = Eoed = γw = D = t = T = U =

permeability stiffness in 1-d compression unit weight of water drainage length construction time dimensionless time factor degree of consolidation

Drained Analysis Drained analysis may be carried out by using a constitutive model based on effective stresses in which the material model is specified in terms of drained parameters.

Modelling Undrained Behavior with PLAXIS Method A (analysis in terms of effective stresses): type of material behaviour: undrained effective strength parameters (MC: c', ϕ', ψ‘) effective stiffness parameters (MC: E50', ν‘) Method B (analysis in terms of effective stresses): type of material behaviour: undrained total strength parameters c = cu, ϕ = 0, ψ = 0 effective stiffness parameters E50', ν' Method C (analysis in terms of total stresses): type of material behaviour: drained total strength parameters c = cu, ϕ = 0, ψ = 0 total stiffness parameters Eu, νu = 0.495

Need to be careful in case of stiff OC clays!

Mohr Coulomb Model for Drained and Undrained Analysis • For drained loading, a total of 5 parameters are required to specify the Mohr-Coulomb model. These are; two strength parameters (c' and φ' ), a dilation angle (ψ) and two elastic parameters. • For undrained calculations, a separate failure model based on an undrained shear strength, cu, is used. Note that cu is not a fundamental property of the soil; it depends on the stress level and also the stress history.

Mohr Coulomb Model for Drained and Undrained Analysis

Drained or Undrained (Approach A)

Undrained (Approach C)

Mohr Coulomb Model for Drained and Undrained Analysis • To analyse a problem using the Mohr-Coulomb model, appropriate values of the material parameters must be selected to provide a good match with the soil being modelled. • The selection of these parameters is complicated by the fact that real soil behaviour often departs considerably from the fundamental assumptions on which the Mohr-Coulomb model is based.

The Mohr-Coulomb Model and Real Soil Behaviour

Shear modulus G/ G/G0 [-]

a) Most real soils do not exhibit linear elastic behaviour prior to failure 1

Retaining walls Foundations Tunnels

Very small strains

Conventional soil testing

Small strains

Larger strains 0 -6

10

-5

10

-4

10

-3

10

Dynamic methods Local gauges

-2

10

-1

10

Shear strain γ[-]

The Mohr-Coulomb Model and Real Soil Behaviour b) The stiffness of soil tends to increase with increasing stress level. In PLAXIS the stiffness can be specified to increase linearly with depth below the soil surface. c) Unloading stiffness differs from stiffness in primary loading

The Mohr-Coulomb Model and Real Soil Behaviour

Triaxial compression test on a sample of Leighton Buzzard sand

The Mohr-Coulomb Model and Real Soil Behaviour d)

The friction angle of a sand depends on its density and stress level. The choice of φ' needs careful consideration of these factors.

The Mohr-Coulomb Model and Real Soil Behaviour

Drained Triaxial Test

Undrained Triaxial Test

Pressuremeter Test

G PL = σ ho + cu 1 + ln cu

The undrained shear strength may be calculated from the limiting cavity pressure PL (for details see Clarke (1995).

Cone Penetrometer Test For penetration in clays, the tip resistance qt is given by:

qt = N kt cu + σ vo where σvo is the total vertical stress in the soil at the level of the cone and Nkt is an empirical factor, typically in the range of 10 to 20. For further details, see Lunne et al, (1997).

Correlations for Undrained Shear Strength (cu)

Undrained Shear Strength from MC Parameters

1 + K0 cu = sin φ ' c' cot φ '+ σ v ' 2

Example: Undrained parameters from MC

1 + K0 cu = sin φ ' c' cot φ '+ σ v ' 2

Example: Undrained parameters from MC

In this example:

cu = cuo + ρz where cuo=4.698 kPa and ρ= 2.326 kPa/m.

