Hydrostructural Geology

Hydrostructural Geology

Thomas D. Gillespie, P.G.

Copyright © 2011, Thomas D. Gillespie, P.G.

Why do we have continuing education requirements for
Professional Geologists?

Excerpted from an Amplified Record of Experience for a
PG Licensing examination application submitted in 2011

The [activity] revealed extensive soil and GW contamination. MWs were installed
into the Precambrian felsic gneiss overburden and sampled.

MWs were installed into the ----------- Wissahickon saprolite to determine the
extent of the GW plume. The -------- Wissahickon sediments accumulated in a rift
basin on top of Laurentian continental crust and consists of muscovite and
tourmaline-apatite-staurolite-kyanite-garnet-bearing metamorphic mineral
assemblages.

Overview of Hydrostructural Geology

Elements of hydrostructural geology - hydrologically relevant structures

Structural domains and structural characterization for hydrostructural
analysis

Natural planar systems

Heterogeneity and Anisotropy

Description and measurement of planes

Statistical management of structural data for hydrologic analysis

Hydrostructural Analysis


An analytical method to:

develop a second order approximation of groundwater flow in
bedrock aquifers;

estimate direction and magnitude of structurally controlled
transport anisotropy;

delineation of groundwater contamination

water resource management


Purpose of model development

Combine non-random structural data with field hydrologic data to model
groundwater flow anisotropy and the distribution of solutes

Apply aquifer hydraulics equations developed from aquifer stress tests to
the non-pumping conditions of the natural field hydraulic gradient to derive
a numerical basis for finite difference modeling, to support predictions of
aquifer responses to extraction and the design of remedial systems

Provide a rapid, cost-effective, theoretically-supported first order
approximation of groundwater flow and solute transport in fractured rock
aquifers to guide additional phases of investigation or to provide the
technical rationale for investigation limits

Predict behavior of aquifer under pumping conditions to support either
extraction or injection based in-situ remedies



Is not:

numeric modeling method

particle tracking method

mass transport model


Hydrostructural Modeling

In contrast to numerical models of fracture flow, hydrostructural
methods are:

Rapid
Inexpensive
Testable

Requires:
Structural data
Hydrologic data


Flow through fractured media

As in porous medium aquifers, there are two physical domains in
fractured rock aquifers:

Solid matrix

Fluid-filled pore space



In a porous medium, the pore spaces:

are distributed uniformly throughout the aquifer

occupy a significant percentage of the total volume

bounded by grain boundaries with generally random orientations

Flow occurs only in the pore spaces



In fractured media, the fluid filled pore spaces:

are planar discontinuities in the otherwise solid matrix

occupy only a small percentage of the total volume

occur at non-random orientations

Flow occurs both in the planar secondary pore spaces as well as in the
primary porosity of the rock matrix.



In modeling a porous medium aquifer the solid matrix is generally
ignored

In a fractured rock aquifer, the matrix must many times be
considered because it is porous and so contributes to the overall flow

Most flow occurs in the fractures, referred to as secondary porosity.
Although only a small component of flow derives from the matrix, it
can be a major component of storage and, in consequence, can not
always be discounted


Many existing models attempt to account for the two different flows:

Dual Porosity Models: Involve a routine to model flow through the
porous matrix in addition to routines to model flow through the
planar discontinuities. In reality, the flow from the solid porous
matrix (primary porosity, is a release from storage and flow does not
occur over any appreciable horizontal distance.

The flow is governed by pressure differences and can be in any
direction as long as it is toward a water-bearing fracture.

As a result they are complicated and similar to the models for
heterogeneous unconsolidated aquifers in which heterogeneity is
assumed to be the result of the presence of multiple but sub-parallel
layers with differing k values.


In those unconsolidated model situations, the real function of the
low k aquitards is storage and release of water – the presumption
in models is that flow through the low k zones between aquifers is
vertical and therefore flow within them is not modeled other than
to determine the flow velocity and release rate.


What is complicated in most fracture flow models is that the sub-horizontal
layers common to unconsolidated aquifers become three-dimensional blocks with
release to planes on all sides.



Existing models of fracture flow are based on measured anisotropy under
stressed conditions – they measure directional anisotropy of permeability
under artificial hydraulic gradients. A model is then constructed using
induced permeability tensors under induced hydraulic gradients as the
anisotropy field and fractures with random orientation and spatial
distribution – in that model, it is the behavior of the water under stress
which is being modeled and the assignation of random fracture orientations
ensures that the matrix and discontinuities are not actually modeled

Hydrostructural begins with the premise that natural groundwater flow
in fractured rock is controlled by a combination of natural hydraulic
potential and the combined orientations of the field hydraulic gradient
and planar discontinuities in the rock mass.


Structural Basis of Hydro-Structural Geology

Non-random nature of planar discontinuities;
Spatial distribution

Plotting and statistical treatment of structural data

Definition of dominant plane sets and ranges of variability

Systematic joints

Non-systematic joints

Fold-Related Shear Joints

Bedding plane partings


Hydro-Structural Geology

Hydro-Structural Theory

Analytical model

Mathematical basis and derivation of equations;

Expansion of well-established mathematics to field conditions and to
incorporate structural data


Utility of Model
predictive model

analytical tool

little hydraulic data and minimal structural data

simple format and data input

supported by hydraulic theory

results in readily testable predictions


Utility of Model
cost-effective

focus additional stages of investigation

supports remedial decisions

basis for remedial design


Limitations

not a dual porosity model – does not account for matrix diffusion and
related tailing/recession effects

can not model complex hydrogeochemical process - not fate and transport
on its own but can be combined w/f&t models

utility within a single structural style – does not translate across formational
boundaries into other rock types with unique structural styles

does not take into account hydraulic effects of fault planes but can be
combined with fault plane solution

graphic output limited – not an illustrative model


Need for hydrostructural methods

Existing fracture flow
models focus on either
pipe flow or parallel plate
flow theory and are
almost devoid of
knowledge of the actual
flow pathway network.

That would be similar to
modeling flow in a
porous medium without
knowing whether the
medium is sand or
gravel.


Groundwater Flow Modeling in Fractured Rock

Currently, there is a great and widespread misunderstanding in the
groundwater science and engineering community about how
groundwater flows in bedrock aquifer systems, with most people making
one of several fundamental errors in concept, typically based on
erroneous assumptions.


