Soil mechanics a[1].ppt

Basic Definitions and Terminology

• Soil is generally a three phase material• Contains solid particles and voids• Voids can contain liquid and gas phases

Solid

Water

Air Vs

Vw

Va

• Soil is generally a three phase material• Contains solid particles and voids• Voids can contain liquid and gas phases

Solid

Water

Air Vs

Vw

Va

• Soil is generally a three phase material• Contains solid particles and voids• Voids can contain liquid and gas phases

Solid

Water

Air

Phase Volume Mass Weight

Air Va 0 0

Water Vw Mw Ww

Solid Vs Ms Ws

Vs

Vw

Va

Units

• Length metres• Mass tonnes (1 tonne = 103 kg)• Density t/m3

• Weight kilonewtons (kN)• Stress kilopascals (kPa) 1 kPa= 1 kN/m2

• Unit weight kN/m3

• Accuracy Density of water, w = 1 t/m3

Stress/Strength to 0.1 kPa

Weight and Unit weight

• Force due to mass (weight) more important than mass• W = M g

• Unit weight

Weight and Unit weight

• Force due to mass (weight) more important than mass• W = M g

• Unit weight

= g

Weight and Unit weight

• Force due to mass (weight) more important than mass• W = M g

• Unit weight

= g

vz v = g z

v = z

Specific Gravity

• Gs 2.65 for most soils

• Gs is useful because it enables the volume of solid particles to be calculated from mass or weight

GD e n s i t y o f M a t e r i a l

D e n s i t y o f W a t e r w

GU n i t W e i g h t o f M a t e r i a l

U n i t W e i g h t o f W a t e r w

This is defined by

Specific Gravity

• Gs 2.65 for most soils

• Gs is useful because it enables the volume of solid particles to be calculated from mass or weight

GD e n s i t y o f M a t e r i a l

D e n s i t y o f W a t e r w

GU n i t W e i g h t o f M a t e r i a l

U n i t W e i g h t o f W a t e r w

This is defined by

VM M

G

W W

Gs

s

s

s

s w

s

s

s

s w

Voids ratio• It is not the actual volumes that are important but rather the

ratios between the volumes of the different phases. This is described by the voids ratio, e, or porosity, n, and the degree of saturation, S.

Voids ratio• It is not the actual volumes that are important but rather the

ratios between the volumes of the different phases. This is described by the voids ratio, e, or porosity, n, and the degree of saturation, S.

• The voids ratio is defined as

Voids ratio• It is not the actual volumes that are important but rather the

ratios between the volumes of the different phases. This is described by the voids ratio, e, or porosity, n, and the degree of saturation, S.

• The voids ratio is defined as

• and the porosity as

Voids ratio• It is not the actual volumes that are important but rather the

ratios between the volumes of the different phases. This is described by the voids ratio, e, or porosity, n, and the degree of saturation, S.

• The voids ratio is defined as

• and the porosity as

The relation between these quantities can be simply determined as follows

Vs = V - Vv = (1 - n) V

Voids ratio• It is not the actual volumes that are important but rather the

ratios between the volumes of the different phases. This is described by the voids ratio, e, or porosity, n, and the degree of saturation, S.

• The voids ratio is defined as

• and the porosity as

The relation between these quantities can be simply determined as follows

Vs = V - Vv = (1 - n) V

Hence

Degree of Saturation• The degree of saturation, S, has an important influence on soil

behaviour• It is defined as

Degree of Saturation• The degree of saturation, S, has an important influence on soil

behaviour• It is defined as

• The phase volumes may now be expressed in terms of e, S and Vs

• Vw = e S Vs Va = Vv - Vw = e Vs (1 - S)

Degree of Saturation• The degree of saturation, S, has an important influence on soil

behaviour• It is defined as

• The phase volumes may now be expressed in terms of e, S and Vs

• Vw = e S Vs Va = Vv - Vw = e Vs (1 - S)

Assuming Vs = 1 m3, the following table can be produced

Phase Volume Mass Weight

Air e (1 - S) 0 0

Water e S e S w e S w

Solid 1 G s w G s w

Unit Weights

• The bulk unit weight

Unit Weights

• The bulk unit weight

• The saturated unit weight (S = 1)