Example: Undrained parameters from MC Note that the correlation is unlikely to give an accurate shear strength profile for an overconsolidated clay. A better estimate is obtained with Critical State models. For an incompressible material, the undrained Poisson’s ratio would be 0.5 (Method C). However, this value cannot be used for finite element calculations, because it would result in an infinite value of bulk modulus. A suitable value of undrained Poisson’s ration for use in FE analyses is νu=0.495. In this case, the appropriate value of undrained Young’s modulus would be 5537 kPa.

Correlations for su based on Cam Clay A useful correlation that is based on Cam Clay theory (and confirmed by the results of laboratory testing) is:

cu cu (OCR )µ = σ 'vi σ 'vi NC where σ’vi is the vertical effective stress at the start of undrained loading and OCR (the overconsolidation ratio) is equal to σ’p/ σ’vi, where σ’p is the vertical (effective) preconsolidation stress. According to data collected by Muir Wood (1990) µ is close to 0.8 and (cu/σ’vi)NC lies between 0.1 and 0.35.

Example At an OC clay site, the water table is at the ground surface. The preconsolidation stresses correspond to the application of a vertical effective stress of 500 kPa at the ground surface. Take (cu/σ’vi)NC as 0.2, µ as 0.8 and the submerged unit weight of the soil as 8 kPa/m.

cu from Index Tests w − wP IL = wL − w P

cu = 2 × 100

(1− I L )

NOTE: This is remoulded strength (intact strength can be much higher)

cu of London Clay

cu of London Clay

Friction and Dilations Angles for Sand

Correlations for Friction Angle Bolton (1986) proposes a relationship

φ ' = φ 'cv +0.8ψ where φ’cv is the critical state friction angle and ψ is the angle of dilation.

Correlations for Friction Angle A study by Bolton (1986 and 1987) on published sand test data, suggested that the maximum dilation rate of a sand depends on a relative density index IR: p ' I R = I D 5 − ln − 1 150

for p ' > 150 kPa

I R = 5I D − 1

for p' < 150 kPa

emax − e ID = emax − emin

Correlations for Friction Angle The following correlations were found by Bolton to give a good fit to the available database of test results:

φ ' peak −φ 'cv = 5 I R

for plane strain

φ ' peak −φ 'cv = 3I R

for triaxial test

For quartz sand, the critical state friction angle φ’cv is approximately 33 degrees.

Correlations for Friction Angle

Determining the relative density of a sand deposit is rather difficult. For correlations that relate cone resistance to relative density are described in Lunne et al. 1997.

Estimation of Stiffness

Stiffness of Clay • Option 1 - Use E50. For problems here relatively large strains are expected (e.g. for foundation bearing capacity and studies of the deformation of soft soil beneath an embankment). • Option 2 - Use a small strain Young's modulus. If the problem involves the calculation of deformations of stiff clay under working conditions (e.g. the analysis of the interaction between a tunnel liner and the surrounding ground) • Option 3 - Use the unloading Young's modulus, Eur. If the problem is dominated by unloading (as may be the case, for example, in an excavation problem)

Measurement of Stiffness in the Triaxial test

Not accurate for strains below 1%

Measurement of Stiffness in the Triaxial test

Correlations for Stiffness Jardine et al. (1984) conducted a series of triaxial tests on a range of soils, using local gauges to measure strains.

Correlations for Stiffness Jardine et al. (1984)

Correlations for Stiffness

Plate loading tests by Duncan & Buchignani (1976). Data correspond to strain values of about 0.1%

Correlations for Stiffness Data from Termaat, Vermeer and Vergeer (1985) may be used to suggest the following correlation for normally consolidated (Dutch) clay:

15000cu E ≈ IP u 50

Case Studies

Stiffness profile for various London clay site (Matthews et al, 2000, re-plotted by Simon and Menzies 2000)

Case Studies

Scott et al. (1999)

Stiffness Anisotropy • Recent studies on natural clays (normally consolidated and overconsolidated) suggest that their stiffness may be anisotropic. Typical data for London clay can be found e.g. in Gasparre et al. (2007)

