Manual on Subsurface Investigations (2019)

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164 C H A P T E R 9 Evaluation of Soil Properties Introduction The mechanical behavior of soils under loading is represented by a suite of parameters that have been established within the context of theoretical backgrounds, primarily via elasticity, plasticity, and cavity expansion, but also using Winkler spring analogies and subgrade reaction models. The assigned values of these parameters can then be used in a variety of engineering analyses, such as stability, foundation bearing capacity, settlement, and time rate of consolidation. However, in certain cases, geotechnical parameters are also estimated from empirical methods, using regression, statistical, and probabilistic analyses. Collectively evaluating of all available geophysical, in situ, and laboratory data is the best approach to obtaining the most reasonable and realistic values for each geotechnical parameter. As discussed in Chapter 3, the type of highway project will dictate the importance of the specific parameter in many cases. For instance, soil shear strength will be paramount in geotechnical site investigations involving embankment and slope stability, foundation capacity, and excavations. In these cases, unit weight will also be necessary, but it is of less importance. In most geotechnical projects, the degree of preconsolidation of the natural soils is particularly significant as it is a state parameter and represents the current and past stress history. The stress history is commonly represented by the OCR: OCR = ⁄ where = preconsolidation stress = current effective overburden stress It is well known that OCR governs the undrained shear strength (su), lateral stress coefficient (K0), pore pressure behavior (Af), elastic moduli (E' and Eu), and small-strain shear modulus (Gmax) of soils. Finally, critical-state soil mechanics (CSSM) is valuable as a rational framework in which to organize the mechanical response of soils to loading, as it offers a simple link between consolidation theory and shear strength response to help explain the following behaviors: • Normally consolidated soils vs. overconsolidated soils • Drained vs. undrained loading • Positive vs. negative pore pressures • Contractive vs. dilative response • Total vs. effective stress analysis • Static vs. cyclic loading A description of CSSM is beyond the scope of this manual, but Mayne et al. (2009) and Holtz et al. (2011) provide summaries of the basic principles. This chapter covers evaluating soil parameters from a variety of laboratory, in situ, and geophysical methods. The emphasis in this chapter is on parameters commonly used in highway analysis and design

165 and, thus, is not intended to be exhaustive. Geotechnical aspects of highway projects are often concerned with pilings, shallow foundations, slopes, earth-retaining structures, roadways, and embankments. As such, geotechnical engineering parameters of usual concern include the following: • Subsurface stratigraphy • Soil classification • Unit weight ( ) • Preconsolidation stress or effective yield stress ( = OCR· ) • Shear strength ( , , ) • Lateral stress state ( ) • Modulus ( , ) • Coefficient of consolidation ( ) Additional details and information may be found in Kulhawy and Mayne (1990), Mayne et al. (2002), and Loehr et al. (2016). Many of these soil properties can be evaluated directly using laboratory tests as described in Chapter 8. The emphasis in this chapter is on using the results of in situ tests to estimate soil properties, often via empirical correlations. For pavements, the following additional parameters are covered in detail by Newcomb and Birgisson (1999): • Soil support value • CBR • Regional factor • Resilient modulus ( ) • Modulus of subgrade reaction (k) Stratigraphy An understanding of the subsurface stratigraphy is essential for every project. The most effective approach for obtaining information about the stratigraphy at a site is to use a combination of geophysical methods, in situ tests, and laboratory tests. 9.2.1 Geophysical Methods Surface geophysics can be performed quickly across a property to map horizontal and vertical variations and show the degree of homogeneity or heterogeneity of the subsurface conditions. The process can be done efficiently and economically using one or more seismic, electrical, electromagnetic, and potential- field methods as discussed in Chapter 4. An example of a subsurface profile developed from a 2D MASW survey is presented in Figure 9-1. The profile indicates the vertical and horizontal variations of shear wave velocity ( ). The results indicate that weak soils ( < 600 ft/s [≈ 200 m/s]) and poor ground conditions exist over the right half of the survey location to depths of approximately 10 ft (3 m). This information is helpful to plan subsequent in situ tests and soil borings to evaluate the weak soils more completely.

166 Source: Ilmar Weemees, Vancouver, BC Figure 9-1. Example subsurface profile developed from a 2D MASW survey 9.2.2 In Situ Tests Direct-push, in situ tests, such as CPT and DMT, offer improved resolution of the stratigraphy because the measurements are taken at higher vertical frequencies and multiple readings are obtained from each sounding. For the DMT, two readings ( and ) are obtained at either 8- or 12-in. (20- or 30-cm) depth intervals. For the CPT, three readings ( , , and ) are recorded at regular depth intervals of 0.4, 0.8, or 2.0 in. (1, 2, and 5 cm); thus providing much higher resolution in delineating soil layer interfaces. An illustrative example of stratigraphic profiling using an array of CPT soundings is shown in Figure 9-2 (Liao 2005). The continuous nature of the CPT cone tip resistance ( ) profiles from six soundings to depths of 52 ft (16 m) aids in defining the presence of six soil layers at the site. Source: Paul Mayne Figure 9-2. Example subsurface profile developed from cone resistances of several CPT records

167 9.2.3 Soil Borings A traditional means of defining subsurface stratigraphy is to conduct a series of soil borings and interpolate or extrapolate the interfaces between the various soil zones or strata (Figure 9-3). In this case, beneath a thin layer of topsoil, the three borings generally show five basic layers with depth. The layers were chosen based on three facets: (i) soil type, (ii) energy-corrected SPT resistance ( ) value, and (iii) soil color. In the boring on the right, layer D appears to be absent; however, it is possible that the layer was missed at this location because SPT split-spoon samples are taken only on 5-ft (1.5-m) intervals and not all samples have full recovery. Furthermore, only one number is obtained ( ) that has been averaged over a 12-in. (30-cm) interval. Considerable speculation concerning layer interfaces and transitions are often required with soil borings because of infrequent sampling. Source: Paul Mayne Figure 9-3. Example subsurface profile developed from soil boring records and SPT values SUBSURFACE PROFILE Note: horizontal and vertical scales are different (as shown) 214 feet 145 feet ELEVATION AGB-3 feet (msl) 1105 AGB-1 AGB-4 Soil Sym. K N60 bpf 1100 Layer A: SC 4 Topsoil 5 Layer B: ML 11 3 1095 9 29 8 Layer C: SP 1090 32 Groundwater Level 25 28 28 1085 Layer D: SW 68 22 63 22 26 1080 Layer E: SM 20 24 1075 1070 20 18 Soil Sym. K N60 bpf 16 27 Soil Sym. K N60 bpf

