Geologic maps and structures

Rocks are rarely found in the flat, horizontal layers in which sediments were first deposited. Plate movements tilt, fold, fracture and displace them, producing geologic structures that control where rock types appear at the surface, how deep a given layer lies beneath a site, and where weak zones and water paths run. A geologic map records this information in two dimensions, and a trained reader can turn it into a three-dimensional picture of the ground. For civil engineers, reading geologic maps and understanding basic structures are essential skills for desk studies, route selection and the interpretation of boreholes.

Strike and dip

The orientation of any planar feature, such as a bedding plane, joint, fault or foliation, is described by its strike and dip. Strike is the compass direction of a horizontal line on the plane, the line along which the plane would meet a horizontal water surface. Dip is the angle between the plane and the horizontal, measured perpendicular to the strike, together with the direction in which the plane slopes down. A bed with strike 040° and dip 30° to the southeast is written 040/30 SE. Many engineers prefer the dip direction and dip notation, which gives the azimuth of the steepest downward direction followed by the dip angle, for example 130/30. This notation is unambiguous and is used by most slope stability software.

On geologic maps, strike and dip are shown by a T-shaped symbol: the long bar is parallel to strike, the short tick points in the dip direction, and the dip angle is written beside it. Special symbols show horizontal and vertical beds, overturned beds and foliation. Field measurements are made with a compass-clinometer, now often supplemented by smartphone applications and by measurements picked from photogrammetric or lidar models of rock faces.

Apparent dip and true thickness

A vertical section, such as a road cut, tunnel wall or cross-section drawn on a map, shows the true dip of a plane only if it is cut perpendicular to the strike. In any other direction it shows a smaller apparent dip. If \(\delta\) is the true dip and \(\beta\) is the angle between the section line and the strike, the apparent dip \(\alpha\) is given by:

When the section is parallel to strike, \(\beta = 0\) and the apparent dip is zero: the beds look horizontal. This matters for interpreting cuts and borehole lines. A tunnel driven nearly parallel to the strike of steeply dipping beds will stay in the same layer for a long distance, while one driven across the strike passes through many layers.

A related calculation finds the true thickness of a dipping layer from its outcrop width. If a layer outcrops on level ground with a width \(w\) measured perpendicular to strike, its true thickness is \(t = w \sin \delta\). Borehole intersections are corrected similarly: a vertical borehole passing through a bed of true thickness \(t\) dipping at \(\delta\) intersects a length \(t / \cos \delta\).

# Apparent dip along different section bearings, and true thickness
import math

strike, dip = 60.0, 28.0          # degrees
for bearing in (60, 75, 90, 105, 120, 150):
    beta = math.radians(abs(bearing - strike) % 180)
    app = math.degrees(math.atan(math.tan(math.radians(dip)) * abs(math.sin(beta))))
    print(f"section bearing {bearing:3d} deg -> apparent dip {app:5.1f} deg")

intersect = 2.4   # m in a vertical borehole
print(f"true thickness = {intersect * math.cos(math.radians(dip)):.2f} m")
outcrop_width = 6.0  # m on level ground, measured perpendicular to strike
print(f"thickness from outcrop width = {outcrop_width * math.sin(math.radians(dip)):.2f} m")

section bearing  60 deg -> apparent dip   0.0 deg
section bearing  75 deg -> apparent dip   7.8 deg
section bearing  90 deg -> apparent dip  14.9 deg
section bearing 105 deg -> apparent dip  20.6 deg
section bearing 120 deg -> apparent dip  24.7 deg
section bearing 150 deg -> apparent dip  28.0 deg
true thickness = 2.12 m
thickness from outcrop width = 2.82 m

Folds

Folds are bends in originally planar layers, formed by compression. An anticline is an upward arch with the oldest rocks in its core; a syncline is a downward trough with the youngest rocks in its core. The hinge is the line of greatest curvature and the limbs are the sides. Folds are described by the attitude of their axial plane and hinge: upright, inclined, overturned or recumbent, and horizontal or plunging. A plunging fold makes a characteristic V- or U-shaped outcrop pattern on a map.

Folds matter for engineering in several ways. Beds dip in different directions on opposite limbs, so a road or tunnel crossing a fold meets favorable and unfavorable slope orientations. Fold hinges are often intensely fractured, and tension cracks open along the crests of anticlines. Anticlines can trap gas and water under pressure, and synclines can collect groundwater and channel it into tunnels. Bedding-plane slip during folding can leave weak sheared clay layers between stronger beds.

