The Foundation Engineering Handbook Chapter 13

The Foundation Engineering Handbook Chapter 13 Geotechnical earthquake engineering can be defined as that subspecialty within the field of geotechnical engineering that deals with the design and construction of projects in order to resist the effects of earthquakes. Geotechnical earthquake engineering requires an understanding of basic geotechnical principles as well as an understanding of geology, seismology, and earthquake engineering. In a broad sense, seismology can be defined as the study of earthquakes. This would include the internal behavior of the earth and the nature of seismic waves generated by the earthquake.

Impact of Groundwater on the Design of Earthen

Structures

Manjriker Gunaratne CONTENTS

13.2 Graphical Solution to Groundwater Problems: Flow Nets 56813.2.1 Estimation of the Coefficient of Hydraulic Conductivity 56913.3 Numerical Modeling of Groundwater Flow 57113.4 Analytical Modeling of Groundwater Flow 573

13.6.1.1 Design Consideration for Clay Liners 57913.6.1.2 Design Considerations for Geomembrane layers 57913.7 Application of Groundwater Modeling Concepts in Environmental

Geotechnology

579

13.7.1 Analysis of Seepage toward Wells 580

13.7.3.1 Derivation of the Location of the Stagnation Point 58313.7.3.2 Determination of the Contamination Zone 584

13.8.2.1 Transmissivity of a Geotextile 58813.8.2.2 Permittivity of a Geotextile 58813.8.2.3 Apparent Opening Size of a Geotextile 588

References 593

13.1 Groundwater and Seepage

Seeping groundwater has a major impact on the design of earthen structures Stability analysis

of soil slopes in groundwater flow regimes requires the knowledge of seepage forces

Furthermore, water-retaining structures are often built in groundwater flow

is essential in the design of water-retaining structures when estimating the uplift forces.

Foundation engineers employ a variety of approaches to understand the effects of

groundwater on structures They can be basically classified as:

1 Graphical approaches based on flow nets

2 Numerical approaches based on the finite difference or the finite element method

3 Analytical approaches based on mathematical transformations

13.2 Graphical Solution to Groundwater Problems: Flow Nets

The most common and the simplest means of seepage analysis is by the method of flow nets

In this method, two orthogonal families of equipotential and flow lines are sketched in theflow domain (Figure 13.1) using the basic concepts defining the two families A flow line is

an identified or a visualized flow conduit boundary in the flow domain An equipotential line,

on the other hand, is an imaginary line possessing the same total energy head (energy per unitweight)

Rules Governing the Construction of a Flow net

1 Equipotential lines do not intersect each other

2 Flow lines do not intersect each other

3 Equipotential lines and flow lines form two orthogonal families

4 In order to ensure equal flow in the drawn flow conduits and equal head drop betweenadjacent equipotential lines, individual flow elements formed by adja¬ cent equipotentiallines and flow lines must bear the same height-width ratio (this is typically selected as 1.0for ease of plotting)

Useful guidelines regarding the plotting of reasonably accurate flow nets for different flowsituations are found in Cedergreen (1989)

With seepage velocities generally relatively low, the pressure (p) exerted by seeping water

and the potential energy contributes to the total hydraulic head (energy per unit weight) ofwater as

where k is the coefficient of permeability (or hydraulic conductivity) at that location while i,

the hydraulic gradient, can be expressed by

(13.3)

FIGURE 13.1

Illustration of a flow net.

13.2.1 Estimation of the Coefficient of Hydraulic Conductivity

The coefficient of hydraulic conductivity of a soil can be estimated in a number of ways:

1 Using laboratory permeameters (falling-head or constant-head) The readers are referred toDas (2002) for experimental details of these laboratory tests

2 Using field pumping tests that are discussed in Section 13.5

3 Using an empirical correlation between k and D10that is listed in Equation (13.38)

(Example 13.6)

It can be shown from Equation (13.2a) that the quantity of seepage in the flow domain can

also be expressed in terms of the number of equipotential drops (ne) and the flow conduits (nf)

as

q=kH[nf/ne]

(13.2b)

Page 570

where H is the total head drop.

The following example illustrates the flow net method of seepage analysis and evaluation

q=3×(10−9

)(0.302)(1.3)(1)m3/sec/m =1.18×10−9m3/sec/m

The following important assumptions made in the above analysis must be noted:

1 The subgrade soil is homogeneous with respect to the coefficient of permeability

2 Bedrock and concrete dam are free of fault or cracks

3 There is no free flow under the dam due to piping (or erosion)

Therefore, the design and installation of an adequate pore-pressure monitoring system that canverify the analytical results is an essential part of the design A piezometer with a

geomembrane or sand filter that can be used for monitoring pore pressures is shown in Figure13.2

FIGURE 13.2

Piezometer probes (From Thilakasiri, H.S., 1996, Numerical Simulation of Dynamic Replacement of

Florida Organic Soils, Ph.D Dissertation, University of South Florida With permission.)

