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18 One can see that the lower the effective stress, as in low-height dams or shallow failure surfaces, the “apparent” cohesion intercepts should be very small. Using high cohesion in low-height dams is rarely justifiable, is very influential to the analysis results, and results in higher calculated factors of safety that are not defendable. A non-linear envelop may be more appropriate in these cases. Typical factors affecting values of φ’ for coarse-grained soils include density, confining pressure, angularity, and gradation. Values of φ’ increase as density increases, confining pressures decrease, particle angularity increases, and the soil gradation becomes broader (a wider range of particle sizes are included). Laboratory tests used to measure values of φ’ for coarse-grained soils include the CD or CU’ triaxial shear test and the DS test (this test is best suited for finer- grained sands). It is difficult, however, to obtain undisturbed granular samples in the field or reconstitute the structure of natural deposits. Laboratory tests are often used to estimate φ’ for coarse-grained soils that will be placed during construction, such as embankment soils. Results from the laboratory tests should be checked against expected values based on gradation, relative density, and/or blow count in an effort to identify any obvious anomaly(ies). The presence of large particles (e.g., scalped samples or rockfill) may make laboratory test results misleading or impractical, and therefore not often warranted. Results of field tests including the Standard Penetration Test (SPT), Cone Penetrometer Test (CPT), and shear wave velocity measurements are more commonly used to estimate values of φ’ for in-place, coarse-grained soils through the application of empirical correlations. Values of φ’ for in-place coarse- grained soils can also be estimated using empirical correlations to relative density and confining pressure, which are easier to measure directly than shear strength. A few of the more common strength correlations are presented below. These correlations, including others, are further described in reference [2], which is one of the more comprehensive references for shear strength characterization. Figures 3 and 4 relate values of φ’ to overburden pressure and SPT blow count and CPT cone resistance, respectively. Relationships between φ’, relative density, and SPT blow count or CPT cone resistance are summarized in Tables 1 and 2. While these tables are easy to use, they do not take into account the effect of confining pressure. Indirect correlations to relative density through SPT blow count or CPT cone resistance and overburden stress are shown in Figures 5 and 6. Figure 3: Relationship among SPT blow count, overburden pressure, and ’ for sands Reference: Duncan, Wright, and Brandon (2014)