CPT Interpretation: Soil Parameters φ’, E, Vs, M

Acknowledgement: This page has been reproduced from P. K. Robertson, K.Cabal, Guide to Cone Penetration Testing, 7th Edition. Gregg Drilling LLC, 2022 with permission from P. K. Robertson.

Peak Friction Angle (φ’)

The shear strength of uncemented, coarse-grained soils is usually expressed in terms of a peak secant friction angle, φ'.

Significant advances have been made in the development of theories to model the cone penetration process in sands (e.g., Yu and Mitchell, 1998). Cavity expansion models are popular since they are relatively simple and can incorporate many of the important features of soil response. However, empirical correlations based on calibration chamber test results and field results are still the most used.

Robertson and Campanella (1983) suggested a correlation to estimate the peak friction angle (φ') for uncemented, unaged, moderately compressible, predominately quartz sands based on calibration chamber test results. For sands of higher compressibility (i.e., carbonate sands or sands with high mica content), the method will tend to predict friction angles values that are too low.

Kulhawy and Mayne (1990) suggested an alternate relationship for clean, rounded, uncemented quartz sands, and evaluated the relationship using high quality field data.

Jefferies and Been (2006) showed a strong link between state parameter (ψ) and the peak friction angle (φ') for a wide range of sands. Using this link, it is possible to link Q_tn,cs with φ', using:

Where φ'_cv = constant volume (or critical state) friction angle depending on mineralogy (Bolton, 1986), typically about 33 degrees for sub-rounded quartz sands but can be as high as 40 degrees for felspathic and carbonate sands.

Hence, the relationship between normalized clean sand equivalent cone resistance, Q_tn,cs and φ' becomes:

The above relationship produces estimates of peak friction angle for clean quartz sands that are like those by Kulhawy and Mayne (1990). However, the above relationship based on state parameter has the advantage that it includes the importance of grain characteristics and mineralogy that are reflected in both φ'_cv, as well as soil type through Q_tn,cs. The above relationship also tends to predict φ' values closer to measured values in calcareous sands where the CPT tip resistance can be low for high values of φ', due to a high value for φ'_cv.

For fine-grained soils, the best means for defining the effective stress peak friction angle is from laboratory on high quality undisturbed samples. An assumed value of φ' = 26° for clays and 30° for silts is often sufficient for many low-risk projects. Alternatively, an effective stress limit plasticity solution for undrained cone penetration developed at the Norwegian Institute of Technology (NTH: Senneset et al., 1989) allows the approximate evaluation of effective stress parameters (c' and φ') from piezocone (u₂) measurements. In a simplified approach for normally to lightly-overconsolidated clays and silts (c' = 0), the NTH solution can be approximated for the following ranges of parameters: 20º ≤ φ' ≤ 40º and 0.1 ≤ B_q ≤ 1.0 (Mayne 2006):

For heavily overconsolidated soils, fissured geomaterials, and highly cemented or structured clays, the above will not provide reliable results and φ' should be determined by laboratory testing on high quality undisturbed samples. The above approach is only valid when positive (u₂) pore pressures are recorded (i.e., B_q > 0.1).

Stiffness and Modulus

CPT data can be used to estimate modulus in soils for subsequent use in elastic or semi-empirical settlement prediction methods. However, correlations between q_c and Young’s moduli (E) are sensitive to stress and strain history, aging, soil mineralogy and microstructure.

A useful guide for estimating Young's moduli for young, uncemented predominantly silica sands is given in Figure 32. The modulus has been defined as that mobilized at about 0.1% strain. For more heavily loaded conditions (i.e., larger strain) the modulus would decrease (see “Applications” section).

Modulus from Shear Wave Velocity

A major advantage of the seismic CPT (SCPT) is the additional measurement of the shear wave velocity, V_s. The shear wave velocity is measured using a downhole technique during pauses in the CPT resulting in a continuous profile of V_s. Elastic theory states that the small strain shear modulus, G_o can be determined from:

Where: ρ is the mass density of the soil (ρ = γ/g) and G_o is the small strain shear modulus (shear strain, γ < 10^-4 %). Hence, the addition of shear wave velocity during the CPT provides a direct measure of small strain soil stiffness.

The small strain shear modulus represents the elastic stiffness of the soil at shear strains (γ) less than 10^-4 percent. Elastic theory also states that the small strain Young’s modulus, E_o is linked to G_o, as follows:

where: υ is Poisson’s ratio, which ranges from 0.1 to 0.3 for most soils.

Application to engineering problems requires that the small strain modulus be softened/reduced to the appropriate strain level. For most well-designed structures, where the average shear strain is relatively small, the degree of softening is often close to a factor of about 2.5. Hence, for many applications the equivalent Young’s modulus (E^’) can be estimated from:

Further details regarding appropriate use of soil modulus for design is given in the section on Applications of CPT Results.

V_s can also be used directly for the evaluation of liquefaction potential. Hence, the SCPT can provide two independent methods to evaluate liquefaction potential in soils with little or no microstructure.

Estimating Shear Wave Velocity (V_s) from CPT

Shear wave velocity (V_s) can be correlated to CPT cone resistance as a function of soil type and SBT I_c. However, shear wave velocity is sensitive to age and cementation, where older deposits of the same soil have higher V_s (i.e., higher stiffness) than younger deposits and likewise for cemented soils. Based on extensive SCPT data (Robertson, 2009), Figure 33 shows a relationship between normalized CPT data (Q_tn and F_r) and normalized shear wave velocity, V_s1, for uncemented Holocene and Pleistocene age soils, where:

V_s1 is in the same units as V_s (e.g., either m/s or ft/s). Younger Holocene age soils tend to plot toward the center and lower left of the SBT_n chart whereas older Pleistocene age soil tend to plot toward the upper right part of the chart.

Constrained Modulus

Consolidation settlements can be estimated using the 1-D Constrained Modulus, M, where:

Where m_v = equivalent oedometer coefficient of compressibility.

Constrained modulus can be estimated from CPT results using the following empirical relationship:

Sangrelat (1970) suggested that α_M varies with soil plasticity and natural water content for a wide range of fine-grained soils and organic soils, although the data were based on q_c. Meigh (1987) suggested that α_M lies in the range 2 – 8, whereas Mayne (2001) suggested a general value of 5. Robertson (2009) suggested that α_M varies with Q_t, such that:

Robertson (2009) set the limit for α_m = 14, but experience has shown that better results are obtained when reduced to 8. Robertson (2009) also suggested a factor α_m = 0.03, but experience shows that a factor of 0.0188 provides a slightly more conservative estimate of M when I_c < 2.2 and is consistent with the observation by Mayne (2001) that M ~ G_o in sands. Estimates of drained 1-D constrained modulus from undrained cone penetration will always be approximate. Estimates can be improved with additional information about the soil, such as plasticity index, natural water content and shear wave velocity. Also α_M can be lower in organic soils and soils with high water content.