Stiffness of Sands • Based on data on undrained triaxial testing of sandfs at different densities by Tokheim (1976) and Leahy (1984)Loose sand

References: • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

Atkinson, J.H. (2000). Non-linear soil stiffness in routine design. Géotechnique 50(5), 487-508 Atkinson, J.H., Richardson, D. and Stallebrass, S.E. (1990). Effect of recent stress history on the stiffness of overconsolidated soil. Géotechnique 40(4) 531-40. Bolton, M.D. (1986). The strength and dilatancy of sands. Géotechnique 36(1), 65-78 Bolton, M.D. (1987). Discussion on the strength and dilatancy of sands. Géotechnique 37(2), 219-226. Burd, H.D. (2007). Soil parameters for drained and undrained analysis. Numerical Methods in Geotechnical Engineering, 12-14 June, 2007, Manchester. Burland, J.B. and Hancock, R.J.R. (1977). Underground car park at the House of Commons: geotechnical aspects. The Structural Engineer, 55(2), 87100 Burland, J.B. and Kalra, J.C. (1986). Queen Elizabeth II conference centre geotechnical aspects. Proc. ICE, Part 1,80. Clarke, B.G. (1995). Pressuremeters in geotechnical design. Blackie Academic. Clayton, C.R.I, and Khatrush, S.A. (1986) A new device for measuring local axial strains on triaxial specimens. Géotechnique 36(4) 593-598. Clayton, C.R.I., Edwards, A. and Webb, J. (1991). Displacements in London clay during construction. Proc. 10th Int. Conf. on Soil Mech and Fdn. Engng, Florence, 2, 791-796. Clayton, C.R.I., Matthews, M.C. and Simons, N.E. (1995). Site Investigation. Blackwell Science. Cole, K.W. and Burland, J.B. (1972). Observations of retaining wall movements associated with large excavation. Proc. 5th European Conf. on Soil Mechanics and Foundation Engineering, Madrid, 1,445-453. Duncan and Buchignani (1976). Gasparre, A., Nishimura, S., Minh, N.A., Coop, M.R. and Jardine, R.J (2007). The stiffness of natural London Clay. Géotechnique 57(1) 33-47 Gordon, M.A. (1997). Applications of field seismic geophysics to the measurement of geotechnical stiffness parameters. PhD Thesis, University of Surrey, Guildford Hope, V.S. (1993). Applications of seismic transmission tomography in civil engineering. PhD Thesis, University of Surrey, Guildford Jardine, R.J. , Symes, M.J. and Burland, J.B. (1984). The measurement of soil stiffness in the triaxial apparatus. Géotechnique 34(3) 323-340. Leahy, D. (1984). Deformation of dense sand, triaxial testing and modelling. PhD thesis, NTNU, Trondheim. Lunne, T., Robertson, P.K. and Powell, J.J.M. (1997) Cone Penetration Testing in Geotechnical Practice. Blackie Academic. Mair, R.J. (1993). Developments in geotechnical engineering research: applications to tunnels and deep excavations. Unwin memorial Lecture 1992. Proc. ICE, 3,27-41. Matthews, M.C., Clayton, C.R.I., and Own, Y. (2000). The use of field geophysical techniques to determine geotechnical stiffness parameters. Proc. ICE (Geotechnical Engineering),143, 31-42. Muir Wood, D.M. (1990). Soil Behaviour and Critical State Soil Mechanics. Cambridge University Press. Scott, P., Talby, R. and den Hartog, N. (1999). Queensbury House, London: a case study of the prediction and monitoring of settlements during the construction of a deep excavation. Proc. Int. Symp. Beyond 2000 in Computational Geomechanics, 163-176. A.A. Balkema. Simons, N. and Menzies, B. (2000). A short course in foundation engineering. Thomas Telford. 2nd Ed. Stevens A. et al. (1977) Barbican Arts Centre. The Structural Engineer, 55(11) 473-485. St. John, H.D., Potts, D.M., Jardine, R.J. and Higgins, K.G. (1993). Prediction and performance of ground response due to construction of a deep basement at 60 Victoria Embankment. Proceedings of the Wroth Memorial Symposium, Oxford, July 1992, 581-608. Thomas Telford. Termaat R.J., Vermeer P.A. and Vergeer G.J.H. (1985). Failure by large plastic deformation. Proc. ICSMFE, 4, 2045-2048. Tokheim, O. (1976). A model for soil behaviour. PhD thesis, NTNU, Trondheim. Wroth, C.P. (1984). The interpretation of in-situ soil tests. 24th Rankine Lecture, Géotechnique, 34(4), 449-89 Wroth, C.P. (1988). Penetration testing - a more rigorous approach to interpretation. Proc. Of International Conf. on Penetration testing, ISOPT-1, Orlando, 1, 303-311.