Assumption: Groundwater flow is either parallel to
the strike or down the dip of planar discontinuities

Strike

Hydraulic Gradient

Water Table – slope of
groundwater surface Sedimentary bedding



The strike of any plane is, by
definition, horizontal and
groundwater only flows down
a gradient. Strike

Groundwater can not flow
Hydraulic
down the dip of a plane Gradient
unless it is the same dip as the
hydraulic gradient.
Water Table – slope
It actually flows at some Sedimentary
of groundwater
“apparent dip” close to the surface bedding
strike of the planes –
effectively, along strike.



In order for there to be a
hydraulic gradient,
Strike
groundwater must flow, on
average, in that direction.
Hydraulic
Gradient

Therefore, there must be
Water Table – slope
cross-strike water-bearing Sedimentary
of groundwater
structures which are NOT surface bedding
formed by the dip of the
plane.


Assumption: Groundwater flow is controlled by a
single fabric element

Strike

Sedimentary bedding
Joint planes



Most investigators and regulators interpret groundwater flow
according to the mantra:

“Groundwater flow is generally parallel to strike.”

Strike of WHAT?


Strike

Sedimentary bedding
Joint planes

Groundwater flow is through an aquifer of finite thickness and
through a network of discontinuity sets of different orientations, all of
which are saturated and transmit water and each of which
contributes to flow pathways and the overall direction of flow.

Assumption: Groundwater flow is dominated by
no single fabric element

Most fracture flow models assume a random distribution of
planar discontinuities where in fact, actual rock fractures are
non-randomly distributed in space and orientation and impart
some anisotropy to flow.


Assumption: Groundwater flow is dominated by
no single fabric element

Dual Porosity Models – assign hydraulic characteristics to both the
fractures and matrix and model the system as a continuum

Discrete Fracture Network Models – use stochastic and deterministic
“fractures” combined with measured hydraulic data to assign values to
a finite element grid based on a Monte Carlo sampling of relevant
distributions


From Fetter, 2001. This is
a non-structural method of
estimating anisotropy
which requires
measurement of the
hydraulic conductivity in
two perpendicular
directions during an
aquifer testing program

Assumption: Increased randomness of planar fabric
elements results in more complex flow patterns

Schematic of
fracture network
traces and
groundwater
elevation contours
and flow arrows at a
CERCLA Site at
which bedrock
aquifer was
contaminated.


Assumption: Increased randomness of planar fabric
elements results in more complex flow patterns

Plan View

3 mm

This example depicts a situation in which randomness of pore
space orientation is maximized but flow is uniform at any
scale above that of the grain size distribution.


Resolved the measured
gradient into the known
orientations of joints
and determined that
flow is not erratic as a
result of joint
distributions and
patterns and that flow
anisotropy is moderate
in two directions and
absent in the third
around the semi-radial
flow pattern


Assumption: The occurrence of multiple, non-random, planar
discontinuity fabric elements increases the potential for dispersion
(lateral spread) and transport in random or unpredictable directions

Plan View


Assumption: Groundwater flow can not be predicted using
overall water balance analyses and domainal scale conceptual
models


Conceptualizing Flow in Fractured Media

The foregoing assumptions have become de facto conclusions which have
been developed and accepted by the industry, in the near- complete
absence of structural geology data and without any structural analysis.

Principle among those conclusions, which are pervasive among
computer modelers are:

the incorrect premise that groundwater flow is controlled by no

the incomplete premise that groundwater flow is controlled by a


Conceptualizing Flow in Fractured Media

In most cases in actual practice, investigators tend to default to
the concept of the Porous Medium Equivalent

Can be valid either for some scales of observation or for studies
in which the domain scale exceeds the Representative
Elemental Volume by a factor large enough to approximate
PME.

Not universally the case and PME does not account for
anisotropy which is inherent in most fractured rock aquifers.


Porous Medium Equivalent

On some scale of observation, a fractured rock aquifer can be
considered homogeneous in terms of the sizes of the solid matrix and
the orientations of bounding fractures.

1m 1,000 m


A few basics :

Several fundamental concepts typical of fractured rock aquifers
and critical to characterizing flow:

Representative Elemental Volume

Domain

Field Gradient


A few basics :

These concepts apply equally to flow in a porous medium on a
micro-scale, but become necessary when considering flow in
fractured media for two reasons:

The blocks of rock matrix tend to be large compared with the
pore spaces so local scale heterogeneities are inherent

The pore spaces are not randomly oriented in fractured rock as
they are in most unconsolidated formations



Begin in familiar
territory – a porous
medium.

A porous medium is
characterized by the
presence of a pervasive
solid phase or matrix.

The remaining volume,
or void space, is occupied
by one or more fluid
phases.



Characteristic of a porous medium is that both the solid phase and void
spaces are pervasive – they are distributed throughout the volume of the
aquifer.

If samples are collected of sufficiently large volumes of the medium at
different locations within the domain, each sample will contain both the solid
phase and void spaces at representative scales and orientations.

Bear, 1993



At the same time, if a sample at some point in the domain must provide
the data to support conclusions or inferences about what happens at that
point and immediately adjacent volume of the medium in terms of
groundwater flow, the size of the sample can not be too large.

The volume of sample which satisfies all the conditions is known as the
Representative Elemental Volume (REV).
Bear, 1993


We can therefore define a porous medium as a
multiphase material characterized by the following
features:
A Representative Elemental Volume which can be identified such that no
matter where a template of the REV is overlaid within the entire volume
of the domain it will contain both a solid phase and void space. If such
an REV can not be identified for a given domain, the latter does not qualify
as a porous medium domain.

The size of the REV is such that the parameters which represent the
distribution of the solid phase and void spaces are statistically
meaningful.
Bear, 1993


The size of an REV, therefore, must be larger than the scale of microscopic
heterogeneities created by individual geometries of the solid phase particles
and void spaces, and much smaller than the scale of the domain of interest.

It is the heterogeneity within the domain of interest which counts when
determining the size of the REV.