168 Soil Classification Traditionally, soil is classified based on recovered soil samples (both drive type and undisturbed tube samples) based on the USCS and AASHTO classification systems as described in Chapter 8. However, it is also possible with direct-push technology, such as CPT and DMT, to assess the soil behavior type (SBT) empirically. 9.3.1 Soil Behavioral Type by Cone-Penetration Tests Because soil samples are not routinely obtained during CPT, determining soil type is done indirectly, using one, two, or three of the readings. A listing of selected methods for evaluating SBT from cone and piezocone soundings is given in Table 9-1. The measured penetrometer readings ( , , and ) provide the net cone resistance ( = − ) and excess pore pressure (Δ = − ), as well as the effective cone tip resistance ( = − ). Dimensionless CPT parameters have been developed to give (i) normalized cone tip resistance: = ⁄ , (ii) normalized sleeve friction: = 100 ⁄ (%), and (iii) normalized pore pressure parameter: = Δ ⁄ . An alternate form for normalized pore pressures is defined by ∗ = Δ ⁄ . Table 9-1. Methods for evaluating SBT from CPTs Method Procedure Reference Rules of Thumb 1. Clean sands: qt > 50 σatm and u2 ≈ u0 2. Clays: qt < 50 σatm (see note a) 2.1 Intact clays: u2 > u0 2.2 Fissured clays: u2 < 0 Mayne et al. (2002) Soil behavioral charts (nonnormalized) 1. qt vs fs 2. qt vs. Bq 3. (qt - u2) vs. fs Kulhawy and Mayne (1990) Senneset et al. (1989) Fellenius and Eslami (2000) Soil behavioral charts (normalized) 1. Q vs F 2. Q vs Bq 3. Q vs U* 4. Qtn vs. IG = G0/qnet (see note b) Robertson (1990, 1991) Lunne et al. (1997) Schneider et al. (2012) Robertson (2016) SBT CPT material index = Ic where Ic = f(Qtn, F) Robertson (2009a) Probability-based relationships Statistical estimates of percentage sand, silt, and clay contents Tümay et al. (2011) Notes: (a) σatm = 1 atm (≈ 1.013 bar = 101.3 kPa = 1.058 tsf = 14.7 psi) (b) used to detect soils with microstructure, bonding, aging, cementation The most popular method to evaluate SBT from CPTs uses SBT charts based on Q, F, and Bq, termed SBTn because the three piezocone readings are normalized. This system classifies soils into nine distinct zones that are presented in two charts: (i) log Q vs. log F charts and (ii) log Q vs Bq charts, as shown in Figure 9-4 (Lunne et al. 1997). Plotting the CPT data onto one or both charts will assign a zone and soil classification.

169 Source: adapted from Robertson (2009a) Figure 9-4. Nine-zone soil behavioral chart for conducting CPTs in soils Robertson (2009a) has developed an alternative SBTn system that uses the CPT material index defined as follows: = (3.47 − ) + (1.22 + ) where = updated normalized cone tip resistance given by: = ( ʹѵ ) ( ) or expressed in dimensionless terms by: = /( ) The exponent n in the expressions above varies with soil type. For clays, the value of n is 1.0, for silts it is approximately 0.75, and for clean quartz sands n is approximately 0.5. The CPT material index Ic physically represents a family of circles with different radii that separate SBT Zones 2 through 7 in the log Q vs. log F chart (Figure 9-5). 1 10 100 1000 0.1 1 10 N or m al iz ed C on e Ti p R es is ta nc e, Q Normalized Friction, Fr = 100 ⋅ fst/(qt - σvo) (%) 9-Zone Soil Behavioral Type Chart for CPT Gravelly Sands (zone 7) Sands (zone 6) Sandy Mixtures (zone 5) Silt Mix (zone 4) Clays (zone 3) Organic Soils (zone 2) Sensitive Clays and Silts (zone 1) Very stiff OC clay to silt (zone 9) Very stiff OC sand to clayey sand (zone 8) 1 10 100 1000 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 No rm al ize d C on e Ti p Re sis ta nc e, Q Normalized Porewater, Bq = Δu2/(qt-σvo) Clays (zone 3) Sensitive (zone 1)Organic(zone 2) Gravelly Sands (zone 7) Sands (zone 6) qt u2 fs

170 Source: Paul Mayne Figure 9-5. Use of CPT material index Ic and algorithms for nine-zone soil behavioral chart Initially the value of Ic is calculated using n = 1.0 (i.e., the original definition of Q). Then, a revised value of Q = Qtn is calculated by updating n from the following (Robertson 2009a): = 0.381 + 0.05( ⁄ ) − 0.05 ≤ 1.0 Then the index Ic is recalculated. Iteration converges quickly, and, generally, only two or three cycles are needed to obtain the value of Ic at each depth. Additional expressions are available to cull the CPTu data for Zone 1 (soft sensitive clays) and Zones 8 and 9 (stiff overconsolidated clays and sands). Once these three zones are identified, the material index Ic is used to separate Zones 2 through 7. Sensitive clays of Zone 1 are identified when: < 12 exp(−1.4 ) The stiff overconsolidated soils of Zone 8 (1.5 < F < 4.5%) and Zone 9 (F ≥ 4.5%) are found when: 0.006( − 0.9) − 0.0004( − 0.9) − 0.002 Then, the remaining soil types are identified by the CPT material index: • Zone 2 (organic soils: Ic ≥ 3.60)