Faults

Faults are fractures along which there has been measurable movement. They are classified by the direction of slip relative to the fault plane. The block above an inclined fault is the hanging wall and the block below is the footwall.

• Normal faults: the hanging wall moves down relative to the footwall. They form where the crust is stretched, such as in rift valleys and the Basin and Range region of the western United States.
• Reverse and thrust faults: the hanging wall moves up relative to the footwall. Thrust faults are low-angle reverse faults, common in mountain belts such as the Rocky Mountain foothills, where they stack older rocks over younger ones.
• Strike-slip faults: the blocks move horizontally past each other. Looking across the fault, if the far side moves to the right the fault is right-lateral (dextral); if to the left, left-lateral (sinistral).

Engineering concerns with faults include the weak, crushed and clay-rich material in fault zones; the contrast in rock type and properties across a fault; groundwater, since faults can act either as conduits or as barriers; and, for active faults, surface rupture and earthquake shaking. A fault is considered active if it has moved in recent geologic time, usually taken as the Holocene, about the last 11,700 years, though definitions differ between agencies and project types. Critical facilities such as dams, nuclear plants and hospitals are not built across active faults, and pipelines and bridges that must cross them are designed to accommodate the expected offset.

Unconformities and contacts

An unconformity is a surface representing a gap in the geologic record, where erosion removed rock or no deposition occurred before younger layers were laid down. An angular unconformity, where tilted older beds are cut off and overlain by flatter younger ones, records a long history of deposition, deformation, uplift and erosion. For engineers, the most common unconformity is the contact between bedrock and the overlying Quaternary deposits: an irregular, eroded surface that may have weathered rock, buried channels, boulders or water-bearing gravel on top of it. Geological contacts of all kinds deserve attention because properties change abruptly across them, and water often flows along them.

Reading a geologic map

A geologic map shows the distribution of rock units at the surface, or beneath a thin cover of soil, with colors and letter symbols keyed to a legend that lists units from youngest at the top to oldest at the bottom. Lines show geological contacts, faults and fold axes, and symbols show measured orientations. Bedrock maps omit the Quaternary cover, while surficial geology maps show the glacial and postglacial deposits; engineers usually need both. Cross-sections drawn along selected lines show the inferred structure at depth.

Several simple rules help interpret map patterns. Horizontal beds outcrop parallel to topographic contours. Vertical beds outcrop as straight lines regardless of topography. Dipping beds make V-shaped patterns where they cross valleys; the rule of Vs states that the V points in the direction of dip, except where the beds dip downstream more gently than the valley floor. On a fold, older rocks are found in the core of an anticline and younger in the core of a syncline. Faults offset contacts and often juxtapose units of different ages.

Geologic maps for the United States are produced by the US Geological Survey and state surveys such as the Washington Geological Survey, many of them available free online through the National Geologic Map Database and state interactive portals with geology, hazard, lidar and borehole layers. For a site investigation, Kestrel's desk study for the hospital began with the state geologic map, a surficial geology map of the Spokane area, and water well logs, which together suggested about 30 to 40 m of glacial flood gravel and lake silt over basalt.

Finding strike and dip from three boreholes

Where a planar contact, such as the top of a bedrock layer or a distinctive clay seam, is found in three boreholes that do not lie on a straight line, its strike and dip can be found from the three elevations. This is the classic three-point problem. The borehole positions and contact elevations define three points on the plane. On the line joining the highest and lowest points, find the location where the contact has the same elevation as the middle point; the line from there to the middle borehole is a strike line. The dip is the slope measured perpendicular to that line. The same result comes from fitting a plane \(z = a x + b y + c\) through the three points, with the dip angle given by \(\tan\delta = \sqrt{a^2 + b^2}\).

The three-point method assumes the contact is a plane over the area of the boreholes, which is reasonable for a tilted sedimentary bed but not for an eroded bedrock surface or a glacial deposit. Its main use is to predict where a dipping layer will be encountered at a new location, such as a proposed footing or a point along a tunnel, and to check whether a fourth borehole agrees with the prediction. When it does not, the disagreement itself is information: there may be a fold, a fault or a channel between the holes.

Stereonets

For rock slopes and tunnels, orientation data from many joints are plotted on stereographic projections. Each plane is represented by its pole, the point where a line perpendicular to the plane pierces the lower half of a reference sphere. Clusters of poles reveal joint sets, and the mean orientation of each set can be compared with the orientation of a slope face or tunnel to check for plane, wedge and toppling failure, as introduced in lesson 4. Modern software contours pole densities, identifies sets and runs kinematic checks automatically, but the engineer still needs to understand what the plot means.