Correlations¶

Olson¶

Most of the values of total unit weight (TUW, a.k.a. moist unit weight), \(\gamma_t\), in Prof. Roy Olson’s database were assumed. If water content, \(w\), was known, it was used to calculate \(\gamma_t\), with an assumed specific gravity, \(G_s\), of 2.72. The equation for \(\gamma_t\) in this case was:

\[\gamma_t = \bigg( \dfrac{1 + w}{1 + w G_s} \bigg) \; G_s \gamma_w\]

Prof. Olson used cases in which water contents were measured to calculate total unit weights for all soils and then performed correlations of those values of total unit weight with whatever other properties were available, meaning undrained shear strength, \(s_u\), for cohesive soils, and SPT-N values for all soils, and used these other properties to estimate total unit weight for cases in which water contents were not defined. These correlations were often bad but at least they gave a consistent basis for estimating \(\gamma_t\). The correlations are shown below for cohesive and cohesionless soils.

Cohesive Soils

Values for undrained shear strength may come from the following:

Field vane shearing strength (\(s_{u.FV}\))
Shearing strength from Torvane, penetrometer, etc (\(s_{u.MS}\))
Shearing strength from triaxial tests (\(s_{u.QT}\))
Unconfined shearing strength (\(s_{u.QU}\))

Priority for choosing a value for \(s_u\) if multiple are available is:

\[s_{u.QT} > s_{u.QU} > s_{u.MS} > s_{u.FV}\]

But use as:

\[\begin{split}s_u = \begin{cases} s_{u.QT} \\ 1.2 \times s_{u.QU} \\ 1.2 \times s_{u.MS} \\ 0.7 \times s_{u.FV} \end{cases}\end{split}\]

For clay (CLAY):

\[\begin{split}\gamma_t = \begin{cases} 113.9 + 9.276 \ln{s_u} \textrm{ in pcf} & \textrm{if } s_u > 0 \textrm{ in ksf} \\ 107.5 + 5.116 \ln{N} \textrm{ in pcf} & \textrm{if } s_u \textrm{ undef. and } N > 0 \\ \textrm{N/A} & \textrm{if both } s_u \textrm{ and } N \textrm{ are undefined} \end{cases}\end{split}\]

For silt/clay (SICL), clay/silt (CLSI) and sand/clay (SACL):

\[\begin{split}\gamma_t = \begin{cases} 113 + 22 s_u \textrm{ in pcf} & \textrm{if } 0.5 < s_u < 1.5 \textrm{ in ksf} \\ 113 + 9.276 \ln{N} \textrm{ in pcf} & \textrm{if } s_u > 0 \\ \textrm{N/A} & \textrm{if both } s_u \textrm{ and } N \textrm{ are undefined} \end{cases}\end{split}\]

Cohesionless Soils

For sand (SAND):

\[\gamma_t = 126 \textrm{ pcf}\]

For silt/sand (SISA), sand/silt (SASI) and silt (SILT):

\[\gamma_t = 125 + 0.15 N \textrm{ pcf} < 135 \textrm{ pcf}\]

For cobble/gravel (CBGV), gravel (GRAV), sand/gravel (SAGV), gravel/sand (GVSA) and cobbles (COBB):

\[\gamma_t = 132 \textrm{ pcf}\]

Olson Soil Classification to USCS

Table 2 Olson Soil Classification to Unified Soil Classification System (USCS)¶
Olson				USCS
Symbol	Description	Category	Count [1]	Symbol	Description
`CLAY`	Clay	Cohesive	2305	`CL`	Inorganic clays of low to medium plasticity, gravelly clays, sandy clays, silty clays, lean clays
`CLSA`	Clay/Sand	Cohesive	3	`SC`	Clayey sands, sand-clay mixtures
`CLSI`	Clay/Silt	Cohesive	20	`ML`	Inorganic silts, and very fine sands, rock flour, silty or clayey fine sands or clayey silts with slight plasticity
`GRAV`	Gravel	Coarse	49	`GW` or `GP`	Well/Poorly-graded gravels, gravel-sand mixtures, little or no fines
`GVSA`	Gravel/Sand	Coarse	45	`GW` or `GP`	Well/Poorly-graded gravels, gravel-sand mixtures, little or no fines
`MISA`	Micaceous Sand	Cohesionless	15	`MH`	Inorganic silts, micaceous or diatomaceous fine sandy or silty soils, elastic silts
`MISS`	Micaceous Sand/Silt	Cohesionless	6	`MH`	Inorganic silts, micaceous or diatomaceous fine sandy or silty soils, elastic silts
`PEAT`	Peat	Cohesive	1	`PT`	Peat and other highly organic soils
`SACL`	Sand/Clay	Cohesive	14	`SC`	Clayey sands, sand-clay mixtures
`SAGV`	Sand/Gravel	Coarse	67	`GW` or `GP`	Well/Poorly-graded gravels, gravel-sand mixtures, little or no fines
`SAND`	Sand	Cohesionless	1780	`SW` or `SP`	Well/Poorly-graded sands, gravelly sands, little or no fines
`SASI`	Sand/Silt	Cohesionless	319	`SM`	Silty sands, sand-silt mixtures
`SHEL`		Coarse	2	`GW` or `GP`	Well/Poorly-graded gravels, gravel-sand mixtures, little or no fines
`SICL`	Silt/Clay	Cohesive	39	`ML`	Inorganic silts, and very fine sands, rock flour, silty or clayey fine sands or clayey silts with slight plasticity
`SILT`	Silt	Cohesionless	198	`MH`	Inorganic silts, micaceous or diatomaceous fine sandy or silty soils, elastic silts
`SISA`	Silt/Sand	Cohesionless	397	`SM`	Silty sands, sand-silt mixtures