Unit Weights

• The bulk unit weight

• The saturated unit weight (S = 1)

• The dry unit weight (S = 0)

Unit Weights

• The bulk unit weight

• The saturated unit weight (S = 1)

• The dry unit weight (S = 0)

• The submerged unit weight

Moisture Content

• The moisture content, m, is defined as

Moisture Content

• The moisture content, m, is defined as

In terms of e, S, Gs and w

Ww = wVw = we S Vs

Ws = s Vs = w Gs Vs

Moisture Content

• The moisture content, m, is defined as

In terms of e, S, Gs and w

Ww = wVw = we S Vs

Ws = s Vs = w Gs Vs

hence

Example 1

Phase Trimmings Mass

(g)

Sample Mass, M

(g)

Sample Weight, Mg

(kN)

Total 55 290 2845 10-6

Solid 45 237.3 2327.9 10-6

Water 10 52.7 517 10-6

• Distribution by mass and weight

Example 1

Phase Trimmings Mass

(g)

Sample Mass, M

(g)

Sample Weight, Mg

(kN)

Total 55 290 2845 10-6

Solid 45 237.3 2327.9 10-6

Water 10 52.7 517 10-6

• Distribution by mass and weight

• Distribution by volume (assume Gs = 2.65)

Total Volume V = r2 l

Example 1

Phase Trimmings Mass

(g)

Sample Mass, M

(g)

Sample Weight, Mg

(kN)

Total 55 290 2845 10-6

Solid 45 237.3 2327.9 10-6

Water 10 52.7 517 10-6

• Distribution by mass and weight

• Distribution by volume (assume Gs = 2.65)

Total Volume V = r2 l

Water Volume

Example 1

Phase Trimmings Mass

(g)

Sample Mass, M

(g)

Sample Weight, Mg

(kN)

Total 55 290 2845 10-6

Solid 45 237.3 2327.9 10-6

Water 10 52.7 517 10-6

• Distribution by mass and weight

• Distribution by volume (assume Gs = 2.65)

Total Volume V = r2 l

Water Volume

Solids Volume

Example 1

Phase Trimmings Mass

(g)

Sample Mass, M

(g)

Sample Weight, Mg

(kN)

Total 55 290 2845 10-6

Solid 45 237.3 2327.9 10-6

Water 10 52.7 517 10-6

• Distribution by mass and weight

• Distribution by volume (assume Gs = 2.65)

Total Volume V = r2 l

Water Volume

Solids Volume

Air Volume Va = V - Vs - Vw

Moisture content

Moisture content

Voids ratio

Moisture content

Voids ratio

Degree of Saturation

Moisture content

Voids ratio

Degree of Saturation

Bulk unit weight

Moisture content

Voids ratio

Degree of Saturation

Bulk unit weight

Dry unit weight

Moisture content

Voids ratio

Degree of Saturation

Bulk unit weight

Dry unit weight

Saturated unit weight

Note that dry < bulk < sat

Example 2Volume and weight distributions

Phase Volume

(m3)

Dry Weight

(kN)

Saturated Weight

(kN)

Voids 0.7 0 0.7 9.81 = 6.87

Solids 1.0 2.65 9.81 = 26.0 26.0

Example 2Volume and weight distributions

Dry unit weight,

Phase Volume

(m3)

Dry Weight

(kN)

Saturated Weight

(kN)

Voids 0.7 0 0.7 9.81 = 6.87

Solids 1.0 2.65 9.81 = 26.0 26.0

Example 2Volume and weight distributions

Dry unit weight,

Saturated unit weight

Phase Volume

(m3)

Dry Weight

(kN)

Saturated Weight

(kN)

Voids 0.7 0 0.7 9.81 = 6.87

Solids 1.0 2.65 9.81 = 26.0 26.0

Example 2Volume and weight distributions

Dry unit weight,

Saturated unit weight

Moisture content (if saturated)

Phase Volume

(m3)

Dry Weight

(kN)

Saturated Weight

(kN)

Voids 0.7 0 0.7 9.81 = 6.87

Solids 1.0 2.65 9.81 = 26.0 26.0