# Weight-Volume Relationships Soil Mechanics

Weight-Volume Relationships

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Introduction

• Soil is a three-phase material consisting of a skeleton of solid particles. • The solid particles encompassing voids filled with water & air. • It is necessary that the constitution of the solidswater-air mixture can be expressed quantitatively in terms of some standard physical properties. • Soil water is commonly known as pore water • If all voids are filled with water = soil is saturated, otherwise will be known as soil is unsaturated. (not all voids are filled with water) • If all voids are filled with air = soil is dry Prepared by:aidsalma@feng.unimas.my 2

At the end of lecture, students should be able to:

• Determine the proportions of the main constituents in a soil • Determine particle size distribution in a soil mass • Classify soils • Determine index properties of soils

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Definition of Key Terms

• Water content (w) is the ratio of the weight of water to the weight of solids • Void ratio (e) is the ratio of the volume of voids to the volume of solids • Porosity (n) is the ratio of the volume of voids to the total volume of soil • Degree of saturation(Sr) is the ratio of the volume of water to the volume of voids • Bulk unit weight (γbulk) is the weight density, the weight of a soil per unit volume • Saturated unit weight (γsat) is the weight of a saturated soil per unit volume • Dry unit weight (γdry) is the weight of a dry soil per unit volume • Effective unit weight (γ') is the weight of soil solids in a submerged soil per unit volume Prepared by:aidsalma@feng.unimas.my 4

Weight-volume relationships

• Soil can be idealized in 3 phases as shown in Fig.1. • The physical properties of soils are influenced by the relative proportions of each of these phases. Solids

Va Void Air Wa

V

Vw

Water

Ww

W

Vs

Solids

Ws

Fig. 1

idealization

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• Referring to Fig. 1, the total volume of the soil is the sum of the volume of solids (Vs), volume of water (Vw), and volume of air (Va):

V Vs Vw Va Vs Vv

Where

VV VW Va

= volume of voids

As the weight of air, Wa = 0, The weight of the soil is: W WS WW Note: *the following equations have been established based on the unit solid volume idealized phases Prepared by:aidsalma@feng.unimas.my 6

Basic quantities of soil components derived from phase diagrams Water content (w) or Moisture Content (m) ratio of weight of water to the weight of solids in soil, often expressed as percentage w Ww x 100% Ws

Void Ratio (e) volume not occupied by solid = volume of voids expressed as a decimal quantity (no dimension)

volume of voids Vv Va Vw Void ratio, e volume of solids Vs Vs Specific Volume (v) volume of soil per unit volume of solids

v

V 1 e Vs

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Porosity (n) ratio of volume of voids to the total volume expressed as percentage n volume of voids Vv total volume V

The void ratio & porosity are inter-related as follows:

e n e , n 1 n 1 e

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It can be proven by:

n Vv VV V Vs Vv VS Vv VS Vs V v Vs e 1 e Notes: Regularly, coarse-grained soils void ratios vary from 1 to 0.3. Clay soils can have void ratios greater than 1

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Specific Gravity (Gs) the ratio of the weight of soil solids to the weight of water of equal volume

W W Gs s s Ww Vs w

Vs Vw

γw = unit weight of water = 9.81kN/m3

Mass of water equal volume;

w

Ww Ww wVw Vw

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Phase Relationships –basic quantities are used to define other quantities in unit solid volume basis Volumes

Va = e (1-Sr) Specific Volume , v = 1 + e e

weight

Air

Wa = 0

Vw = wGs = Sre

Water

Ww = wGsγw

Vs = 1

Solids Figure 2

Ws = Gsγw

Referring to Figure 2...

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