UNIVERSIDADE DE BRASÍLIA. DEPARTAMENTO DE ENGENHARIA CIVIL E AMBIENTAL

PROGRAMA DE PÓS-GRADUAÇÃO EM GEOTECNIA

WATER IN SOIL AND ROCK MASS

Prof.: Hernán Eduardo Martínez -Carvajal, PhD

Design based on empirical rules

1930 (oral tradition)

Note: The theoretical basis for a rational

analysis were already known.

1856 Henri Darcy

GENERAL

STATEMENT

1880 Forcheimer

Hydraulic Head function

To satisfy the continuity

equation

Explain the flux

in porous

media

Continuity

equation

Basis for developing the graphic method

known as FLUX NETWORKS

Laplace

GENERAL

STATEMENT

1937 A. Casagrande

(“Seepage Through Dams” _ Contributions to

Soil Mechanics 1925 – 1940. Boston Society of

Civil Engineers 1940).

Graphic solution to LAPLACE equation

Ξ FLOW NETWORKS-

GENERAL

STATEMENT

¿ Why is important to solve problems related to

flow in porous media?R/ To obtain information about:

1. INFILTRATION THROUGH REGIONS SUBMETED TO FLOW – Earth

dams (Quantification of the flow).

2. INFLUENCE OF THE FLOW ON THE GLOBASL STABILITY OF THE

SOIL MASS – Slope stability.

a. Direction of the flow (hydrodynamic pressure)

b. t =( - u) tg

3. INTERNAL EROSION – Piping

(Earth dams, embankments, slopes, retaining walls)

GENERAL

STATEMENT

CONCEPT of

PRESSURE (STRESS)

P=F/S

Hydraulic Jack Volume compatibility : S1 . L1 = S2 . L2

Work compatibility : F1 . L1 = F2 . L2

1

2

1 2F2

F1

L1

L2

BASIC CONCEPTS

s2

s1

The Hydrostatic Paradox

Before the principles of hydrostatics were understood, the behavior of liquids was

often very puzzling. For example, Figure 1 shows a vessel with two interconnected

chambers which are open at the top and have bottom openings with the same

cross-sectional areas. If you pour water into either chamber, it flows up into the

other one until the water levels in both are identical. Is this not a paradox? Surely

the chamber containing the larger volume of water must have a greater force per

unit area at its base, and shouldn't this make the water in the smaller chamber rise

to a higher level?

Blaise Pascal asked this question nearly 300 years ago. He even built an

apparatus, now known as 'Pascal's vases', to demonstrate the paradox.

This apparent paradox can be easily resolved by the application of some elementary

mechanics. The pressure at a point in a static liquid is due entirely to the weight of

liquid (plus the atmosphere) directly above it.

An even more striking paradox is that associated with the horizontal

pressures on a dam.

The explanation follows the same reasoning as above: the horizontal pressure at a point must be equal to the vertical pressure, but the vertical pressure depends only on the depth of the water, not on its horizontal extent.

Hydrostatic pressure

Pe

A

h

BASIC CONCEPTS

ATMOSPHERIC PRESSURE

Mercury (Hg)

Hg = 13.6 g/cm3 = 13600 kg/m3

To sea level, h = 76cm

Units: * International System Patm = N/m2

Patm = 760 mmHg = 1 standard atmosphere= 1.033 kgf/cm2

1 technical atmosphere= 1 kgf/cm2

Patm

A

h

BASIC CONCEPTS

A B

PA= .g.hA PB= .g.hB

PA> PBbecause h2> h1

FLUIDS MOVEMENT OCCURS BECAUSE OF THE ENERGY

DIFERENCES

hA

Experience: Opening the valve movement toward 1

Experience: PRESSURE (Expressed as a height)

BASIC CONCEPTS

hB

A B

What happens in point C at equilibrium?

PC= Patm. And PA > PC nevertheless

there is no movement! Why?

HAhA

BASIC CONCEPTS

(by unit weight)

HAhA

0

BASIC CONCEPTS

g

gHE A

potC

g

VE cin

C

2

21

APLICATIONS: OPEN TUBE (CASAGRANDE)

hBZA

ZB

A

B

N.R. (Z=0)

0

BASIC CONCEPTS

YZA

ZB

A

B

N.R. (Z=0)

Inside the pipe there is no loss of head, so the piezometric heights of A and B are

the same.

Pressure in point B :

“The height of the water column indicated by an open piezometer in any point of a

terrain is equal to the static pressure of water on the point divided by the

volumetric weight of the water”.

BASIC CONCEPTS

PÉRDIDAS DE CARGA

Situación ideal en régimen estacionario

V1V1

A B N.R.