171 • Zone 3 (clays: 2.95 ≤ Ic < 3.60) • Zone 4 (silt mixtures: 2.60 ≤ Ic < 2.95) • Zone 5 (sand mixtures: 2.05 ≤ Ic < 2.60) • Zone 6 (sands: 1.31 ≤ Ic < 2.05) • Zone 7 (gravelly to dense sands: Ic ≤ 1.31). The red dashed line at Ic = 2.60 in Figure 9-5 represents an approximate boundary separating drained soil response (Ic < 2.60) from undrained behavior (Ic > 2.60). The CPT material index (Ic) may also be used to estimate the preconsolidation pressure ( ) and other geotechnical parameters (Mayne 2016). 9.3.2 Soil Classification by Flat Dilatometer Tests For the flat plate dilatometer, soil types are made based on DMT material index, ID, as follows: = − − In the case where ID < 0.6, the presence of clay soils is indicated; whereas when ID > 1.8, the prevailing soil type is sand. A more detailed soil classification for the DMT is given in Table 9-2. Table 9-2. Soil classification using the DMT Soil Type Peat or Mud Mud Clay Silty Clay Clayey Silt Silt Sandy Silt Silty Sand Sand ID = < 0.1* < 0.6* < 0.33 0.33 to 0.6 0.6 to 0.8 0.8 to 1.2 1.2 to 1.8 1.8 to 3.3 > 3.3 Source: after Marchetti et al. (2006) *with additional restriction that ED < 12 bar, where ED = 34.7(p1 - p0) = dilatometer modulus Soil Unit Weight Soil unit weight ( ) is needed for the following: • To evaluate total ( ) and effective overburden ( ) stresses • To convert shear wave velocity (Vs) to small-strain shear modulus (Gmax) • To evaluate net cone resistance and normalized CPT parameters, as well as DMT horizontal stress index (KD). Unit weight is related to mass density (ρ) by the following: = where g = acceleration due to gravity = 9.8 m/s2 = 32.2 ft/s2. Unit weights can be determined in the laboratory using weight-volume relationships as discussed in Chapter 8, or they can be estimated based on empirical equations for direct-push probes and geophysical measurements.

172 9.4.1 Unit Weight from Shear Wave Velocity Total unit weight is correlated to shear wave velocity (Vs), as illustrated by Figure 9-6 using data reported in Mayne et al. (2009). The regression expressions are given as follows: (pcf) = 49.8 log( ) − 26.5 with in ft/s kN m3⁄ = 7.83 log( ) − 0.125 with in m/s These data are obtained from a variety of uncemented soils, including clays, silts, sands, gravels, and mixed soils, as well as some peats, where the measured unit weights were obtained from undisturbed sampling and the majority (92 percent) of shear wave velocities were measured using seismic DHTs. For the remaining data, measured Vs were obtained from either crosshole or SASW tests. Note that for Vs > 3,000 ft per second (fps), the materials are likely to be rocks, and therefore the expressions above are not applicable. Source: after Mayne et al. (2009) Figure 9-6. Soil unit weight relationship with shear wave velocity 9.4.2 Unit Weight from Cone Penetration Tests For the CPT, an empirical correlation relates the total unit weight to the measured CPT sleeve friction (Figure 9-7). The method is applicable to uncemented, insensitive, and inorganic soils, and the dataset includes unit weights measured on clays, silts, sands, and mixed soils. The trendline from regression analysis is given in dimensionless form as follows (Mayne 2014): = 1.22 + 0.345 log(100 + 0.01⁄ )

173 Source: after Mayne (2014) Note: 1 atm = 1.058 tsf = 1.013 bars = 101.3 kPa = 14.7 psi Figure 9-7. Soil unit weight estimated from CPT sleeve friction 9.4.3 Unit Weight from Flat Dilatometer Tests When results from DMT are available, the total unit weight can be estimated from the following relationship (Mayne et al. 2009): = 1.12 ( ⁄ ) . ( ) . Data from several sites are shown in Figure 9-8 in support of this trend.

174 Source: Mayne et al. (2009) Figure 9-8. Soil unit weight estimated from DMT readings Preconsolidation or Effective Yield Stress The preconsolidation (or yield) stress ( ) is the maximum past loading that was exerted on the soil and is commonly associated with overburden stress removal due to erosion. Preconsolidation stress also commonly occurs in areas of glaciation due to the removal of heavy ice loading. A more general term used is effective yield stress ( ) because soils can develop a quasi-preconsolidation or apparent overconsolidation due to other factors (e.g., aging and creep, exposure to cyclic temperatures, groundwater fluctuations, repeated wet-dry cycles, diagenesis, bonding). 9.5.1 Effective Yield Stress from Cone-Penetration Tests For uncemented and low-sensitivity soils composed of basic minerals (e.g., quartz, kaolin, illite), the effective yield stress is related to the net cone resistance (Figure 9-9) and is given by the following expression (Mayne et al. 2009): = 0.33 ( 100⁄ ) The exponent depends upon the type of soil. The parameter is defined as the slope of log ( ) versus log ( ), as illustrated above. For intact inorganic clays, = 1.0. For silts = 0.85, and for clean quartz-silica sands, = 0.72. For organic clays and silts, = 0.9 is recommended.

175 Source: after Mayne et al. (2009) Figure 9-9. General relationship for effective yield stress and CPT net cone resistance in soils For intact inorganic soils, the CPT material index (Ic) can be used to assign the appropriate value of for the assessment of σp', (Figure 9-10). The relationship is given by the following: = 1 − 0.281 + 2.65 for < 3.5 In the case of heavily overconsolidated and fissured clays, a value of of approximately 1.1 or higher may be appropriate, depending upon the extent of discontinuities, jointing, spacing, and frequency of fissures, as well as other factors.