Bibliography • Further information on the topics discussed in this lecture can be found in the following books: • Simons, N., Menzies, B. and Matthews, M. (2002). A short course in geotechnical site investigation. Thomas Telford • Potts, D.M. and Zdravkovic, L. (2001). Finite element analysis in geotechnical engineering. Application. Thomas Telford • Loo, B. (2007). Handbook of Geotechnical Investigations and Design Tables. Taylor & Francis.

View more...
Introduction • The aim is to discuss the choice of parameters for the Mohr-Coulomb model. • More advanced soil models may have some advantages over the Mohr-Coulomb model (but require the specification of a larger number of parameters) • Typical experimental methods currently used to measure the soil parameters are briefly discussed. • It is also useful, however, to estimate values of soil properties based on previous experience, and on correlations with other soil parameters.

Undrained and Drained Loading • In carrying out any analysis in geotechnical engineering it is usually necessary to distinguish between drained and undrained loading. • The soil may also be partially drained which means that it lies between these two extremes.

Undrained and Drained Loading • drained analysis appropriate when – permeability is high – rate of loading is low – short term behavior is not of interest for problem considered

• undrained analysis appropriate when – permeability is low and rate of loading is high – short term behavior has to be assessed

Undrained and Drained Loading Suggestion by Vermeer & Meier (1998) T < 0.10 (U < 10%)

undrained analysis

T > 0.40 (U > 70%)

drained analysis

k E oed T= t 2 γw D

k = Eoed = γw = D = t = T = U =

permeability stiffness in 1-d compression unit weight of water drainage length construction time dimensionless time factor degree of consolidation

Drained Analysis Drained analysis may be carried out by using a constitutive model based on effective stresses in which the material model is specified in terms of drained parameters.

Modelling Undrained Behavior with PLAXIS Method A (analysis in terms of effective stresses): type of material behaviour: undrained effective strength parameters (MC: c', ϕ', ψ‘) effective stiffness parameters (MC: E50', ν‘) Method B (analysis in terms of effective stresses): type of material behaviour: undrained total strength parameters c = cu, ϕ = 0, ψ = 0 effective stiffness parameters E50', ν' Method C (analysis in terms of total stresses): type of material behaviour: drained total strength parameters c = cu, ϕ = 0, ψ = 0 total stiffness parameters Eu, νu = 0.495

Need to be careful in case of stiff OC clays!

Mohr Coulomb Model for Drained and Undrained Analysis • For drained loading, a total of 5 parameters are required to specify the Mohr-Coulomb model. These are; two strength parameters (c' and φ' ), a dilation angle (ψ) and two elastic parameters. • For undrained calculations, a separate failure model based on an undrained shear strength, cu, is used. Note that cu is not a fundamental property of the soil; it depends on the stress level and also the stress history.

