Geotech Test 2

What is E?

- energy used for compacting unit volume of soil

- ___ = [(# of layers)(# of blows per layer)(weight of hammer)*(height drop of hammer)]/volume of mold

As the compaction energy increases:

- the max dry unit weight increases

- the optimum moisture content decreases

Field compaction steps:

- compacted in layers of approx. 8 in (suggestion)

- surface of each compacted layer should be scarified to provide bonding between layers

- most field compaction is done with rollers

- handheld vibrating plates may be used for compaction over a small area

Types of rollers used for compaction

- smooth wheel

- pneumatic rubber-tired

- sheepsfoot

- vibratory

Field compaction requirement is specified in terms of __________

Relative Compaction

Factors affecting field compaction

- moisture content

- soil type

- number of roller passes (energy supplied)

- layer (lift) thickness

- intensity of pressure (area over which the force is applied by a given compacting equipment)

Moisture conditioning in the field for economic compaction

- contractors have freedom to choose appropriate equipment, lift thickness, # of passes, etc. to achieve the required relative compaction

- contractors ALWAYS want to achieve the required relative compaction with minimal compaction effort (cost effective)

- moisture content is an important factor for achieving the required relative density with minimum compaction effort

field compaction curve - compaction effort and moisture conditioning in the field

in the field, if there is one moisture content that can't be changed, then changing the compaction effort will help to achieve the required compaction

Smooth wheel rollers

- effective for proof rolling of subgrade and finishing (sand and clay)

- 100% coverage -> low pressure -> not good for thick layers

- 310-380 kN/m^2 contact pressure

Pneumatic rubber-tired rollers

- effective method for sand and clay

- 70-80% coverage

- 600-700 kN/m^2 contact pressure

Sheepsfoot rollers

- effective method for clayey soils

- 1400-1700 kN/m^2 contact pressure under projections

Vibratory rollers

- effective method for granular soils

- vibrators can be attached to other equipment

Methods of determining dry unit weight in the field

- sand cone method (ASTM D1556)

- drive cylinder method (ASTM D2937)

- rubber balloon method (ASTM D2167)

- water ring method (ASTM D5030)

- nuclear method (ASTM D2922)

How do we know that we have achieved the required minimum dry unit weight?

measure the dry unit weight of the compacted soil and compare

Methods of determining moisture content in the field

- standard method cannot be used in the field bc it requires 24 hr oven drying

- stir-frying

- speedy moisture tester

- microwaving

Stir-frying

- stir fry the soil sample in a drying pan over a portable stove

- fast and gives reasonably accurate results for sand and gravel

Speedy moisture tester

- add calcium carbide to the soil container known as speedy moisture tester

- calcium carbide reacts with the water in soil and produces acetylene gas

- moisture content is computed based o the acetylene pressure

Sand Cone Method

- measure the weight of the soil collected from the test hole (weight of the soil plus bucket - weight of bucket)

- fill the test hole with standard sand (Ottawa sand) and calculate the volume with known unit weight

- V(test hole) = V(soil) = V(ottawa sand) = W(ottawa)/unit weight(ottawa)

Drive Cylinder Test

- measure the weight of the excavated soil (weight of soil plus cylinder - weight of cylinder)

- volume of test hole = volume of cylinder

- faster than the sand cone method but slightly less precise

- good for silty or clay soils (enough friction to keep the sample in the cylinder)

Rubber Balloon Method

- similar to sand cone method but the volume of the excavated soil is measured using a liquid

- need to prevent liquid from seeping in the soil

- use rubber membrane (rubber balloon)

- volume of the test hole = volume of liquid used to fill the test hole

Water Ring Test

- used when soil consists of cobbles and small boulders

- use larger hole to reduce error

Nuclear method

- nuclear density meters use radioactive isotope sources

- dense soil absorbs more gamma radiation than loose soil

- the meters operate either in drilled holes or from the soil surface

- needs special training to use this equipment

Flow is due to ____________

gradient difference

Definition of Head

- an element of groundwater contains energy in various forms including: potential, strain, and kinetic energy

- this energy is expressed in terms of ______

- the energy per unit weight (mass x gravitational acceleration)

Potential energy

- due to elevation above the datum

- z

Strain energy

- due to pressure in the water

- u/γ(w)

Kinetic energy

- due to velocity of the water

- (V^2)/2g

Total head at point in water is _________

the algebraic sum of the elevation head, pressure head, and velocity head

Application for Bernoulli's equation to flow through soils

- for the flow of water through soils, the flow velocity is very small

- the velocity head can be neglected and the head is given by: h = z + u/γ(w)