13.3 Numerical Modeling of Groundwater Flow

If it is assumed that the water flow in a saturated soil is laminar, continuous (without anylosses or gains in water due to the presence of sinks or sources), and steady with respect totime, the following partial differential equation can be written for continuity of two-

dimensional (2D) flow conditions at any given point in the flow domain:

(13.4)

where u and v are the velocities in the X and Y directions.

Using Equation (13.3), the hydraulic gradients in the respective directions can be expressedas

(13.5a)

(13.5b)

u=k x i x and v=k y i y

where k x and k y are the hydraulic conductivities in the X and Y directions, respectively, in a

generally anisotropic soil

Then, by substituting in Equation (13.4) along with Equation (13.5), the Laplace equationfor 2D flow is obtained as

where the corresponding hydraulic heads hs are defined inFigure 13.3(where a grid of length

interval l is plotted), one obtains the following numerical form of Laplace’s equation:

Then, h0can be expressed in Equation (13.8) to obtain the hydraulic head at any point interms of the hydraulic heads of its neighboring nodes as

FIGURE 13.3

Finite difference grid for solution of the seepage problem.

Knowing the boundary conditions, which are the hydraulic head values of the interfaces ofsoil with free water (i.e., head water and tail water), and the hydraulic conductivities in eachdirection, Equation (13.8) can be conveniently coded in the computer to derive the hydraulic

heads of the entire flow domain Then, once the hydraulic heads, h, are available, Equations

(13.3) and (13.2) can be used in steps to evaluate the hydraulic gradient at any desired

location in the flow domain and the flow within any grid element

13.4 Analytical Modeling of Groundwater Flow

Groundwater problems can be analytically solved using transformation methods Generally,the first step in this regard is to mathematically define the family of equipotential lines andflow lines based on the potential function and the stream function (ψ) It is also noted that

the potential function is related to the hydraulic head by Equation (13.9)

(13.9)

Then, a 2D groundwater regime in the x-y plane can be transformed to the domain using

an appropriate transformation that accounts for the boundary equipotential lines

and flow lines (ψ=constant) in the flow domain (x-y plane) This is initiated by defining the

above functions in terms of the flow velocities using the Cauchy– Reimann relationships

(13.10a)

(13.10b)

It can be shown mathematically that and ψ are orthogonal to each other.

13.4.1 Conformal Mapping

The actual flow domain in the X-Y plane can be conveniently mapped onto the potential

function-flow function domain using the following complex variables that reduce theamount of mathematical manipulation required:

z=x+iy

(13.11a)

(13.11b)

Then, one can define appropriate conformal mapping functions in the following formats:

ω=f(z)

(13.12)

FIGURE 13.4

Unconfined flow under a concrete dam.

Example 13.3

It can be shown that the following transformation is adequate to describe the seepage under

a concrete earth dam shown in Figure 13.4

since it satisfies the known equipotential surfaces (soil-free water interfaces A and B) and the

flow boundary at the dam bottom, k is the hydraulic gradient of the foundation soil The above

expression can be used to plot the flow lines and equipotential lines for the above flow

(assume that b=5 m and h=6 m).

Using the following transformation:

(13.13)

and substituting the complex relations in Equation (13.11),

(13.14)

Equation (13.14) can be manipulated using complex algebra to obtain expressions for and ψ

in terms of x and y Then, by eliminating from the two equations, the flow lines can be

plotted using the following equation (Figure 13.5):

FIGURE 13.5

Flow lines drawn for selected flow quantities indicated in the legend.

Also, at the bottom of the dam since y=0, using Equations (13.1) and (13.9), the pressure

distribution under the dam can be expressed as (Figure 13.7)

(13.17a)

The total uplift force at the bottom of the dam and its moment about the toe of the dam areimportant parameters for the design of the dam They can be obtained as follows:

FIGURE 13.7

Pressure distribution under the bottom of the dam.

(13.17c)The above integrals can be evaluated using any numerical integration package

13.4.2 Complex Flow Velocity

The complex flow velocity in Equation (13.18) provides another useful relation that can beused to obtain the flow velocity components directly from the derivative of the transformation

(13.18)

Example 13.4

If a certain seepage flow situation can be modeled by the transformation w=2z− z2

, find theresultant velocity at the point (1, 2) represented by

z=1+2i

Using Equation (13.18),

where u=0 and v=4 Hence, the magnitude of the flow velocity is 4 units in the +y direction.