Mohr Coulomb Model for Drained and Undrained Analysis

Drained or Undrained (Approach A)

Undrained (Approach C)

Mohr Coulomb Model for Drained and Undrained Analysis • To analyse a problem using the Mohr-Coulomb model, appropriate values of the material parameters must be selected to provide a good match with the soil being modelled. • The selection of these parameters is complicated by the fact that real soil behaviour often departs considerably from the fundamental assumptions on which the Mohr-Coulomb model is based.

The Mohr-Coulomb Model and Real Soil Behaviour

Shear modulus G/ G/G0 [-]

a) Most real soils do not exhibit linear elastic behaviour prior to failure 1

Retaining walls Foundations Tunnels

Very small strains

Conventional soil testing

Small strains

Larger strains 0 -6

10

-5

10

-4

10

-3

10

Dynamic methods Local gauges

-2

10

-1

10

Shear strain γ[-]

The Mohr-Coulomb Model and Real Soil Behaviour b) The stiffness of soil tends to increase with increasing stress level. In PLAXIS the stiffness can be specified to increase linearly with depth below the soil surface. c) Unloading stiffness differs from stiffness in primary loading

The Mohr-Coulomb Model and Real Soil Behaviour

Triaxial compression test on a sample of Leighton Buzzard sand

The Mohr-Coulomb Model and Real Soil Behaviour d)

The friction angle of a sand depends on its density and stress level. The choice of φ' needs careful consideration of these factors.

The Mohr-Coulomb Model and Real Soil Behaviour

Drained Triaxial Test

Undrained Triaxial Test

Pressuremeter Test

G PL = σ ho + cu 1 + ln cu

The undrained shear strength may be calculated from the limiting cavity pressure PL (for details see Clarke (1995).

Cone Penetrometer Test For penetration in clays, the tip resistance qt is given by:

qt = N kt cu + σ vo where σvo is the total vertical stress in the soil at the level of the cone and Nkt is an empirical factor, typically in the range of 10 to 20. For further details, see Lunne et al, (1997).

Correlations for Undrained Shear Strength (cu)

Undrained Shear Strength from MC Parameters

1 + K0 cu = sin φ ' c' cot φ '+ σ v ' 2

Example: Undrained parameters from MC

1 + K0 cu = sin φ ' c' cot φ '+ σ v ' 2

Example: Undrained parameters from MC

In this example:

cu = cuo + ρz where cuo=4.698 kPa and ρ= 2.326 kPa/m.

Example: Undrained parameters from MC Note that the correlation is unlikely to give an accurate shear strength profile for an overconsolidated clay. A better estimate is obtained with Critical State models. For an incompressible material, the undrained Poisson’s ratio would be 0.5 (Method C). However, this value cannot be used for finite element calculations, because it would result in an infinite value of bulk modulus. A suitable value of undrained Poisson’s ration for use in FE analyses is νu=0.495. In this case, the appropriate value of undrained Young’s modulus would be 5537 kPa.

Correlations for su based on Cam Clay A useful correlation that is based on Cam Clay theory (and confirmed by the results of laboratory testing) is:

cu cu (OCR )µ = σ 'vi σ 'vi NC where σ’vi is the vertical effective stress at the start of undrained loading and OCR (the overconsolidation ratio) is equal to σ’p/ σ’vi, where σ’p is the vertical (effective) preconsolidation stress. According to data collected by Muir Wood (1990) µ is close to 0.8 and (cu/σ’vi)NC lies between 0.1 and 0.35.

Example At an OC clay site, the water table is at the ground surface. The preconsolidation stresses correspond to the application of a vertical effective stress of 500 kPa at the ground surface. Take (cu/σ’vi)NC as 0.2, µ as 0.8 and the submerged unit weight of the soil as 8 kPa/m.

cu from Index Tests w − wP IL = wL − w P

cu = 2 × 100

(1− I L )

NOTE: This is remoulded strength (intact strength can be much higher)

cu of London Clay

cu of London Clay

Friction and Dilations Angles for Sand

Correlations for Friction Angle Bolton (1986) proposes a relationship

φ ' = φ 'cv +0.8ψ where φ’cv is the critical state friction angle and ψ is the angle of dilation.