Bear, 1993

Considering groundwater flow on the domainal scale, the size of an REV
must be larger than the scale of microscopic heterogeneities created by
individual geometries of the solid phase particles and void spaces, smaller
that the scale of the domain of interest but must also contain all elements
which not only contain and convey groundwater, but which also affect the
overall flow characteristics.



In terms of groundwater flow, the REV must include the solid phase and all
of the boundaries along which water moves past each portion of matrix.

In fractured rock, it is
apparent that the REV must
include the rock matrix and
all fracture sets which occur
pervasively throughout the
formation.

The elements of the REV impart heterogeneity to groundwater flow on the
scale of the REV.


In the case of porous media, the boundaries occur at random
orientations but typically within a finite and regular maximum
distance.

In the case of fractured rock, the orientations are generally regular
but the distances are variable


REV Scale Heterogeneity also Occurs in Porous Media.

Grain boundaries deflect groundwater in cross-gradient pathways so the
REV must be large enough to encompass all dimensions and orientations of
grains. This becomes more critical in non-arenaceous unconsolidated
deposits in which mineral habits are plate-like or acicular.


So, even in a porous medium in which flow is considered mostly
homogeneous there is no such thing as flow directly down the average
hydraulic gradient on scales of the REV. Flow only becomes uniform in
relation to the overall flow field (defined by contour lines) on scales of the
domain.


Domain

The previous description of flow provides a default definition for the
concept of the domain for groundwater flow.

The domain is the scale of observation which is larger than the REV within
which average flow can be described and predicted to be essentially
homogeneous* within the context of the problem of interest.

That is obviously a subjective designation and one which can be fluid if, for
example, the area of interest increases beyond a site boundary.

* This does not imply isotropy


Domain

In terms of a porous medium, the REV is small so heterogeneity of flow can
be ignored on most scales of observation.

Domain
The same definition of the domain applies to flow
through a fracture network.
The Representative Elemental Volume

Plan View

The smallest volume of aquifer matrix
which contains at least one of each of
the water-bearing fabric elements

Domain
In this schematic there are two REVs, but both have similar
domains.


This pronounced difference between REV and Domain in
fractured rock aquifers can be understood by the differences
between flow under the influence of the Field Hydraulic Gradient
compared with the In-Plane Hydraulic Gradient

The Representative Elemental Volume

In fractured rock
aquifers the hydraulic
gradient on the scale of
the domain is referred to
as the
Plan View
Field Hydraulic Gradient


Example

A site in a jointed
diabase intrusion into
the Newark-Gettysburg
Basin.

Groundwater contours
on the site revealed a
semi-radial flow from a
high toward two steams

Obtained 1906 USGS
topo maps and mapped
features absent modern
development.

Streams described a
radial pattern from top
of ridge created by
diabase.

Watershed boundaries.

A divide crosses the site
exactly in the center of
the semi-radial flow
pattern

Groundwater flow
arrows using divides
and perennial streams

The hydrology made
sense.

In this case the domain
is the multi-acre site,
but could be defined as
the area within which
linearly averaged flow
intercepts the measured
contours normally.


Example 2


Groundwater Flow in Planar Discontinuities
Field vs. In-Plane Hydraulic Gradients
The designation of the Field Hydraulic Gradient for bedrock flow
problems is predicated on the complimentary condition that the
hydraulic gradient(s) within the different components of the REV
differ from the Field Gradient.

Need to begin with the examination of flow through a single planar
discontinuity


Flow through a plane can be complicated by variables such as aperture
and wall roughness, but the geometry and mechanics of flow can be
understood and modeled with relative ease, regardless of the orientation
of the overall flow field.

Most fracture flow models
focus on a mathematical
description of flow through
individual fractures and focus
on directional anisotropies of
hydraulic gradients.


Understanding and modeling flow through that same plane is a
completely different problem when other, connected planes are present at
different orientations.

As all pore spaces below the phreatic surface are saturated, flow occurs
in all of them. How can the influence of each on the overall flow field be
understood and modeled?


The first issue to resolve is the geometry of how water moves through a
planar discontinuity.

Flow occurs within the void space of a planar discontinuity and the flow
components within the discontinuity must be resolved to understand the
flow, especially in situations in which more than one plane and multiple
orientations are present.



The need to resolve the flow into components derives from the fact the
groundwater flow is a vector and the discontinuity is planar.

In most cases the orientation of the plane is not parallel to the flow vector



Except for absolutely vertical and horizontal planes, each plane can be
described in terms of a strike and a dip.

Groundwater flow does not flow precisely parallel to either of those.


Groundwater can not flow down the dip of a plane in a situation in
which the dip direction is the same as the hydraulic gradient but at a
different angle.

The hydraulic gradient, by definition, is the dip angle which is
constrained by the difference in hydraulic potential between points
and, therefore, is the numeric representation of the driving force of
groundwater flow.



e.g., in a porous
medium, flow is
constrained by the
difference in head
potential and does
not flow down a
pathway because it
is available.



Likewise, groundwater can’t flow down the dip of a plane in a
situation in which the dip direction is opposite the hydraulic
gradient.

How does groundwater flow within a plane and why?


Resolution of the Field Hydraulic Gradient into a
Sub-Vertical Plane

Because hydraulic
gradients are close to
horizontal,
groundwater
generally flows along
the strike of the
plane but can not
flow precisely
Xtaln Rock parallel to strike.


Resolution of the Field Hydraulic Gradient in a
Sub-Vertical Plane
The upper surface of the water table as resolved into the plane occurs at an
in-plane gradient equal to the apparent dip observed in that plane.

In such a case, the
magnitude of the field
hydraulic gradient is
greater than the
magnitude of the
resolved hydraulic
gradient.

Sub-Vertical Plane
The only exception to that general condition is where the strike of the
plane is coincident with the azimuth of the flow vector in which case
flow would be precisely parallel to strike and the field gradient would
be equal to the in-plane gradient.

Viewed normal to the plane, the true dip of the field hydraulic
gradient is greater than the apparent dip of the in-plane gradient.

ΔX
Strike of Plane

ΔY ip
i Dip of Plane

Field Hydraulic
Gradient i

In-plane Hydraulic Plane A
Copyright
Gradient ip © 2011,
Thomas
Δ X1 Vertically D.
exaggerated Gillespie,
P.G.
Therefore, groundwater flow through planes at any angle to the field
hydraulic gradient flows under a lesser gradient than the field gradient.