BASIC CONCEPTS

PÉRDIDAS DE CARGA

Situación real en régimen estacionario

hf

BASIC CONCEPTS

PÉRDIDAS DE CARGA

Situación real en régimen estacionario.

Cambio de sección= cambio de velocidad

Head lost (without

friction)

+ Head lost due to

friction

AB

BASIC CONCEPTS

PIEZOMETRIC HEAD IN SOIL MASS

DIFFERENCE IN ENERGY CAUSES

MOVEMENT OF FLUIDS

V is very low compared with

other components so

consider negligible

POSITIONPRESSURE VELOCITY

Water moves form high piezometric heads to low piezometric

heads.

BASIC CONCEPTS

GRADIENT

Gradient = = i

L

A

B

h

N.R.

Lost of head (h = hA – hB)

In a lenght L

h

L

BASIC CONCEPTS

QUALITATIVE INTERPRETATION OF THE GRADIENT

L

hkAQ L

h2

h2 h

h

QQA BC

BASIC CONCEPTS

Tres situaciones

adicionales de

gradientes variables:

•Implicaciones en la

permeabilidad.

•Tipos de suelo

•Suelos estratificados

•Suelos con

permeabilidad variable

INTERPRETACIÓN CUALITATIVA DEL GRADIENTE

BASIC CONCEPTS

FREE WATER

FREE WATER

FREE WATER

How to produce this situations?

DARCY´S LAW

1. INCREASING (Q)

ALSO INCREASES hL

2. INCREASING L

DECREASE Q

3. INCREASING A

ALSO INCREASES Q

Sectional

area, A

N.R.

BASIC CONCEPTS

1 3 42

k : hydraulic

conductivity

BASIC CONCEPTS

L

hkAQ L

L

hA L

Q

UNITS

L

hAkQ

**

hA

LQk

*

*

T

LQ

LA

LL

Lh

3

2

T

L

LL

LT

L

*

*

2

3

BASIC CONCEPTS

FACTORIZATION OF THE DEPENDENCY

Cases:

•Different terrains

•Water? Other fluid?

(change the

permeability)

•Temperature

•Salt content

m = viscosidad dinámica

del fluido

DARCY:

By definition, a material of 1

darcy permits a flow of 1 cm3/s

of a fluid with viscosity 1 cP (1

mPa.s. Water at 20°C ) under a

pressure gradient of 1 atm/cm

across an area of 1 cm2.

m

m

gkkk

** 00

Depends on

the material

Depends on

the fluid

BASIC CONCEPTS

Typical values (cm/s)

Tomado de Juarez-Badillo & Rico Rodriguez. “Fundamentos de la Mecánica de Suelos”

BASIC CONCEPTS

VELOCITIES: DISCHARGE, FILTRATION AND FLOW

l

Av

As

kiv

A

Qv

vAkiAQ

e

ev

A

A

A

Q

A

Qv

vv

f

1*

e

e

V

V

LA

AL

vv

1

(Discharge velocity)

Filtration velocity

v

See that:

BASIC CONCEPTS

Attention! Pores and pipes are not rectilinear

but highly curvilinear.

l

lvv R

fR(Real velocity or flow

velocity)

“sinuosity” factor = f(lR)

lR : real length of flow

UNKNOWN!!!

BASIC CONCEPTS

representative values, Castany (1963)

Tomado de Vélez Otálvaro, M.V. “Hidráulica de Aguas Subterráneas”

BASIC CONCEPTS

APLICABILIDAD DE LA LEY DE DARCY

EXISTE UNA RELACIÓN

LINEAL ENTRE EL

GRADIENTE HIDRÁULICO

Y LA VELOCIDAD DE

DESCARGA DEL FLUJO A

TRAVÉS DEL MEDIO

POROSO.

D

TfvC ,

1T: temperatura

D: Diámetro de la conducción en [cm]

Turbulento

Laminar

vc

i

6.5vc v

BASIC CONCEPTS

m

vDR

V : Velocidad de drenaje [cm/s]

D: Diámetro prom. partículas [cm]

: Densidad del fluido [gr/cm3]

m: Coef. viscosidad [(gr*s)/cm2]

En medios porosos: Reynolds (1883)

El valor limite del numero de Reynolds para que un fluido

cambie de laminar a turbulento oscila entre 1 y 12

R (agua) ≤1 con v= 0.25 cm/s y D <0.4mm (arena gruesa)

Flujo laminar válida la Ley de Darcy

BASIC CONCEPTS

HYDROGEOLOGY

Where is Earth's water located?

Picture of Earth showing if all Earth's

water (liquid, ice, freshwater, saline) was

put into a sphere it would be about 860

miles (about 1,385 kilometers) in

diameter.