Correlations for Friction Angle A study by Bolton (1986 and 1987) on published sand test data, suggested that the maximum dilation rate of a sand depends on a relative density index IR: p ' I R = I D 5 − ln − 1 150

for p ' > 150 kPa

I R = 5I D − 1

for p' < 150 kPa

emax − e ID = emax − emin

Correlations for Friction Angle The following correlations were found by Bolton to give a good fit to the available database of test results:

φ ' peak −φ 'cv = 5 I R

for plane strain

φ ' peak −φ 'cv = 3I R

for triaxial test

For quartz sand, the critical state friction angle φ’cv is approximately 33 degrees.

Correlations for Friction Angle

Determining the relative density of a sand deposit is rather difficult. For correlations that relate cone resistance to relative density are described in Lunne et al. 1997.

Estimation of Stiffness

Stiffness of Clay • Option 1 - Use E50. For problems here relatively large strains are expected (e.g. for foundation bearing capacity and studies of the deformation of soft soil beneath an embankment). • Option 2 - Use a small strain Young's modulus. If the problem involves the calculation of deformations of stiff clay under working conditions (e.g. the analysis of the interaction between a tunnel liner and the surrounding ground) • Option 3 - Use the unloading Young's modulus, Eur. If the problem is dominated by unloading (as may be the case, for example, in an excavation problem)

Measurement of Stiffness in the Triaxial test

Not accurate for strains below 1%

Measurement of Stiffness in the Triaxial test

Correlations for Stiffness Jardine et al. (1984) conducted a series of triaxial tests on a range of soils, using local gauges to measure strains.

Correlations for Stiffness Jardine et al. (1984)

Correlations for Stiffness

Plate loading tests by Duncan & Buchignani (1976). Data correspond to strain values of about 0.1%

Correlations for Stiffness Data from Termaat, Vermeer and Vergeer (1985) may be used to suggest the following correlation for normally consolidated (Dutch) clay:

15000cu E ≈ IP u 50

Case Studies

Stiffness profile for various London clay site (Matthews et al, 2000, re-plotted by Simon and Menzies 2000)

Case Studies

Scott et al. (1999)

Stiffness Anisotropy • Recent studies on natural clays (normally consolidated and overconsolidated) suggest that their stiffness may be anisotropic. Typical data for London clay can be found e.g. in Gasparre et al. (2007)

Stiffness of Sands • Based on data on undrained triaxial testing of sandfs at different densities by Tokheim (1976) and Leahy (1984)Loose sand