176 Source: Mayne (2017) Figure 9-10. General trend for yield stress exponent and CPT material index 9.5.2 Effective Yield Stress from Flat Dilatometer Tests The effective yield stress of nonfissured soils can be evaluated from the results of DMT soundings using the following expression (Mayne et al. 2009): = 0.5 ( − ) The data trend between measured by consolidation tests and field values of net contact pressure from the DMT at the same elevation is presented in Figure 9-11.

177 Source: after Mayne et al. (2009) Figure 9-11. General relationship for effective yield stress and DMT net contact pressure in soils 9.5.3 Effective Yield Stress from Standard Penetration Tests For SPT resistances that have been corrected for hammer energy, an approximate estimate of the effective yield stress of soils that are not soft or sensitive can be made (Figure 9-12). The generalized relationship can be represented by the following equation (Mayne 2007a): = 0.47 ( ) where the exponent Y is 1.0 for clays, 0.8 for silts, 0.75 for sandy silts, 0.70 for silty sands, and 0.60 for clean quartz-silica sands. The expression above does not apply to soils that are organic, cemented, structured, fissured, or sensitive.

178 Source: Mayne (2007a) Figure 9-12. General relationship for effective yield stress and energy-corrected SPT N60 resistance in soils 9.5.4 Effective Yield Stress from Shear Wave Velocity Using the results of shear wave velocity measurements, the effective yield stress of intact clays, silts, and sands has been expressed by Mayne (2007b) in dimensionless form by the following: = 0.101( ) . ( ) . ( ) . where = the initial tangent shear modulus Data from 22 soft intact clays, 2 calcareous clays, 1 silt, and 3 sands are shown in Figure 9-13. In addition, results from 3 fissured clays are presented solely for comparison; they are not included in the regression. 0.1 1 10 100 1 10 100 Pr ec on so lid at io n σ p ' ( ba rs ) Energy-Corrected SPT N60 (bpf) σp' = 0.47 σatm (N60)Y Exponent Y = 1 (intact clays) = 0.8 (silts) = 0.6 (sands) N60 (t sf )

179 Source: after Mayne (2007b) Figure 9-13. General relationship for effective yield stress and shear wave velocity in soils Effective Stress Strength Parameters The effective stress strength of soils is commonly represented by a Mohr-Coulomb criterion: = + where = shear strength (i.e., maximum shear stress) = effective cohesion intercept = effective normal stress = effective stress friction angle A traditional means of evaluating the effective stress strength parameters and has been via laboratory strength tests, such as the DS, CIU with pore pressure measurements, and CD tests. These tests are presented and described in Chapter 8. The focus in this section is on evaluating these parameters via in situ tests. 9.6.1 Effective Strength Parameters from Cone-Penetration Tests Cone penetration can be evaluated from solutions based on the following: • Limit equilibrium • Plasticity • Cavity expansion • Strain path • Finite elements • Discrete elements • Finite differences • Empirical approaches

180 For CPT soundings in sands, the standard penetration rate of 0.787 in./s (20 mm/s) is essentially a drained condition (∆ = 0), and the results can be used to interpret the peak effective stress friction angle ( ) with the assumption that = 0. In terms of the CPT material index, drained conditions are prevalent when Ic < 2.60. In this case, the magnitude of of clean quartz-silica sands is obtained from the relationship shown in Figure 9-14 using normalized cone tip resistance: = 17.6° + 11.0° ( ) Source: after Mayne (2007b) Figure 9-14. Effective friction angle of sands from CPT-normalized cone resistance When the penetrometer is advanced into intact clays and silts, generally an undrained condition prevails (Ic > 2.60) and excess pore pressures (∆ 0) develop. For undrained penetration, an effective stress limit plasticity solution has been developed for in terms of normalized CPTu parameters Q and Bq (Senneset et al. 1989; as presented in Figure 9-15, designated NTH for Norwegian Institute of Technology). In this graph, the solution for = 0 has been adopted; however, in the full theoretical formulation, it is possible to also interpret a paired set of and values (Mayne 2016).

181 Source: Paul Mayne Figure 9-15. Effective stress friction angle of clays from CPTu via NTH solution The rigorous NTH solution for = 0 and = 0° (i.e., constant volume) can be arranged to express normalized cone tip resistance (Q) in terms of pore pressure parameter ( ) and effective stress friction angle ( ): = tan 45° + 2 ∙ ( ∙ tan ) − 11 + 6 ∙ tan ∙ (1 + tan ) ∙ An extensive calibration of this approach has been made using results from field tests, mini-CPT in calibration chamber tests, and centrifuge clay deposits. For illustration, data from 105 clay sites where both CPTu soundings and triaxial (CIU and CAU) tests were conducted have been reviewed by Ouyang and Mayne (2018a). Figure 9-16 shows the statistical validity and verification of the NTH approach. While a direct expression for in the theoretical form is not possible, the value of effective friction angle for CPTu during undrained penetration in soft to firm clays may be obtained from the approximation: = 29.5° ∙ . ∙ 0.256 + 0.336 + ( ) Which is applicable over the following ranges: 0.1 < < 1.0 and 20° < < 45°.