An aquifer is a geological formation capable of yielding useful

groundwater supplies to wells and springs. All aquifers have two

fundamental Characteristics: a capacity for groundwater storage and a

capacity for groundwater flow. But different geological formations vary

widely in the degree to which they exhibit these properties and their

areal extent can vary with geological structure from a few km2 to many

thousands of km2.

HYDROGEOLOGY

The most significant elements of hydrogeological diversity are:

● major variation of aquifer unit storage capacity (storativity), between

unconsolidated granular sediments and highly-consolidated fractured rocks

● wide variation in aquifer saturated thickness between different

depositional types, resulting in a wide range of groundwater flow potential

(transmissivity).

The vast storage of many groundwater systems (much larger than that of the

Biggest man-made reservoirs) is their most distinctive characteristic. In

consequence most groundwater is in continuous slow movement from areas of

natural aquifer recharge (from rainfall excess to plant requirements) to areas of

aquifer discharge (as springs and seepages to watercourses, wetlands and coastal

zones).

What is the relationship between groundwater and surface water?

• Streams and rivers on which an aquifer is dependent as a significant source of its overall recharge

• Rivers that in turn depend significantly on aquifer discharge to sustain their dry-weather flow.

Why is the estimation of aquifer replenishment important?

● Contemporary aquifer recharge rates are a fundamental consideration in the sustainability of groundwater resource development. Furthermore, understanding aquifer recharge mechanisms and their linkages with land-use is essential for integrated water resources management.● The quantification of natural recharge, however, is subject to significant methodological difficulties, data deficiencies and resultant uncertainties because of:

● wide spatial and temporal variability of rainfall and runoff events● widespread lateral variation in soil profiles and hydrogeological conditions.

How can the ‘safe yield’ of an aquifer be defined?

All groundwater flow must be discharging somewhere, and

abstraction will reduce these discharges. But the source of

groundwater pumped can be complex. So-called ‘safe

yield’ is clearly bounded by the current long-term average

rate of aquifer recharge

Conceptual effects of abstraction on the groundwater resource balance

● discharge to freshwater systems required to sustain downstream water-supply or river ecosystems

● discharge via natural vegetation, including that sustaining ecologically and/or economically valuable freshwater wetlands

● discharge to saline areas, including coastal waters, salt lakes and pans and make allowances for those parts of these discharges which need to be conserved.

When can an aquifer said to be ‘overexploited’?

The term ‘aquifer overexploitation’ is an emotive expression not capable

of rigorous scientific definition. But it is a term which water resource

managers would be wise not to abandon completely, since it has clear

register at public and political level. Some regard an aquifer as being

overexploited when its groundwater levels show evidence of ‘continuous

long-term’ decline.

In practice, when speaking of aquifer overexploitation we

are invariably much more concerned about the

consequences of intensive groundwater abstraction

than in its absolute level.

Thus the most appropriate definition is probably an

economic one: that the ‘overall cost of the negative

impacts of groundwater exploitation exceed the net

benefits of groundwater use’, but of course these

impacts can be equally difficult to predict and to cost.

Water yiels and subsidence induced settlements in Mexico City

22 /4,3/2

1,55,6

cmkgcmkgmv

1cm2/kg=0,01m2/kN

1600 water wells

80 m3/s

Piezometric depletion 10 m

in 15 years (down town)

Qual é a situação atual dos projetos de aproveitamento racional

do aquífero Guaraní?

Rio

K=1x10-6 m/s

Mina

1. Piezometric head in points A, B and C in natural conditions (before the mine).

Explain each calculation

2. If the mine is instantly opened. Is there any flow of water into the excavation?

Explain your answer.

3. In steady state regime (time after the excavation) calculate piezometric head

in points A, B and C. Explain.

4. Considering vertical flow only how much water enters into the excavation?

Justify your answer.

Imagine at least three different possible

conditions for the groundwater condition

for this geological situation, in terms of

the piezometric and phreatic heads.

CONCEITOS BÁSICOS DE FLUXO DE

AGUA EM SOLOS

PRESSÃO HIDROSTÁTICA

GRADIENTE

LEI DE DARCY

PERMEABILIDADE

EQUAÇÃO DE BERNOULLI

VELOCIDADE DE DESCARGA, DE

INFILTRAÇÃO E REAL.

SEGUE:

SOLUÇÃO DA EQUAÇÃO DE

LAPLACE

ANÁLISE BASEADO EM MÉTODOS

GRÁFICOS

EFEITO DA AGUA EM ESCAVAÇÕES E

TALUDES

TENSÕES TOTAIS, EFETIVAS E

NEUTRAS

TUDO ENTRA NA PROVA!!!!

RESUMO