Sub-Vertical Plane

Because:

flow is within a planar discontinuity;

that discontinuity is a saturated, three-dimensional pore space;

water flows approximately parallel to the strike of the plane but
down a gradient which is not equal to the field hydraulic gradient;

the In-Plane Hydraulic Gradient (ip) can be resolved and quantified
both graphically and mathematically.


Sub-Vertical Plane
Plane A
N Plan View intercepts the
Field Hydraulic
Gradient at some
angle.

Flow sub-parallel
to the strike of
the plane results
in an in-plane
Plane A gradient which is
different than the
field gradient


Sub-Vertical Plane
Plan View

Δ Y /Δ X = i
Field Hydraulic Gradient ΔX
Δ X1

Δ Y/Δ X1 = ip

Plane A
In-plane Hydraulic Gradient

ΔX

ΔX
Ө1
Δ X1
Δ X1 > Δ X
Δ Y = Const. Δ Y /Δ X = i > Δ Y /Δ X1 = ip

Resolution of the Field Hydraulic Gradient to an
In-Plane Gradient
The in-plane gradient (ip) for any sub-vertical plane striking Ө°
from the azimuth of the field gradient (i) can be calculated.

Δ X1
Ө1
ip
i Δy
Δ X1

ΔX
Plane A

ΔX Δ X1 = ΔX/cos Ө1
ip = Δy/(ΔX/cos Ө1)


Natural Systems of Planar Discontinuities

In most settings, fractures do
not occur as individual
randomly oriented planes or as
sub-parallel ‘sets’ with only a
single orientation. In other
words, fractures occur in
multiple sets at statistically
predictable, non-random
orientations.


As a result, the sum total of planar discontinuities in rock masses can
be categorized into a hierarchy based on the structures present,
structural relations, respective frequencies of the structures and the
scale of observation.
The simple problem of resolving
Strike
the in-plane hydraulic gradient
within a single plane must be
expanded to incorporate the
various planar systems within a
rock mass to determine whether
there is a single structural
control and anisotropy, or
whether the network forms a
Joint planes Porous Medium Equivalent.


Began with a single plane at some angle to the field hydraulic gradient,
and the resolution of flow onto that plane.
We can increase the complexity of the system by adding additional sets
of discontinuities. That becomes the basis of hydrostructural modeling,
as well as the basis of the fundamental units of the hydrostructural
framework.

But first . . . .

Joint traces


The Structural Geology of
Planes

STRIKE & DIP
STRIKE = trend (azimuth, bearing) Another definition of Strike =
of a structural contour on a plane. trend of a line connecting points of
equal elevation on a plane.
………of a horizontal line on a
plane.

……….water level line on a plane.

In the field this horizontal line is
defined by using bulls eye level to On a plane, structural contours
hold compass as a horizontal plane will be straight lines with equal
and placing edge of compass against spacing – and all are parallel to
surface to be measured. strike.

Hence measuring strike of a plane is
the determination of a structural
Source: Donald Wise
contour line on the plane.

STRIKE & DIP
DIP = the angle from the horizontal to the
plane as measured in a plane
perpendicular to strike (or perpendicular
to a structural contour) .

NOTE: Dip must be measured in the
vertical plan (compass must be held in
vertical plane).

Dip is measured in direction of maximum
inclination ( normal to strike)

Measured in any direction other than
normal to strike, one measures an
APPARENT DIP which is somewhat less
than true dip.

NOTE: Apparent dip on any plane
measured parallel to strike is 0. (i.e. the
dip on a structural contour is zero)
Source: Donald Wise

REPRESENTATION OF A PLANE ON A MAP.
Ideal is structural contours on the plane (for a true planar surface they
are straight lines with equal spacing and all parallel to each other).
MAPS

Vertical plane 1000, 2000, 3000 contours all in same place.

Closer the spacing of the structural contours the steeper the dip of the plane.

Vertical plane has all the contours at the same place.

Commonly we only measure a tiny bit of the total plane and hence use the
symbol

If we are measuring a parallel set of planes (pile of dipping
sediments) they all will have the same strike and dip.

Source: Donald Wise

DETERMINING DIP FROM STRUCTURAL
CONTOURS - RIGHT SECTIONS
A right section is a view of the
plane running along a line at
right angles to strike.

Draw some convenient line (AB)
perpendicular to strike.

Draw line AB off the map,
marking off points A, B &
elevation points.

USING SAME SCALE AS MAP
go down to proper elevations,
draw plane & measure dip.

Source: Donald Wise

BASIC METHOD : RIGHT SECTIONS

A sandstone bed strikes N30W and dips 30 Either mentally or
SW. Its outcrop width on a flat surface is physically fold the
100m. Find its true stratigraphic thickness. paper along this line to
make a right section
If we could look at a true cross-section drawn below the line.
at right angles to the strike, we could measure
off the true thickness (to scale. Below = 1 cm Because this is a right
= 100 m). section the full dip of
30’ can be used to draw
Draw any random line FF’ at right angles to top and bottom of the
strike. bed in the cross-section.

Measure true thickness
in right section, normal
to bed, using map scale.

Source: Donald Wise

RIGHT SECTIONS AT RIGHT PLACES
A Coal Bed striking N20E, 50 NW Draw a line through the shaft,
crops out as shown. A mine shaft is to perpendicular to strike.
be drilled 500 meters due west of the
outcrop. How deep is the coal bed in Make this line FF’ a fold line to
the shaft? draw a right section which will
contain the shaft.
Select come convenient scale and
draw the map. Draw the dipping coal bed and the
shaft in this section.
Using the scale, measure the depth
of the shaft (550m).

Source: Donald Wise

The top and bottom of a
sandstone crop out at
elevations of 600 and 200
meters, respectively, at the
locations shown on the map.

The strike and dip at both
locations is N60~E, 20 NW.

Calculate the thickness of
the sandstone.

Source: Donald Wise

GREASY DRIP SANDSTONE AREA
The Greasy Drip Sandstone is a major
reservoir rock in the Petroleum Patch
Quadrangle. A small exploration
company owned by W.E. Findum and
U.R. Lost has hired you to get some
data from the outcrop above.