Hunt¶

Roy Hunt on his 1984 book, the “Geotechnical Engineering Investigation Manual”, offers typical values for common properties including relative density, \(D_r\), dry density, \(\gamma_{dry}\), void ratio, \(e\), and strength, \(\phi\), as related to gradation and SPT-N. For cohesionless soils these typical values are presented in Table 3.

For cohesive soils, common properties, including relationships between consistency, unconfined compressive strength, \(q_u\), saturated weight, \(\gamma_{sat}\), and SPT-N are given on Table 4. Furthermore, typical properties of cohesive materials classified by geologic origin, including density, \(\gamma_{dry}\), natural moisture contents, \(w\), plasticity indices, \(PI\) and strength parameters, \(s_u, c, \phi\), are given on Table 5.

Table 3 Common Properties of Cohesionless Soils (after Hunt 1984)¶
Material	Compactness	\(D_r\), %	N [2]	\(\gamma_{dry}\) [3], lbf/ft³	Void Ratio, \(e\)	Strength [4], \(\phi\)
GW: well-graded gravels, gravel- sand mixtures	Dense	75	90	138	0.22	40
	Medium dense	50	55	130	0.28	36
	Loose	25	< 28	123	0.36	32
GP: poorly graded gravels, gravel- sand mixtures	Dense	75	70	127	0.33	38
	Medium dense	50	50	120	0.39	35
	Loose	25	< 20	114	0.47	32
SW: well-graded sands, gravelly sands	Dense	75	65	118	0.43	37
	Medium dense	50	35	112	0.49	34
	Loose	25	< 15	106	0.57	30
SP: poorly graded sands, gravelly sands	Dense	75	50	110	0.52	36
	Medium dense	50	30	104	0.60	33
	Loose	25	< 10	99	0.65	29
SM: silty sands	Dense	75	45	103	0.62	35
	Medium dense	50	25	97	0.74	32
	Loose	25	< 8	93	0.80	29
ML: inorganic silts, very fine sands	Dense	75	35	93	0.80	33
	Medium dense	50	20	88	0.90	31
	Loose	25	< 4	84	1.00	27

Table 4 Common Properties of Cohesive Soils (after Hunt 1984)¶
Consistency	N	Hand test	\(\gamma_{sat}\) [5], lbf/ft³	Strength [6], \(q_u\), kip/ft²
Hard	> 30	Difficult to indent	> 140	> 8.2
Very stiff	15 - 30	Indented by thumbnail	130 - 140	4.1 - 8.2
Stiff	8 - 15	Indented by thumb	120 - 130	2.0 - 4.1
Medium (firm)	4 - 8	Molded by strong pressure	110 - 120	1.0 - 2.0
Soft	2 - 4	Molded by slight pressure	100 - 110	0.5 - 1.0
Very soft	< 2	Extrudes between fingers	90 - 100	0.0 - 0.5