182 Source: Ouyang and Mayne (2018a) Figure 9-16. Calibration of NTH solution with lab triaxial and in situ CPTu data from 105 clay sites 9.6.2 Effective Strength Parameters from Flat Dilatometer Tests A similar approach is available for the DMT, whereby two equations are available specifically for sands with drained loading and clays with undrained loading. For the case of drained loading, it can be taken that the DMT material index > 1, and the expression for the effective friction angle is given by either of the two equations shown in Figure 9-17. The hyperbolic formulation gives the following: = 20° + 10.04 + 0.06 where = ( − )⁄ = horizontal stress index

183 Source: Paul Mayne Figure 9-17. Effective friction angle of sands from DMT horizontal stress index For DMT in clays, a nexus has been established between the CPTu and DMT via spherical cavity expansion (SCE) theory. The equivalent normalized cone resistance for the DMT is , and the corresponding equivalent porewater parameter is that are given by the following: = (2.93 − 1.93 − )⁄ = ( − ) (2.93 − 1.93 − )⁄ These are used in the above equation (Section 9.6.2) to obtain the effective in clays and clayey silts: = 29.5° ∙ . ∙ 0.256 + 0.336 + ( ) Which is applicable over the following ranges: 0.1 < < 1.0 and 20° < < 45°. Data from 46 clays tested by DMT have been reviewed with their corresponding laboratory triaxial values. Figure 9-18 shows the comparison between calculated and measured values of (Ouyang and Mayne 2018b).

184 Source: Ouyang and Mayne (2018b) Figure 9-18. Calibration of NTH solution with lab triaxial and in situ DMT data from 46 clays 9.6.3 Effective Strength Parameters from Standard Penetration Test For SPTs in clean quartz-silica sands, results from triaxial compression tests on undisturbed sand samples indicate a trend with stress-normalized and energy-corrected N-values (Figure 9-19) expressed by the following equation: = 20° + 15.4 ( ) There is no known relationship for estimating in clays and silts from SPT N-values. Geoprofessionals should use laboratory tests or the empirical relationships presented above based on CPTu and DMT as an alternative.

185 Source: Paul Mayne Figure 9-19. Empirical relationship for effective friction angle of sands from stress-normalized SPT N60 value using data from undisturbed sampling techniques Total Stress Strength Parameters The undrained shear strength of fine-grained soils can be estimated via (i) the effective stress friction angle and the stress history (i.e., OCR) using CSSM principles; (ii) empirical correlations with CPT, DMT, or SPT; or (iii) direct measurements with VST, PMT, and other tests. 9.7.1 Undrained Shear Strength from Critical State Soil Mechanics For the DSS mode of failure, the undrained shear strength can be estimate from CSSM based on and OCR: , = ( 2⁄ ) ∙ ∙ where Λ = 1 − ⁄ = plastic strain potential Cs = swelling index Cc = virgin compression index

186 Because the ratio of 0.1 < ⁄ < 0.2 for many soils, the value of Λ is within the range: 0.8 ≤ Λ ≤ 0.9. Figure 9-20 shows a summary of normalized undrained shear strengths with OCR from several clays tested via DSS tests. For the triaxial compression mode of failure, the value of undrained strength is higher and calculated from the following: , = ( 2⁄ ) ∙ ( 2⁄ ) ∙ where = 6 sin (3 − sin )⁄ . For fissured clays, the above expressions should be reduced to one-half the calculated values to account for additional planes of weakness afforded by the presence of joints, discontinuities, and fissures. Source: Paul Mayne Figure 9-20. Normalized undrained shear strength ratio vs. OCR for clays tested in DSS mode 9.7.2 Undrained Shear Strength from Cone-Penetration Tests For the CPT, the most common approach links with (Lunne et al. 1997): = ⁄ where = cone bearing factor Mayne and Peuchen (2018) reviewed 407 high-quality CAU triaxial tests and field piezocone results from 62 different clays sorted into five groups: • Soft to firm onshore (blue) • Soft to firm offshore (green) • Sensitive (pink) • Overconsolidated (yellow) • Fissured (brown)

187 As shown in Figure 9-21, the cone factor decreases with according to the following: = 10.5 − 4.6 + 0.1 Source: Mayne and Peuchen (2018) Figure 9-21. Cone bearing factor Nkt for obtaining undrained shear strength in clays An alternate CPT-based method to evaluate in intact clays is to (i) evaluate the yield stress using the method described in Section 9.5.1 (ii) calculate the OCR, (iii) measure or estimate , (iv) assume Λ = 0.8, and (v) use the CSSM equations given in Section 9.7.1. 9.7.3 Undrained Shear Strength from Flat Dilatometer Tests The usual practice of evaluating from DMT is from an empirical equation often associated as a DSS mode of failure (Marchetti et al. 2006): = 0.22 (0.5 ) . where = ( − )⁄ = horizontal stress index An alternate DMT-based method to evaluate in intact clays is to (i) evaluate the yield stress using the method described in Section 9.5.2 (ii) calculate the OCR, (iii) measure or estimate , (iv) assume Λ = 0.8, and (v) use the CSSM equations given in Section 9.7.1. 9.7.4 Undrained Shear Strength from Standard Penetration Test For soft to firm intact clays and structured or sensitive clays, the dynamic energy of the SPT is inappropriate, and SPT should not be used to estimate . In the case of stiff to hard, insensitive clays, the SPT may be used to estimate an approximate value of the undrained shear strength. One relationship suggested is that given by Stroud and Butler (1975):

188 = where f1 = an empirical parameter that depends upon the geologic setting, plasticity, origin, and other aspects of the clay formation While f1 has been correlated with PI (in percent), results reported by Sowers (1979) indicate f1 increases with PI, while other studies of clays and tills by Stroud and Butler (1975) show that f1 decreases with PI (Figure 9-22). Most likely, a site-specific correlation is needed for a given clay in a particular geologic setting. Source: Paul Mayne Figure 9-22. Trends reported between undrained shear strength and SPT resistance 9.7.5 Undrained Shear Strength from Vane Shear Tests, Pressuremeter Tests, and Other Tests The undrained shear strength of clays and clayey silts can also be evaluated from VST and PMT as detailed by Schnaid (2009). The VST allows a direct in situ determination of the clay sensitivity. For very soft clays ( < 200 psf or 9.6 kPa), using full-flow penetrometers offers better resolution than most of the aforementioned tests because their design makes better use of the load cell range (Randolph 2004). Such tests include the T-bar and ball penetrometer (DeJong et al. 2010). Lateral Stress State The geostatic lateral stress state in the ground is represented by the coefficient = ⁄ . For special cases, the magnitude of can be measured directly in situ using the following: • Push-in spade cells or total stress cells • Self-boring PMT • Hydraulic fracturing • Iowa stepped blade 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0 10 20 30 40 50 60 70 80 SP T Pa ra m et er , f 1 (a tm ) Plasticity Index, PI (%) SPT-su Relationships Stroud & Butler 1975 Sowers 1979 - high plasticity Sowers 1979 - medium plasticity Sowers 1979 - low plasticity su = f1 · σatm · N60