What is the strike of the sandstone?
_____
What is the dip of the sandstone?
_____ to the _____?
The thickness of the sandstone is
_____?
The depth to the top of the sandstone
at Grimy Station is _____?
What is the vertical thickness of the
Greasy Drip SS that would be
intersected in a coring made at Grimy
Station? _____
Source: Donald Wise

GREASY DRIP SANDSTONE AREA

Source: Donald Wise

ONE POINT PROBLEMS
Given one point on a map where the strike, dip, and elevation of a planar bed
are known, draw the structural contours for this bed throughout the map area.

For example, in an area of very sparse exposure, you have only one outcrop of
a coal bed, point A, at an elevation of 1900 feet and strike N60W, 30 SW.
Nevertheless, you need to complete a geologic map of the concealed line of
outcrop of the bed across the area and get the predicted dill depths to the coal.
These determinations will require a knowledge of the structural contours
across the area.

ONE POINT PROBLEMS
Extend the line of strike from A to some convenient place off the map. This line is a
structural contour and all locations along it are at 1900 foot elevation.

Draw a line perpendicular to the structural contour. This will be a right section.
The line is at the same elevation as the structural contour (1900 feet). Using the
same scale as the map, put in the elevation lines below the 1900 foot elevation line of
DCE and mark their elevations as shown.

This is a right section, so the true 30 degree dip can be plotted starting from point C
(which is at 1900 feet elevation).

Find the intersections of the dipping plane in the cross section with the
appropriate elevations (F, G, H, I, etc.) and project them up to the surface as
L, M, N, O, etc. These are now map points below which the elevations of the
plane are known.

Structural contours can now be drawn through each of these points parallel
to the main 1900 foot contour (AB). The same spacing and trend of contours
can be continued across the entire map.

Source: Donald Wise

How deep
would you
need to drill
a well at
Point B to
intersect the
top of the
formation
which
outcrops at
Point A?

Contour Interval = 100 m

Two-Point Problems
Determine the Strike and Dip

Three Point Problems
Given 3 points on a planar Draw structural contours through the
surface, find the strike & dip high and low points parallel to the
of that plane. strike. (AE&CG)

Connect the highest and lowest Draw a fold line perpendicular to strike.
of the three points on the map. Decide on elevation of this line using
(A&C) same scale as map, draw elevation lines
below the fold line for cross-section.
Interpolate between these
points for a point of elevation Project the structural contours of high
the same as that of the and/or low points onto the cross-section
intermediate elevation point. and draw the dipping plane on this right
(B) section.

Join these two points of equal *Measure its dip (Angle GEH).
elevation as a line of strike.
(BD)
*Read off this strike with
respect to north

Source: Donald Wise

Three Point Problem - Method 2
Draw two lines connecting the highest elevation point with both the lowest and
intermediate points: (AC; AB).
Scale off divisions of equal elevations along each line.
Connect points of equal elevations with structural contour lines.
Construct right section as in Method 1.

Interpolation
A common geologic problem is to be given some numerical value (elevation,
for example) at two locations on a map. Intermediate values need to be
calculated or INTERPOLATED as proportional distances along the line
joining the two points.

THE PROBLEM: Two points A and B are located on a map as shown and
have elevations of 435 and 715 feet respectively. Find a location
proportionally spaced between them which would have a proportional
elevation of 683 feet. While you are at it, find the proportional locations for
500, 600, and 700 feet elevations.
B 715
A 435

Draw the line connecting the two locations, A and B.

Source: Donald Wise

Interpolation

From the end of this line with the lower elevation (point A in this case)
draw a random line (AC) at about 30 to 45 degrees from AB.

Use some scale of a ruler (in tenths) with values which correspond to the
elevation differences between A and B. Put the 4.35 value of the ruler on
the 435 ft elevation of point A and locate point D at the same value as the
elevation point B (7.15 for the 715 foot elevation in this case).

B 715
A 435

Source: Donald Wise

Interpolation
Using the scale of the ruler mark off on line AD all the locations corresponding to all
the elevations you seek (6.83, 500, 600, 700).

Make a large triangle by connecting points D and B. By ruling parallel to line DB
make a series of similar triangles through each of the points you located in the above.

A THEOREM OF PLANE GEOMETRY IS THAT DISTANCES WHICH ARE
PROPORTIONAL TO THE LENGTHS OF LEGS OF ONE SET OF SIMILAR TRIANGLES
ARE ALSO PROPORTIONAL TO THE OTHER LEGS OF THOSE TRIANGLES.

Thus, the locations along line AB have
spacing proportional to their elevations.

Outcrop Patterns

If the structural contour on some horizon has the same elevation as the
topography at that point, then that bed crops out at that location.

Conversely, if an outcrop occurs at some location, the structural contour
of that elevation on that unit passes through that point.

Source: Donald Wise

Outcrop Patterns
In general, the outcrop of a dipping plane will “V” in crossing a valley,
such that the “V” will point in the direction of dip.

With flat dips and steep stream gradients these V’s might point in
other direction.

If there is no V at all, then the plane is very steep to vertical.

This V principal applies to all kinds of planes: beds, dikes, faults,
unconformities.

Source: Donald Wise

A planar coal bed crops
out a points A, B and C.

What is the bed’s
orientation _______

Draw the outcrop
pattern

How deep would you
need to dig at point D to
intersect the coal?
__________

Source: Donald Wise

Horsefeather Creek Area

Structural Contours on top of Horsefeather Sandstone. Construct a right
section.
What is the orientation of the unit? __________
How deep would you drill at P _______ and Q________ to intersect the
unit?
Draw the outcrop pattern. Source: Donald Wise

Draw section FF’, the axial trace, and fully describe the structure
(The numbers represent stratigraphic superposition)

Source: Donald Wise

Describe the structure at
left.

What is the direction of
dip of the ss? _______

What is its strike?
_________

Source: Donald Wise

The St. Valentine Sandstone
crops out along ILUVU
Creek Valley as shown.

Sketch Section A-B.

Source: Donald Wise

Faults
Can be either a barrier to groundwater flow, or a conduit

Tend to be the cause of linear topographic regional lows (valleys)

Important in hydrologic evaluations

Use law of V’s to get dip directions.

Erosion on upthrown side will make the outcrop of a dipping bed migrate
in the direction of dip.

