Topic7 -Time+rate+of+consolidation

TABLE OF CONTENTS

PREVIEW .................................................................................................................... 7.2 Introduction ............................................................................................................. 7.2 Objectives ................................................................................................................. 7.2

PREFACE .................................................................................................................... 7.2

TERZAGHI’S ONE-DIMENSIONAL CONSOLIDATION EQUATION. ........... 7.2

DETERMINATION OF C V ........................................................................................ 7.5 Displacement vs log(time) – Casagrande (1938) ................................................... 7.5 Displacement vs squareroot (time) – Taylor (1948) ............................................. 7.5

SECONDARY COMPRESSION ............................................................................... 7.6

REVIEW QUESTIONS .............................................................................................. 7.7

PREVIEW

Introduction

In Topic 7, the time dependent behaviour of consolidation was introduced. The oedometer test was also introduced as one method to determine the likely volume changes that resulted from the consolidation process. The oedometer test can also tell us how long it will take for consolidation to occur. This is an important practical problem, because it is essential that we know how fast a structure will settle. Objectives

∙To understand Terzaghi’s one-dimensional consolidation theory and be able to apply it to practical problems

∙To be able to interpret oedometer tests to determine properties for estimating the rate at which consolidation occurs

∙To differentiate between primary and secondary consolidation and be able to estimate secondary consolidation settlement.

PREFACE

Consolidation results from the dissipation of excess pore water pressures which generates movement of pore water within the soil. The amount of water that is squeezed out is directly proportional to the amount of excess pore water pressure that is dissipated. It follows then, that the rate of consolidation is directly related to the rate of excess pore pressure dissipation.

TERZAGHI’S ONE-DIMENSIONAL CONSOLIDATION EQUATION. As introduced in Topic 2 and will be dealt with in the unit CIV3248 Groundwater and Environmental Engineering in Semester 2, the movement of pore water is governed by Darcy’s law. Darcy’s law tells us that the quantity of flow depends on the hydraulic gradient and the permeability of the soil. By equating the volume change of the soil due to water egress with the volume change of the soil due to change in effective stress, it is possible to derive the following differential equation which governs

one dimensional consolidation. Here u is the pore water pressure, c v is

the coefficient of consolidation (a soil “property”), t is time and z

denotes the position where u is determined - u is a function of both z

and t.

This equation was first suggested as a model of consolidation by Terzaghi in 1925. It can also be derived in three dimensions, but for most practical applications the one-dimensional equation is usually assumed.

Note that the rate of consolidation is governed by the coefficient of consolidation not the permeability. c v depends on the permeability, k,

and compressibility, m v, of the soil. This implies that for a soil and rock

with the same permeability, the pore pressures will dissipate faster in the rock because it has lower compressibility (or greater stiffness)

v

w

v m

k c

γ

=

t

u

z

u

c

2

2

v∂

∂

=

∂

∂