189 • Paired sets of directional shear waves In lieu of direct measurement of , the value may be estimated from the relationship shown in Figure 9-23 and given by the following expression, which applies to soils that have been loaded-unloaded: = (1 − ʹ) ∙ ʹ ≤ where = (1 + ) (1 − ) ⁄ = Rankine passive stress coefficient Source: Paul Mayne Figure 9-23. General relationships between K0 and OCR in soils for loading-unloading Modulus The stiffness of soils can be represented by a variety of different parameters, depending upon the type of project and analytical model that is adopted. In geotechnical engineering, the most common parameters are the elastic moduli including Young's modulus (E), shear modulus (G), and constrained modulus (M). Other stiffness parameters used for specific applications are the resilient modulus ( ), subgrade reaction coefficient ( ), and CBR for pavement evaluations (Brown 1996), falling weight deflectometers (Newcomb and Birgisson 1999), and nonlinear moduli (Vardanega and Bolton 2013). From elastic theory, the relationships for G and M in terms of E are given as follows: = 2(1 + )

190 = (1 − )(1 + )(1 − 2 ) where ν = Poisson's ratio The stiffness of soils is highly nonlinear, beginning in the linear region and extending into intermediate strains to strains at peak strength. Moreover, in some cases, a softening after peak may occur in sensitive clays, structured soils, and dilative soils. Thus, it is not possible to assign a single value of modulus because the value will depend on the level of strain, or stress level, as well as effective confining stress, drainage conditions, and actual point on the stress-strain curve (Casey et al. 2016). For triaxial compression testing, Young's modulus (E) is determined as the slope of the applied deviator stress ( = − ) vs. axial strain ( ). As shown by Figure 9-24, the type of E can be further defined by loading conditions and specific point on the stress-strain curve, including (i) initial value in linear range ( ); (ii) secant value: = ⁄ ; (iii) tangent modulus: = Δ Δ⁄ ; and (iv) unload-reload modulus, . Source: Paul Mayne Figure 9-24. Representative stress-strain-strength curve of soil in triaxial compression mode Values of Young’s modulus applicable to drained and undrained conditions are denoted and , respectively. Similar notation is used for G and M. Poisson’s ratio for drained conditions ( ) is often assumed to approximately equal 0.2; for undrained conditions, = 0.5. 9.9.1 Elastic Modulus from Shear Wave Velocity Shear and compression wave velocities can be used to directly measure initial tangent moduli based on the theory of elasticity: = ∙

191 = ∙ = 2 (1 + ) The values of or can be obtained from undisturbed soil samples in the laboratory using resonant column tests (Section 8.9.1), bender elements, or special triaxial apparatuses outfitted with local strain measurements. Better yet, in situ tests are more reliable because they are unaffected by sample disturbance, stress relief, and small specimen size effects. In situ measurement of seismic velocities can be made using the surface and borehole seismic methods described in Section 4.3.1 and 4.4.1, respectively. The initial tangent shear and Young's modulus can be used directly when strains are small: < 10-6 (e.g., dynamically loaded foundations, site amplification for low-intensity ground motions); however, in many cases, a modulus reduction factor (MRF) must be used to adjust the value of shear or Young’s modulus to the appropriate level of strain (ε or γ) or mobilized stress (q/qmax or τ/τmax). For cyclic loading, the use of resonant column tests can be used to obtain the shear modulus reduction curve as discussed in Section 8.9.1. For monotonic (i.e., static) loading, torsional shear tests and special triaxial tests with local strain sensors provide the MRF curves for each soil. For empirical estimates, MRF values for cyclic loading may found from well-known modulus reduction relationships (e.g. Vucetic and Dobry 1991, Darendeli 2001). A recent method for MRF curves for both monotonic and cyclic loading of clays is presented by Vardanega and Bolton (2013). For first-time monotonic loading of soils, the MRF trend in Figure 9-25 is shown in terms of mobilized stress, which is the reciprocal of the factor of safety: 1 = = ⁄⁄⁄ . The data are derived from both undrained and drained resonant column-torsional shear tests and specially instrumented triaxial tests conducted on both sands and clays. An algorithm that expresses the trend is given by the following: = 1 − ( ⁄ ) = 1 − ( )⁄ = 1 − (1 )⁄ where g = fitting parameter The value of for triaxial compression is given by the expressions shown in Figure 9-25 for either undrained or drained loading. For DSS conditions, the value of is taken as either the undrained ( = ) or drained ( = + ∙ tan ). For an initial estimate, the exponent g generally takes a value of approximately 0.3 for uncemented sands and inorganic clays of low sensitivity. Thus, the relevant value of G or E for a particular problem can be obtained from the following: = ∙ = ∙ For an FS = 2, an approximate value of MRF = 0.30 would be applicable. Otherwise, it is possible to generate a continuous curve using the expression above. For instance, a complete stress-strain curve can be developed by calculating the axial strains for triaxial compression: = ⁄ , or alternatively, shear stress vs. shear strain for simple shear mode: = ⁄ , where each pair of q-ε or τ−γ values are associated with their respective FS.