Upthrown side brings up deeper, older rocks for exposure by erosion.


Hydrogeologic Nature of Faults and Fault Zones

The presence of faults / fault zones can have many and varied effects on
groundwater flow systems depending on the spatial relationships between
rock types on opposing fault blocks, the orientation of the fault in relation
to recharge and discharge areas, the degree to which brecciation has
resulted in a fault gouge infilling

There are some things that most faults have in common which can be used
in the development of conceptual hydrogeologic models before designing
any kind of exploration program.



Faults / fault zones are:

Zones of fluid accumulation
Integral components of Secondary Porosity Network
Brecciation

Zones of fluid storage
Fault gouge forms a porous medium

Pathways of fluid movement
mineral / ore deposits
seismic pumping, natural hydraulic fracturing



Faults tend to be long in comparison to local domains of
water-bearing structural rock fabrics; i.e., faults tend to
cross formational contacts and, therefore, create pathways
for water to move from one flow domain to another.

Consequently, faults can provide the regional hydrogeologic
continuity necessary for regional water budget balance.


Fault Zone Effects on Local / Regional Hydrogeology


Regional faults are easily eroded and tend to form linear topographic
lows, with the result that groundwater in both fault blocks is at a higher
hydraulic potential than is the water in the fault zone. In such cases,
groundwater flow must be along the fault zone, and dissolved regulated
compounds can not be transported to the opposite fault block.


Fault Problems

Source: Donald Wise

What kind of fault?
Which way does dike A-B dip? Why?

Which side went up?
Give approximate azimuth and plunge of
the net slip and explain how you got it.

M, S, T are all faults.

Which is the oldest fault?

If all the fault movements are dip slip, mark
the up and down for those faults where it
can be determined.
Source: Donald Wise

Guano Creek Field Area

Source: Donald Wise

Guano Creek Field Area
Two of the more intrepid members of our class, Jon and Dave, have been mapping in
the Guano Creek region, so named for the famed bird rookeries at its headwaters.
(The nearly extinct “tweety bird” is rumored to roost in that area.) They are trying
to locate the source of the sulfide ores which oxidize to form a high concentration of
sulfuric acid in Guano Creek, a condition which prompted them to make a boat out
of lead to withstand these corrosive waters. Using this field vehicle, they have
produced the accompanying map but are still up the creek, still in their water craft,
still without finding the ores. They need help (in many ways). Should you wish to
give a concise one-line description of their condition, please feel free to do so. In
addition please answer for them:
Why is the outcrop width of the Sludge Bucket Sandstone (stippled pattern on the
map) three times as wide on the SW side as on the NE side?
Describe the Guano Creek fold in as full a detail as possible, including the general
orientation of cleavage you might expect associated with it.
In as much detail as possible describe Jon’s major fault (including approximate
strike, dip direction, approximate motion sense, fault type, relative age).
In as much detail as possible describe the Tweety Bird fault (same items as above).

Source: Donald Wise

Guano Creek Field Area – Solutions

Why is the outcrop width of the Sludge Bucket Sandstone (stippled
pattern on the map) three times as wide on the SW side as on the NE side?

Asymmetric fold – N.E. limb is close to vertical.

Describe the Guano Creek fold in as full a detail as possible, including the
general orientation of cleavage you might expect associated with it.

Asymmetric, N.W. Plunging Anticline.

In as much detail as possible describe Jon’s major fault (including
approximate strike, dip direction, approximate motion sense, fault type,
relative age).

080 ° - 90, Right Lateral Transform, younger fault.

In as much detail as possible describe the Tweety Bird fault (same items
as above).

045, Dipping S.E., Reverse, older fault.
Source: Donald Wise

Systems of Planar Discontinuities

Planar discontinuities do not occur randomly within a rock mass.

Occur in response to stresses in the rock mass which can be:

Tectonic

Residual

Unloading


Occur in sub-parallel sets which are pervasive and are oriented along
preferential orientations

Tectonic Joints

Generally occur in sub-vertical, near-orthogonal conjugate sets of tension
joints

One set forms first and is referred to as the
Systematic Joint Set

The second set is the Non-Systematic Joint Set, also known as Cross
Joints.


Tectonic Joints

Source :Twiss & Moores, 2007

Tectonic Joints
Systematic Joint Sets are the longest of the two and can intersect
numerous non-systematic joints.

Non-Systematic Joint Sets extend only from one systematic joint plane to
the adjacent plane – they can not cross a systematic joint because tensile
failure cannot be propagated across a void.

Non-Systematic Joint Sets, therefore, are composed of a series of short,
offset joints which connect the longer systematic joint planes. They tend to
occur at more varied orientations within a lrger range than systematic
joints.


Fold-Related Joints

Although also the result of tectonic stresses, fold-related joints are shear
joints and occur in distinct patterns of conjugate sets.

Source :Twiss & Moores, 2007

Fold-Related Joints
A series of tension joints can also be superimposed on conjugate shear
joint sets.


Fold-Related Joints


Residual Stress Joints
Tension joints which form in
two distinct situations:

Cooling joints – tend to
be sub-vertical, but can
occur locally at any
orientation

Unloading joints – tend
to be sub-horizontal


Description of Joints –USEPA, Manual of Field Procedures

Description of Bedding or of Joint or Fracture Spacing: Description
should be according to the following:

Spacing Joints Bedding or Foliation

< 2 in. Very close Very thin
2 in. to 1 ft Close Thin
1 ft to 3 ft Moderately close Medium
3 ft to 10 ft Wide Thick
>10 ft Very wide Very thick
(after Deere, 1963)

Description of Joints –USEPA, Manual of Field Procedures
Weathering: Terms used to describe weathering are described below:
Descriptive Term Defining Characteristics

Fresh Rock is unstained. May be fractured, but discontinuities
are not stained.

Slightly Rock is unstained. Discontinuities show some staining on
the surfaces of rocks, but discoloration does not penetrate
rock mass.
Moderate Discontinuity surfaces are stained. Discoloration may
extend into rock along discontinuity surfaces.
High Individual rock fragments are thoroughly stained and can
be crushed with pressure hammer. Discontinuity surfaces
are thoroughly stained and may be crumbly.
Severe
Rock appears to consist of gravel-sized fragments in a
“soil” matrix. Individual fragments are thoroughly
discolored and can be broken with fingers.