When one needs to develop an appropriate transformation for a specific flow situation, onecan use the Schwarz-Christoffel transformation technique, which is widely used in suchformulations The reader is referred to Harr (1962) for analytical details of the Schwarz-Christoffel transformation-based groundwater seepage solutions

13.5 Dewatering of Excavations

Construction in areas of shallow groundwater requires dewatering prior to excavation

Although contractors specialized in such work determine the details of the dewatering

program depending on the field performance, a preliminary idea of equipment requirementsand feasibility can be obtained by a simplified analysis.Figure 13.8shows the schematicdiagram for such a program

It also shows the elevations of the depressed water table at various distances from thecenter of the well Observation wells (or piezometers) can be placed at intermediate locations,

such as those shown at distances of r1and r2, to monitor the water table depression In

analyzing a seepage situation like this, Dupuit (Harr, 1962) assumed that (1) for a smallinclination of the line of seepage the flow lines are horizontal and (2) the hydraulic gradient isequal to the slope of the free surface and is invariant with depth

underlying assumption is that the entire soil stratum can be considered as homogenous with

the average hydraulic conductivity represented by k

(13.19)

Noting that q is constant throughout the flow regime, Equation (13.19) can be integrated between distances r1and r2to obtain

(13.20)

One can define the extent of dewatering, using parameters r1, r 2 , h1, and h2, and utilize the

above expression to determine the capacity requirement of the pump Alternatively,

expression (13.20) can be used to estimate the average permeability coefficient of the soilstratum

If the site where the dewatering program is executed contains a number of layers withdifferent soil properties, i.e., coefficients of permeability, then Equation (13.20) has to bemodified to incorporate properties of all the layers in the area of influence of dewatering Thereader is referred to Cedergreen (1989) for expressions applicable to such complicated siteconditions

13.6 Basic Environmental Geotechnology

Environmental geotechnology is a relatively new civil engineering discipline that is concernedwith the design of earthen structures that are utilized in assuring environmental safety Someexamples of such structures include protective clay liners for landfills, soil or soil-fabricfilters that control erosion due to groundwater, and earthen barriers against seepage of

contaminated groundwater

Page 578

FIGURE 13.9

Typical cross section of a geomembrane-lined landfill.

landfills cannot be overemphasized Although the construction of landfills involves politicaland legal issues, properly designed, constructed, and maintained landfills have proven to besecure, especially if they are provided with lined facilities These are installed at the bottom orsides of a landfill to control groundwater pollution by the liquid mixture (leachate) formed bythe interaction of rainwater or snowmelt with waste material

Types of liners for leachate containment are basically (1) clay liners, (2) geomembranes,and (3) composite liners consisting of geomembranes and clay liners Of these, until recently,the most frequently used liners were clay liners, which minimized leachate migration byachieving permeability values as low as 5×10−8to5×10−9cm/sec However, owing to the largethickness (0.6 to 2 m) requirement and chemical activity in the presence of organic-solventleachates, geomembranes have been increasingly utilized for landfills

13.6.1 Design of Landfill Liners

As shown inFigure 13.9andFigure 13.10, the important components of a solid materialcontainment system are (1) a leachate collection or removal system, (2) a primary leachatebarrier, (3) a leachate detection or removal system, (4) a secondary leachate barrier, and (5) afilter above the collection system to prevent clogging Some of the design criteria (Koerner,1998) are as follows:

1 The leachate collection system should be capable of maintaining a leachate head of lessthan 30 cm

2 Both collection and detection systems should have 3-cm-thick granular drainage layers thatare chemically resistant to waste and leachate, and that have

FIGURE 13.10

Typical cross section of a clay/geomembrane-lined composite landfill.

3 The minimum bottom slope of the facility should be 2%

13.6.1.1 Design Consideration for Clay Liners

In the case of clay liners, the U.S Environmental Protection Agency (EPA) requires that thecoefficient of permeability be less than 10−7cm/sec This can be achieved by meeting thefollowing classification criteria:

1 The soil should be at least 20% fine (Section 1.2.1)

2 The plasticity index should have been greater than 10 (Section 1.2.2)

3 The soil should not have more than 10% gravel size (>4.75mm) particles

4 The soil should not contain any particles or chunks of rock larger than 50 mm

It is realized that liner criteria can be satisfied by blending available soil with clay materialslike sodium bentonite

13.6.1.2 Design Considerations for Geomembrane layers

Geomembranes are mainly used in geotechnical engineering to perform the functions of (1)separation, (2) filtration, and (3) stabilization In this application of geotextiles, the functions

of separation and, to a lesser extent, filtration are utilized Owing to the extreme variation ofsolid waste leachate composition from landfill to landfill, the candidate liner should be testedfor permeability with the actual of synthesized leachate

In addition to the permeability criterion, other criteria also play a role in geomembraneselection:

1 Resistance to stress-cracking induced by the soil or waste overburden

2 Different thermal expansion properties in relation to subgrade soil

3 Coefficient of friction developed with the waste material that governs slope stability criteria

4 Axisymmetry in tensile elongation when the material is installed in a landfill that is

founded on compressible subgrade soils

In selecting a geomembrane material for a liner, serious consideration should also be given toits durability, which is determined by the possibility of leachate reaction with the

geomembrane and premature degradation of the geomembrane For more details on

geomembrane durability and relevant testing, the reader is referenced to Koerner (1998).According to the U.S EPA regulations, the minimum required thickness of a geomembraneliner for a hazardous waste pond is 0.75 mm

13.7 Application of Groundwater Modeling Concepts in Environmental

Geotechnology

A major challenge that goetechnical engineers face in the design of earthen structures

associated with environmental protection is the evaluation of the effects of pollutant or

contaminant migration with groundwater such as the rate of seepage, the extent of the