192 Source: Mayne (2007b) Figure 9-25. Modulus reduction factor of sands and clays in drained and undrained loading expressed in terms of mobilized strength 9.9.2 Elastic Modulus from Cone Penetration Test With SCPTu, the shear wave velocity is measured directly and can be used to calculate Gmax or Emax using the expressions in Section 9.9.1. If only CPT or CPTu data are available, the in situ shear wave velocity can be estimated from the penetrometer readings, as summarized by Wair et al. (2012). They recommend using the average of the following three empirical expressions, applicable to all soil types: (m/s) = 118.8 ∙ log ( ) + 18.5 (m/s) = 2.62 ∙ . ∙ . ∙ . ∙ (m/s) = (10 . ∙ . ) ∙ ( − ) )⁄ . where , , and are input in kPa, depth D in meters ASF = age scaling factor (= 0.92 for Holocene and 1.12 for Pleistocene deposits) If a quick estimate of the drained Young’s modulus from CPT is desired, a rough approximation for clays, silts, and sands may be taken as (Mayne 2007b): = 5 ∙ ( − )

193 This relationship is corroborated by an independent CPT-DMT study by Robertson (2009b) shown in Figure 9-26 and approximated by the following: ≈ 5 ∙ ( − ) Source: Robertson (2009b) Figure 9-26. Dilatometer modulus vs. net cone resistance for different soils 9.9.3 Elastic Modulus from Flat Dilatometer Tests With seismic DMT, the shear wave velocity is measured directly and can be used to calculate Gmax or Emax using the expressions in Section 9.9.1. For the standard DMT, a value of constrained modulus is obtained from the dilatometer modulus ( ) and material index ( ) using the formula given in Table 9-3 with the relationship (Marchetti et al. 2006): = ∙ Table 9-3. Relationships for constrained modulus from DMTs in various soil types Criteria Relationship for Factor RM = M'/ED Notes If ID < 0.6 RM = 0.14 + 2.36 log KD Clay soils If ID > 3 RM = 0.50 + 2.0 log KD Clean (quartz) sands If 0.6 < ID < 3 RM = RM0+ (2.5-RM0) log KD where RM0 = 0.14+0.15(ID-0.6) Silts to silty sands If KD > 10 RM = 0.32 + 2.18 log KD High values If RM < 0.85 Set RM = 0.85 Minimum Source: after Marchetti et al. (2006) Notes: (a) ED = 34.7·(p1-p0) = dilatometer modulus

194 (b) ID = (p1-p0)/(p0-u0) = DMT material index (c) KD = (p0-u0)/σvo' = horizontal stress index If an estimate of the small-strain shear modulus (Gmax) is needed from DMT readings in soils, the expressions in Table 9-4 can be used. Table 9-4. Expressions for estimating Gmax from DMT readings in various soil types Soil Type Range of Material Index, ID Expression for Small-Strain Shear Modulus: Gmax Clays ID < 0.6 Gmax = 26.2 · MDMT · KD -1.007 Silts 0.6 < ID < 1.8 Gmax = 15.7 · MDMT · KD -0.921 Sands ID > 1.8 Gmax = 4.56 · MDMT · KD -0.797 Source: Marchetti et al. (2008), Amoroso (2014) 9.9.4 Elastic Modulus from Standard Penetration Test It is viable to measure Vs during SPT by using an uphole geophysical method (Giacheti et al. 2013). Therefore, with the seismic SPT, one can use the procedures given in Section 9.9.1 to obtain either Gmax or Emax. In the case of conventional SPTs, the in situ Vs can be estimated by using the N60 as shown in Figure 9-27 or by using one of the available correlations reviewed by Wair et al. (2012). Source: data from Imai and Tonouchi (1982) Figure 9-27. Estimate for Vs from SPT For a direct approach to estimating moduli in soils, N60 should be used in local site-specific correlations for the particular geology. This may require calibrations with reference moduli obtained from a variety of

195 sources, such as (i) back-calculated values of E' from field performance of foundations, (ii) PLTs, (iii) pressuremeter data, (iv) DMTs, and (v) laboratory triaxial and consolidometer results. For instance, Mayne and Frost (1988) developed a correlation between the dilatometer modulus and SPT N60 value in the Piedmont and Blue Ridge geologies that was verified with back-calculated E' values from foundation settlement data on full-scale buildings. The derived relationship has been updated and is presented in Figure 9-28. Source: Paul Mayne Figure 9-28. Geologic-specific relationship between equivalent elastic modulus and energy- corrected SPT N60 from DMTs and foundation performance Rigidity Index The rigidity index is defined as the ratio of the shear modulus to shear strength ( = ⁄ ) and can be used to calculate undrained distortional displacements of shallow foundations, pile bearing capacity, and solutions for pore pressure dissipation that are based in cavity expansion, strain path method, and finite elements. The undrained rigidity index ( = ⁄ ) from the CE-CSSM solution is given by the following: = ( − )( − ) ∙ 1.5 + 2.925 − 2.925 where Mc = 6 ∙ sin ʹ (3 − sin ʹ⁄ ) The value of the first fractional term within the brackets can be found over the depth range of interest by plotting = ( − ) vs. = ( − ). The relationship for is depicted in Figure 9-29 in terms of the ratio ⁄ for various values of .

196 Source: Paul Mayne Figure 9-29. Rigidity index from spherical cavity expansion (SCE-CSSM) in terms of ϕ’ and CPT resistance An alternative means of evaluating the magnitude of in clays is via a method developed from SCPTu results. The value of rigidity index at 50 percent mobilized strength ( ) can be calculated from (Krage et al. 2014): = 1.81 ( ) . ( ) . where , , and are in consistent units is dimensionless A third method for estimating comes from an empirical approach developed from triaxial test data and related to the OCR and PI (Keaveny and Mitchell 1986, Mayne 2007b): = (137 − )/231 + 1 + ( − 1) . /26 . Flow Parameters Flow characteristics of soils are represented by their hydraulic conductivity (K) and coefficient of consolidation (cv). These two parameters are interrelated by the following consolidation theory: = ∙ ⁄ As described in Chapter 8, can be measured on undisturbed soil specimens using 1D consolidation or triaxial tests. The hydraulic conductivity (K) can be measured using flexible-wall or rigid, compaction- mold permeameters. In the field, the coefficient of consolidation is commonly obtained using piezocone dissipation tests. A dissipation test is also available for the DMT. Hydraulic conductivity can be measured using pumping or 0 100 200 300 400 500 1.0 1.5 2.0 2.5 Ri gi di ty In de x, I R = G/ s u Ratio (qt - σvo)/(qt - u2) φ' = 20° 25° 30° 35°40°45°