Formation-Specific Jointing Styles
Different rock formations respond to tectonic stresses differently with the
result that joint styles can vary from one stratum to the next within a
sequence.


Statistical Evaluation of Planar Discontinuities

Because joints tend to form along preferred orientations within a rock
mass, but there is some variation, the data set of planar orientations must
be treated statistically to determine the mean or statistically averaged
orientation of each set

This is done graphically, rather than with actual statistics using lower-
hemispheric projections of planar data.


If we divide a circle into ten
Contouring Structural Data zones of equal width, the
innermost circle will contain
1% of the area. The next circle
is twice as large and will
contain 4%, but 1% is in the
inner circle, so the annulus will
contain 3% of the area, and so
on.

If we stack triangles, each row
will contain 1, 3, 5... triangles. A
stack ten rows high will contain
100 triangles.

If we divide a 60 degree sector
of the circle into triangles of
equal area, each sector will
contain 100 triangles, each with
1% of the area of the sector.
From:http://www.uwgb.edu/dutchs/structge/SL133Kalsbeek.HTM

Contouring Structural Data
The Kalsbeek counting
net is based on this
principle. It consists of
ten equally spaced
circles. Each annulus is
divided into triangles.
Altogether there are 600
triangles. At each vertex,
six triangles meet. The
hexagon of triangles
around each vertex
contains 1% of the area
of the net.


Plot the data on an equal
Contouring Structural Data area net then transfer the
overlay to the counting net.
Of course, the two nets must
be the same diameter!


At each vertex, count the
number of points in the
surrounding six triangles
and plot the number at the
vertex. You may want to do
this on a second overlay
above the data overlay.

Each triangle is common to
three hexagons so every
point is counted three times.
(No, this does not mean the
densities have to be divided
by three.) Be certain to check
every vertex close to the data
points to be sure of not
missing any.


Remove the
numbered
overlay and
contour the
data.



Place the contoured
data over a Schmidt
Net and rotate it so
the highest
concentration data
is on the E-W
diameter



Construct a plane
90° from the central
cluster of the data
and read the dip
angle directly off the
E-W diameter



Rotate the entire
overlay back to
north and read off
the predominant
orientation of the
joint set.



Combined hydraulic and structural data

Step 1: Meld calculated in-plane flows with multiple planar sets within a
formation

Define the REV

Define the Domain

Resolve in-plane flows for all discontinuity sets

Model the anisotropy




Step 2: Superimpose flow modeled for each formation onto local
variability between formations and/or regional setting

Identify changes in structural styles including joint styles, orientations,
inter-joint spacing and frequency distribution

Identify larger scale structures which cross formational boundaries –
e.g., faults, dikes

Reconcile domainal flow with local and regional hydrologic regimes



formation
In flow modeling using a N
contour map in
unconsolidated geologic
settings, the model results in
a two-dimensional, or
vectoral representation of
Meter
the direction of
s
groundwater flow with a 0 100
graphical azimuth and a
gradient expressed as a
unitless value.
In this case we can reconstruct groundwater contours in the absence of
any other data.



formation

Because the flow arrow is a vector (should be a vector), it is also a
lineament.

As such it can be treated as structural data - a line with a trend and
plunge:

0° 0’10” 110°

and can be represented along with structural data in a three
dimensional graphical model.



Because the dip of the gradient of groundwater expressed in degrees is
essentially zero, at least in terms of trend and plunge measurements, the
groundwater flow vector will plot on the primitive of a three-dimensional
plot of structural data.


Hydro-Structural Flow Modeling,
Gillespie and McLane, 2009


Example: Formations with sedimentary bedding as well as
fractures. Fractures (joints) tend to be sub-vertical

Groundwater flow is
through all planes. Those
planes which are oriented
closer to the azimuth of
the hydraulic gradient
will exert the greatest
control on groundwater
flow direction and will
impart some degree of
anisotropy.
Joint planes


Planar
Joint Discontinuities Joint
Δx1
Set 1
Δx2 Set 2

Δx

Groundwater
Contours
Field Hydraulic θ1
Gradient In-Plane
(Δh/Δx) Flow
Gradient in Plane A = Δh / Δx1,
Where: Δx1= Δx / cosθ1
Groundwater flow within an individual planar discontinuity is
approximately sub-parallel to strike. The lesser the angle between the
strike of a water-bearing discontinuity and the azimuth of the field
hydraulic gradient, the greater is the correspondence between the
equipotential lines of the field hydraulic gradient and those within the
discontinuity, with maximum correspondence in a plane with a strike
equal to the azimuth of the hydraulic gradient and least correspondence
where strike and hydraulic gradient are normal.

Planar
Joint Discontinuities Joint Δx1x1
?
Δ x2 Set 2 Set 1

Δx
?x
Ө1
Groundwater
Contours
Field Hydraulic
Gradient In-Plane
Flow
Gradient in Plane A = Δh / Δx1
Where: Δx1= Δx / cos Ө1


A particle of water at the intersection of
planes of Joint Sets 1 and 2 (see previous Joint
figure) could flow into either Set 1
discontinuity but with a greater tendency Joint
Set 2
to flow into the plane with the highest
θ2
gradient. The azimuth of Joint Set 1 is at
a lesser angle (θ1) to the azimuth of the
Δx2
field hydraulic gradient than is that of Δx1
Joint Set 2 (θ2). Comparing the in-plane Δx θ1
hydraulic gradients for the planes and
keeping Δx at unity, the gradient in Joint
Set 1 exceeds that in Joint Set 2 by a Field Hydraulic
factor of: Gradient
(Δh/Δx)
ip= (Δh/Δx1 )/(Δh/Δx2)


and the preferential tendency for a
hypothetical particle of water to flow
into Joint Set 1, expressed as a
percentage, is given by:

Cos θ1/Cos (180-θ2) · 100
Joint Set 1
Field Hydraulic
For a hypothetical case in which θ1 = Gradient
20° and θ2 = -65° the flow ratio into
planes in Joint Sets 1 and 2 is 2.2:1 for a
70% potential for flow into Joint Set 1 Joint Set 2
and a 30% potential for flow into Joint
Set 2.