Water flows only when there is a __________

total head difference (head loss or gain)/energy difference

Water always flows from a point of (a) ___________ to a point of (b) ____________

(a) high total head

(b) low total head

Pressure heads are measured using open standpipes called _______________

piezometers

Elevation head is measured from _________

a common datum

Total head difference between two points:

Δh = h(A) = h(B) = [z(A) + u(A)/γ(w)] - z(B) + u(B)/γ(w)]

Hydraulic gradient

i = Δh/L

Zone on Velocity vs Hydraulic Gradient Graph

- Zone 1: Laminar Flow Zone

- Zone 2: Transition Zone

- Zone 3: Turbulent Flow Zone

Within laminar flow (Zone 1)...

velocity is directly proportional to hydraulic gradient

Darcy's Law

- average discharge velocity (________ velocity) of water through a saturated soil is proportional to hydraulic gradient

- units of v and k are same because i is unitless

What is k?

coefficient of permeability/hydraulic conductivity

Discharge velocity

- does not account for voids

- q = vA = v (A(s) + A(v))

Seepage velocity

- actual velocuty

- q = v(s) * A(v)

- A(v): area of void in the cross section

Relationship between discharge and seepage velocity

V(s) = V / n

- V(s): seepage velocity

- V: discharge velocity

- n: porosity

Hydraulic conductivity depends on many factors including fluid...

- viscosity

- pore-size distribution

- grain-size distribution

- void ratio

- soil saturation

Factors that affect permeability of clays

- ionic concentration

- thickness of the layers of water held to the particles

Lab methods for determining permeability of soils (undisturbed sample)

- constant head method (used for coarse grained soils)

- falling head method (used for fine grained soils)

Empirical methods for determining permeability of soils

- granular soils: Hazen's eqn, Kozeny-Carman eqn, Chapuis eqn, and Amer & Awad eqn

- cohesive soils: Taylor eqn, and Samarasinghe et al eqn

In situ methods for determining permeability of soils (field)

- pumping tests

- constant head borehole permeameter

- boutwell permeameter

- porous probes

Measurements needed for Constant Head Method

- cross sectional area of the sample, A

- length of the sample, L

- head difference across the sample, h

- duration, t2-t1

- total volume collected, Q

Measurements needed for Falling Head Method

- cross sectional area of the pipe, a

- length of the sample, L

- cross sectional area of the sample, A

- head difference at time t1, h1

- head difference at time t2, h2

Hydraulic conductivity of most soils varies with ____________

the direction (vertical or horizontal) of the flow

What is k(V)

hydraulic conductivity in the vertical direction

What is k(H)

hydraulic conductivity in the horizontal direction

Relationship between k(V) and k(H)

k(H) is generally higher than k(V)

k(H) equivalent for flow parallel to soil layers in steady flow

- q(equiv) = q1 + q2 + q3 + ... + q(n)

- h(equiv) = h1 = h2 = h3 ... = h(n)

k(V) equivalent for flow normal to soil layers in steady flow

- q(equiv) = q1 = q2 = q3 ... = q(n)

- h(equiv) = h1 + h2 + h3 + ... + h(n)

Equation for V (velocity) given k (hydraulic conductivity) and i (hydraulic gradient)

v = k * i

Equation for Q (volume) given q (flow rate) and t (time)

Q = q*t

Equation for q (flow rate) given v (velocity) and A (area)

q = v*A

Equation for i (hydraulic gradient) given Δh (head loss) and L (length)

i = Δh/L

Permeability test in the field by pumping from wells for unconfined permeable layer

- soil is assumed to be homogeneous, isotropic, and infinite

- water is pumped out at a constant rate (q) from the test well

- observation wells (at least two) are used to locate the draw-down curve after reaching steady state condition

- flow rate into the test well is equal to the rate of pumping (q) at steady state condition

Permeability test in the field by pumping from wells for confined permeable layer

- flow area is fixed

- due to confinement, the water pressure is higher than static pressure

Solution methods to 2D steady flow equation

- graphical solution (flow net)

- analytical solution (simplified graph)

Graphical Solution to Laplace Equation: Flow Net

gives two orthogonal families of functions (Curves):