Table 5 Typical Properties of Formations of Cohesive Materials (after Hunt 1984)¶
Material	Type	Location	\(\gamma_{dry}\), lbf/ft³	\(w\), %	LI, %	PI, %	\(s_u\), kip/ft²	\(\bar{c}\), kip/ft²	\(\bar{\phi}\)	Remarks
CLAY SHALES (WEATHERED)
Carlisle (Cret.)	CH	Nebraska	92	18				1.024	45	\(\phi\) extremely variable
Bearpaw (Cret.)	CH	Montana	90	32	130	90		0.717	15
Pierre (Cret.)	CH	South Dakota	92	28				1.843	12
Cucaracha (Cret.)	CH	Panama Canal		12	80	45				\(\phi_r = 10^\circ\)
Pepper (Cret.)	CH	Waco, Texas		17	80	58		0.819	17	\(\phi_r = 7^\circ\)
Bear Paw (Cret.)	CH	Saskatchewan		32	115	92		0.819	20	\(\phi_r = 8^\circ\)
Modelo (Tert.)	CH	Los Angeles	90	29	66	31		3.277	22	Intact specimen
Modelo (Tert.)	CH	Los Angeles	90	29	66	31		0.655	27	Shear zone
Martinez (Tert.)	CH	Los Angeles	104	22	62	38		0.512	26	Shear zone
(Eocene)	CH	Menlo Park, Calif.	103	30	60	50		Free swell 100%; P = 20.5 kip/ft²
RESIDUAL SOILS
Gneiss	CL	Brazil; buried	81	38	40	16		0.000	40	\(e_0 = 1.23\)
Gneiss	ML	Brazil; slopes	84	22	40	8		0.799	19	\(c, \phi\): unsoaked
Gneiss	ML	Brazil; slopes	84		40	8		0.573	21	\(c, \phi\): unsoaked
COLLUVIUM
From shales	CL	West Virginia		28	48	25		0.573	28	\(\phi_r = 16^\circ\)
From gneiss	CL	Brazil	69	26	40	16		0.410	31	\(\phi_r = 12^\circ\)
ALLUVIUM
Black swamp	OH	Louisiana	36	140	120	85	0.307
Black swamp	OH	Louisiana	62	60	85	50	0.205
Black swamp	MH	Georgia	60	54	61	22	0.614			\(e_0 = 1.7\)
Lacustrine	CL	Great Salt Lake	49	50	45	20	0.696
Lacustrine	CL	Canada	69	62	33	15	0.512
Lacustrine (volcanic)	CH	Mexico City	18	300	410	260	0.819			\(e_0 = 7\), \(S_t = 13\)
Estuarine	CH	Thames River	49	90	115	85	0.307
Estuarine	CH	Lake Maricaibo		65	73	50	0.512
Estuarine	CH	Bangkok		130	118	75	0.102
Estuarine	MH	Maine		80	60	30	0.410
MARINE SOILS (OTHER THAN ESTUARINE)
Offshore	MH	Santa Barbara, Calif.	52	80	83	44	0.307			\(e_0 = 2.28\)
Offshore	CH	New Jersey		65	95	60	1.331
Offshore	CH	San Diego	36	125	111	64	0.205			Depth = 6.56 ft
Offshore	CH	Gulf of Maine	36	163	124	78	0.102
Coastal Plain	CH	Texas (Beaumont)	87	29	81	55	2.048	0.410	16	\(\phi_r = 14^\circ\), \(e_0 = 0.8\)
Coastal Plain	CH	London	100	25	80	55	4.096
LOESS
Silty	ML	Nebraska-Kansas	77	9	30	8		1.229	32	Natural \(w\) %
Silty	ML	Nebraska-Kansas	77		30	8		0.000	23	Prewetted
Clayey	CL	Nebraska-Kansas	78	9	37	17		4.096	30	Natural \(w\) %
GLACIAL SOILS
Till	CL	Chicago	132	23	37	21	7.169
Lacustrine (varved)	CL	Chicago	106	22	30	15	2.048			\(e_0 = 0.6\) (OC)
Lacustrine (varved)	CL	Chicago		24	30	13	0.205			\(e_0 = 1.2\) (NC)
Lacustrine (varved)	CH	Chicago	74	50	54	30	0.205
Lacustrine (varved)	CH	Ohio	60	46	58	31	1.229			\(S_t = 4\)
Lacustrine (varved)	CH	Detroit	75	46	55	30	1.639			\(e_0 = 1.3\) (clay)
Lacustrine (varved)	CH	New York City		46	62	34	2.048			\(e_0 = 1.25\) (clay)
Lacustrine (varved)	CL	Boston	84	38	50	26	1.639			\(S_t = 3\)
Lacustrine (varved)	CH	Seattle		30	55	22			30	\(\phi_r = 13^\circ\)
Marine [7]	CH	Canada-Leda clay	56	80	60	32	1.024			\(S_t = 128\)
Marine [7]	CL	Norway	84	40	38	15	0.266			\(S_t = 7\)
Marine [7]	CL	Norway	81	43	28	15	0.102			\(S_t = 75\)

[1]	Count in Olson ‘APC’ and ‘CT’ databases.

[2]	\(N\) is blows per foot of penetration in the SPT. Adjustments for gradation are after Burmister (1962).

[3]	Density given is for \(G_s = 2.65\) (quartz grains)

[4]	Friction angle \(\phi\) depends on mineral type, normal stress, and grain angularity as well as \(D_r\) and gradation.

[5]	\(\gamma_{sat} = \gamma_{dry} + \gamma_w \Big( \dfrac{e}{1+e} \Big)\)

[6]

Unconfined compressive strength, \(q_u\), is usually taken as equal to twice the cohesion, \(c\), or the undrained shear strength, \(s_u\). For the drained strength condition, most clays also have the additional strength parameter, \(\phi\), although for most normally consolidated clays, \(c = 0\). Typical values for \(s_u\) and drained strength parameters are given in Table 5.

[7]	(1, 2, 3) Marine clays strongly leached.

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Correlations¶

Olson¶

Hunt¶