The same result can be obtained by a
graphical vector resolution (see adjacent
figures) of the field hydraulic gradient
and the two planes.


The non-random partitioning
of flow into the joint sets and
the differences in plane length
and inter-plane spacing
between systematic and non-
systematic joint sets creates
anisotropy on the scale of the
representative elemental
volume which can extend to
larger scales in formations with
heterogeneous distributions of On a local scale (~102 m) the reticulated
non-random planes. nature of joint networks typically
precludes pronounced linear
anisotropies but the flow partitioning
into different joint sets and/or bedding
planes provides for prediction of the
fracture-controlled deviation of flow
direction from the field hydraulic
gradient and of solute deflection.

Using the 2.2:1 partitioning
ratio in the example, the
deflection of solutes over a
hypothetical distance of 200 m
would be -4o from the field
gradient with solute deflection of
20m from a linearly interpolated
transport line.


Non-Random planar fabric elements in consolidated rock formations are
structurally dependent, occur in sets with statistically consistent
preferential orientations and form the majority of water-bearing planes.
The differences of mean plane lengths, frequencies and spacings between
the planar elements impart strong anisotropy to groundwater flow on the
scale of the Representative Elemental Volume of the planar network, which
tend to be defined on the scale of 100 to 101 m. On the scale of most flow
and solute transport investigations (101 to 102 m) the reticulated nature of
systematic and non-systematic joint sets with or without bedding plane
partings, tend to preclude development of strong aquifer anisotropy on the
scale of the observations being made.
The REV-imposed anisotropy is manifest on the scale of most study areas,
however, in the deflection from the field hydraulic gradient of mean
groundwater flow direction and solute transport. Testable predictions of the
angle and distance of deflection at compliance points based on this model
can be used to select monitoring locations for plume delineation and
monitoring.


Comparing Hydrostructural Methods…

Planar
Δx1
Set 1
Δx2 Set 2

Δx

Groundwater
Contours
Field Hydraulic θ1
Gradient In-Plane
(Δh/Δx) Flow

To non-structurally
based methods
(e.g., fetter, 2001)…


The measured directional anisotropy in hydraulic conductivity
will vary significantly depending on the location of the pumping
well and the structural relations between joint sets, bedding
planes, etc.
Planar
For example, an Joint Discontinuities Joint
Δx1
Set 1
extraction well Δx2 Set 2

along strike of Δx
systematic Joint
Groundwater
Set 1 at Point A, Contours
would result in a Field Hydraulic θ1
Gradient In-Plane
different (Δh/Δx) Flow
anisotropy than a Gradient in Plane A = Δh / Δx1,
well along strike Where: Δx1= Δx / cosθ1
of non-systematic A
Joint Set 2 at B
Point B


This is because anisotropy results from preferential flow into the set of
discontinuities which strikes at the lowest angle to the field gradient .
Changing the magnitude and direction of the field gradient changes
the entire flow regime. Models based on measured hydraulic gradients
during aquifer stress tests are subject to induced error as a result.

Planar
Δx1
Set 1
Δx2 Set 2

Δx

Groundwater
Contours
Field Hydraulic θ1
Gradient In-Plane
(Δh/Δx) Flow
A
B

Case Study

Groundwater flow in a fractured sedimentary rock formation
in the Newark-Gettysburg Basin.

Bedding dips at a low angle toward the northwest and there
are two sub-vertical joint sets.

Problem: use structural data to predict the distribution and
width of a solute plume at the location of second order stream


N

Field Hydraulic Gradient (Green arrow: azimuth ~095°) superimposed
on principal bedrock groundwater-transmitting structural fabric
elements. White lines: S1 joints (045°-90) - strike is approximately
coincident with bedding plane strike but bedding dips NW; Red lines: S2
joints (105°-85NE); Buff lines: generalized groundwater elevation
contours.

Lower hemisphere projection of planar fabric elements depicting the
orientation of the field hydraulic gradient (red circle) in relation to measured
structural fabric elements. Bedding plane partings (blue) strike 50° from the
field gradient, dip in the opposite direction and, consequently, exert little to no
control on groundwater flow direction. Planar element intersections are not
aligned with measured groundwater flow, plunging 80° toward 075° (joints)
and 5° toward 300° (joints w/bedding). The S2 joint set is the pervasive fabric
element with a strike azimuth nearest that of the field hydraulic gradient

Resolution of in-plane hydraulic
gradients in S1 and S2 joints (bedding
plane has similar strike to S1 – dip
direction and angle are not relevant to
the model solution). Geometric
resolution results in a preferential
tendency for groundwater and solutes
to flow into S2 joint planes with a
pathway ratio (S2 : S1) of 1.53:1.


Model prediction is that solute deflection will be toward the north 65
m for every 100 m of transport along the field gradient, or a
distance of approximately 300 m over the 450 m study area distance
to the stream discharge.


Superimposed on an aerial photograph of the site, the model predicted that
solutes should be discharging to the stream only in the shaded zone shown at
left. Regulatory review had required monitoring wells both east and west
banks along the entire length of the stream near the site.


The Mathematics Behind It
(Some of it)

For the problem of two sub-vertical joint sets where the hydraulic gradient
i is within the horizontal plane, the x and y components of ground water
flow are given by:

Copyright © 2011, Thomas D. Gillespie, P.G. and Charles McLane, P.G.

Using the Structural Data measured earlier, calculate the direction and degree
of anisotropy for the following situation:

Joint Set No 1 – 049 60NW

Joint Set No. 2 – 336 56 NE

Field Hydraulic gradient - 0.05 180°


100 ft

Ө1 = 24°
Ө1
Ө2 = 45°
Δx – 100 ft
Δh – 5 ft

Ө2

100 ft

ip1 = Δx / cos Ө1 = 100/.91 = 109.9
(Δh/ ip2)/(Δh/ ip1 ) = 1.3
ip2 = Δx / cos Ө2 = 100/.91 = 141.4
Ө1

Ө2

100 ft

1.3

100 ft

1.0

9 ft

Current Research

The simple partitioning of groundwater into intersecting joints is
complicated by the differential partitioning which occurs between
upgradient-facing and downgradient-facing intersections

Plan View

Hydrostructural Geology

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