- flow line or streamline

- equipotential line

flow line or streamline

- two of these can never intersect

- line along which water molecules travel from upstream o downstream

equipotential lines

- same _______ = exact same energy

- line along which the head (total head) is constant

Rules for constructing flow nets

- flow domain must be drawn to scale

- flow lines and equipotential lines intersect at right angles for isotropic soils and form curvilinear square flow elements

- no two flow lines can intersect

- no two equipotential lines can intersect

- upstream and downstream surfaces (horizontal) of the permeable layer are equipotential lines

- boundaries of the impervious layer and impervious structure are flow lines

Procedure for creating flow nets

- trial and error

- sketch the flow domain to scale

- identify boundary conditions

- sketch initial flow lines and equipotential lines to form curvilinear squares, correct errors if needed, and finalize flow nets

A correctly drawn flow net can be used for calculating ____________

seepage and uplift pressure

Flow net under a sheet pile: Nf (# of flow channels) and Nd (# of potential drops) will vary with...

with depth of embedment of sheet pile and thickness of previous layer

Flow net under a concrete dam: Nf (# of flow channels) and Nd (# of potential drops) will vary with...

with width of the impervious hydraulic structure and the thickness of the pervious layer

Uplift pressure under hydraulic structures using flow nets

- has to be determined to calculate the total uplift force on the structure

- if the pressure distribution is known, uplift force (per unit length) is the area under the pressure diagram

Resultant uplift force and its location can be calculated by _______

force and moment equilibrium

When are simplified chart solutions applicable for single row of sheet pile

- seepage under single row of sheet pile wall

- isotropic and homogeneous soils

What data is needed for simplified chart solutions for single row of sheet pile

- S: embedded depth

- T': thickness of the pervious layer

- H: head difference

- k: permeability of the soil

Procedure for using simplified charts for single row of sheet pile

- calculate S/T

- obtain q/(kH) from figure 8.12: AKA n

- calculate q: q = kHn

When are simplified chart solutions applicable for an impervious hydraulic structure

- seepage under an impervious hydraulic structure

- isotropic and homogeneous soils

What data is needed for simplified chart solutions for an impervious hydraulic structure

- B: width of structure

- S: embedded depth of pile

- T': thickness of the pervious layer

- H: head difference

- k: permeability

- x: see figure

Procedure for using simplified charts for an impervious hydraulic structure

- calculate S/T

- calculate x/b

- calculate b/T'

- obtain q/(kH) from figure 8.13

- calculate q

Two methods for simplified chart solutions for seepage through earth damns constructed on impervious base

- Dupuit's solution or Schaffernak's solution

- Casagrande's solution

Dupuit's solution or Schaffernak's solution

gives better estimate for α <= 30

Casagrande's solution

gives better solution for α > 30

For 3 dimensional case there will be (a) ______ normal stresses and (b) ______ shear stresses at a point in soil

(a) three

(b) three

in geotechnical engineering, compressive normal stresses are ________

positive

If the ground surface is horizontal (level ground) we will only have normal stresses, therefore __________________

shear stresses will be zero

sources of stress in soil

- in situ (geostatic) stress

- induced stress

in situ (geostatic) stress

due to self weight of the soil above the point being excavated

induced stress

due to external loads such as structural foundation, earth fill, vehicles, etc

What is the name for the vertical normal stress due to solid particles

effective stress

Vertical normal stress due to water is the same as _________

water pressure at point P

Notation for vertical normal stress due to solid particles

σ'

Notation for vertical normal stress due to water

u

What is effective stress?

- load is transferred through the inter particle contacts

- ________ is the average stress carried by the particles through the inter particle contact

Terzaghi's effective stress concept

- one of the most important concept in geotechnical engineering

- effective stress at a point in saturated soils = (total stress - pore water pressure)

- governs the mechanical behavior (shear strength and volume change) of saturated soil

- applicable to normal stress only

- total and effective stresses are same for shear stresses because water can not take shear

- seepage will alter the effective stress because of seepage forces on particles

Upward seepage

- effective stress decreases

- critical in geotech

- may cause piping or sand boiling which should not be allowed in design

Downward seepage

effective stress increases

For steady seepage condition, the total stress will ___________

not be affected because total stress is due to the weight of water and soil above the point of interest that is constant

How does seepage effect the effective stress?

pore water pressure changes due to seepage

Pore water pressure with upward seepage

pressure without seepage + pressure increase due to seepage

Pressure increase due to seepage

difference in water4 level in tubes

What is the only thing that can be changed in the formula: σ'(c) = γ' z - iz*γ(w)

I: hydraulic gradient