References: • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

Atkinson, J.H. (2000). Non-linear soil stiffness in routine design. Géotechnique 50(5), 487-508 Atkinson, J.H., Richardson, D. and Stallebrass, S.E. (1990). Effect of recent stress history on the stiffness of overconsolidated soil. Géotechnique 40(4) 531-40. Bolton, M.D. (1986). The strength and dilatancy of sands. Géotechnique 36(1), 65-78 Bolton, M.D. (1987). Discussion on the strength and dilatancy of sands. Géotechnique 37(2), 219-226. Burd, H.D. (2007). Soil parameters for drained and undrained analysis. Numerical Methods in Geotechnical Engineering, 12-14 June, 2007, Manchester. Burland, J.B. and Hancock, R.J.R. (1977). Underground car park at the House of Commons: geotechnical aspects. The Structural Engineer, 55(2), 87100 Burland, J.B. and Kalra, J.C. (1986). Queen Elizabeth II conference centre geotechnical aspects. Proc. ICE, Part 1,80. Clarke, B.G. (1995). Pressuremeters in geotechnical design. Blackie Academic. Clayton, C.R.I, and Khatrush, S.A. (1986) A new device for measuring local axial strains on triaxial specimens. Géotechnique 36(4) 593-598. Clayton, C.R.I., Edwards, A. and Webb, J. (1991). Displacements in London clay during construction. Proc. 10th Int. Conf. on Soil Mech and Fdn. Engng, Florence, 2, 791-796. Clayton, C.R.I., Matthews, M.C. and Simons, N.E. (1995). Site Investigation. Blackwell Science. Cole, K.W. and Burland, J.B. (1972). Observations of retaining wall movements associated with large excavation. Proc. 5th European Conf. on Soil Mechanics and Foundation Engineering, Madrid, 1,445-453. Duncan and Buchignani (1976). Gasparre, A., Nishimura, S., Minh, N.A., Coop, M.R. and Jardine, R.J (2007). The stiffness of natural London Clay. Géotechnique 57(1) 33-47 Gordon, M.A. (1997). Applications of field seismic geophysics to the measurement of geotechnical stiffness parameters. PhD Thesis, University of Surrey, Guildford Hope, V.S. (1993). Applications of seismic transmission tomography in civil engineering. PhD Thesis, University of Surrey, Guildford Jardine, R.J. , Symes, M.J. and Burland, J.B. (1984). The measurement of soil stiffness in the triaxial apparatus. Géotechnique 34(3) 323-340. Leahy, D. (1984). Deformation of dense sand, triaxial testing and modelling. PhD thesis, NTNU, Trondheim. Lunne, T., Robertson, P.K. and Powell, J.J.M. (1997) Cone Penetration Testing in Geotechnical Practice. Blackie Academic. Mair, R.J. (1993). Developments in geotechnical engineering research: applications to tunnels and deep excavations. Unwin memorial Lecture 1992. Proc. ICE, 3,27-41. Matthews, M.C., Clayton, C.R.I., and Own, Y. (2000). The use of field geophysical techniques to determine geotechnical stiffness parameters. Proc. ICE (Geotechnical Engineering),143, 31-42. Muir Wood, D.M. (1990). Soil Behaviour and Critical State Soil Mechanics. Cambridge University Press. Scott, P., Talby, R. and den Hartog, N. (1999). Queensbury House, London: a case study of the prediction and monitoring of settlements during the construction of a deep excavation. Proc. Int. Symp. Beyond 2000 in Computational Geomechanics, 163-176. A.A. Balkema. Simons, N. and Menzies, B. (2000). A short course in foundation engineering. Thomas Telford. 2nd Ed. Stevens A. et al. (1977) Barbican Arts Centre. The Structural Engineer, 55(11) 473-485. St. John, H.D., Potts, D.M., Jardine, R.J. and Higgins, K.G. (1993). Prediction and performance of ground response due to construction of a deep basement at 60 Victoria Embankment. Proceedings of the Wroth Memorial Symposium, Oxford, July 1992, 581-608. Thomas Telford. Termaat R.J., Vermeer P.A. and Vergeer G.J.H. (1985). Failure by large plastic deformation. Proc. ICSMFE, 4, 2045-2048. Tokheim, O. (1976). A model for soil behaviour. PhD thesis, NTNU, Trondheim. Wroth, C.P. (1984). The interpretation of in-situ soil tests. 24th Rankine Lecture, Géotechnique, 34(4), 449-89 Wroth, C.P. (1988). Penetration testing - a more rigorous approach to interpretation. Proc. Of International Conf. on Penetration testing, ISOPT-1, Orlando, 1, 303-311.

Bibliography • Further information on the topics discussed in this lecture can be found in the following books: • Simons, N., Menzies, B. and Matthews, M. (2002). A short course in geotechnical site investigation. Thomas Telford • Potts, D.M. and Zdravkovic, L. (2001). Finite element analysis in geotechnical engineering. Application. Thomas Telford • Loo, B. (2007). Handbook of Geotechnical Investigations and Design Tables. Taylor & Francis.

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