197 slug tests as described in Chapter 7, or using push-in piezometers or piezocone penetration tests with dissipation measurements (Mayne et al. 2002). 9.11.1 Coefficient of Consolidation from Piezocone Dissipation Tests The in situ is assessed using field dissipation tests by monitoring the dissipation of excess pore pressure with time using push-in piezometers or CPTù. In the case of clean sands, the dissipation is essentially immediate. An example of dissipation in soft to firm clay is depicted in Figure 9-30. During CPT penetration at 20 mm/s, excess pore pressures are seen to be approximately 4 to 5 times hydrostatic. After a waiting period of some 2,000 seconds (approximately 33 minutes), the measured excess pore pressure has not returned to equilibrium conditions. The degree of consolidation (U) can be represented by the relative change in excess pore pressures: − 1 − Δ Δ⁄ , where Δ represents the measured Δ = ( − ) at initial time (i.e., during penetration). Source: Paul Mayne Figure 9-30. Representative monotonic dissipation record from CPTu2 in Mud Island For estimating , an analytical, numerical, or theoretical solution must be adopted. The hybrid spherical cavity expansion-critical state soil mechanics (SCE-CSSM) solution by Burns and Mayne (2002) indicates the following: = ∙ ∙ . where = dimensionless time factor depending on degree of consolidation (U) = radius of the probe = ⁄ = soil rigidity index

198 t = measured time to reach the selected U The respective radii for 10-cm2 and 15-cm2 cone penetrometers are ac = 1.78 cm and ac = 2.20 cm. For a monotonic response, the various time factors ( ) from SCE-CSSM are presented in Figure 9-31. It is common in geotechnical practice to use a value for 50 percent consolidation (U = 50%), and thus the appropriate time factor is = 0.030. The corresponding measured time to reach this value ( ) is defined in Figure 9-31 for a monotonic pore pressure response. Source: Paul Mayne Figure 9-31. Dissipation time factors from SCE-CSSM solution at different degrees of consolidation The porewater response of driven piles, push-in piezometers, and cone penetrometers can also display a dilatory behavior as shown in Figure 9-32. In this situation, the porewater readings initially increase in magnitude and eventually reach a peak, thereafter decreasing with time until hydrostatic pore pressures are measured. For dilatory pore pressures, the initial value can be corrected by using a square root plot (Madmoodzadeh and Randolph 2014), as illustrated by Figure 9-33. This allows for the proper selection of t50 and use of the same simple analytical solution given above.

199 Source: Paul Mayne Figure 9-32. Definitions of monotonic vs. dilatory type for pore pressure response Source: Paul Mayne Figure 9-33. Correction of dilatory dissipation tests using square root time plots to get t50 9.11.2 Coefficient of Consolidation from Dilatometer Dissipation Tests For the DMT, dissipation of the A-reading with time may be recorded at selected test depths (Marchetti et al. 2006). The solution is given by the following: cv (cm2/s) = 7/tflex where = time (seconds) corresponding to the inflection point in measured A-readings 0 1 2 3 4 1 10 100 1000 10000 Po re W at er P re ss ur e, u 2 (ts f) Time (s) Mud Island CPTu Dissipations, Memphis, TN Depth = 23.3 feet Depth = 36.4 feet Monotonic Response Dilatory Response

200 An example of the dissipation of DMT A-readings is shown in Figure 9-34 (Marchetti and Totani 1989), illustrating the selection of the = at the inflection point of the curve. A more theoretical approach has been proposed by Kim and Paik (2006). Source: data from Marchetti and Totani (1989) Figure 9-34. Dissipations from DMT A-reading with time 9.11.3 Hydraulic Conductivity from Piezocone Dissipation Tests An approximate means to estimate the hydraulic conductivity (K) from piezocone dissipation tests uses the characteristic time (t50) reported in seconds as shown in Figure 9-35. This method is based on monotonic-type responses recorded by Parez and Fauriel (1988). The approximation shown by the red- dashed line can be expressed as follows: (cm/s) ≈ 1251 ∙ ( ) .

201 Source: relationship from Parez and Fauriel (1988) Figure 9-35. Interpreted coefficient of permeability from monotonic t50 dissipations in soils 9.11.4 Hydraulic Conductivity Estimated from CPT Material Index The CPT material index ( ) has been empirically correlated to the hydraulic conductivity (Lunne et al. 1997). For CPT SBTs in Zones 2 through 7, Robertson and Cabal (2015) suggest a two-part approximation for these values. A simpler, single equation is sufficient (Figure 9-36), which can be expressed as follows: (m/s) = (1.0⁄ ) Source: Paul Mayne Figure 9-36. Coefficient of permeability expression from CPT material index in soils 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 0.1 1 10 100 1000 10000 Hy dr au lic C on du ct iv ity , k (c m /s ) Measured Dissipation Time, t50 (sec) Sand and Gravel Sand Silty Sand to Sandy Silt Silt Clay u2 ≈ 1251 · ( ) .

202 Special Considerations Under certain circumstances, the interpretation of laboratory and field tests will require special attention, especially for soils with complex behavior and constituency, including organic clays, sensitive fine-grained soils, collapsible geomaterials, lateritic and residual soils, loess, and other types of problematic soils. For fissured clays that have experienced landsliding and undergone slope failure, the use of residual strength parameters (ϕr' and cr' = 0) will be appropriate. Details on the evaluation of drained residual strength parameters are given by Stark et al. (2005).

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