Structural Geology

Learning Objectives

  • Describe planar orientation using strike, dip, and dip direction.
  • Distinguish folds, faults, joints, and joint sets from their geometry and movement.
  • Explain what stereographic projection contributes to a rock-slope kinematic screen.
  • Relate true dip to apparent dip in an oblique section.
  • Recover a plane from suitable section measurements and recognize non-unique cases.
  • Resolve prescribed fault slip into components and separate geometric screening from stability.

Planar Orientation

Strike

The compass trend of the horizontal line formed where a plane intersects a horizontal reference plane. Strike is an undirected line, so its two bearings differ by 180°.

Dip

The maximum inclination of a planar geologic feature below horizontal, measured in the direction perpendicular to strike. A complete orientation also states the dip direction.

Using Strike and Dip

Record the orientation convention with every measurement. The right-hand rule is one common convention; dip direction and dip-and-direction notation avoid ambiguity when discontinuities are used in engineering analysis. Strike and the horizontal dip direction are perpendicular, while dip angle is measured in a vertical section normal to strike.

Here, azimuth increases clockwise from north: north is 000∘000^\circ, east 090∘090^\circ, south 180∘180^\circ, and west 270∘270^\circ. Under the right-hand rule (RHR), the dipping side is 90∘90^\circ clockwise from the recorded strike. Thus RHR strike 045∘045^\circ and dip 30∘30^\circ describe dip direction 135∘135^\circ; strike 225∘225^\circ would select the opposite dipping side. An undirected strike line alone does not distinguish these planes.

Record whether north is true, grid or magnetic, together with the measurement convention and any correction. Bearings referenced to different north directions must be reconciled before comparison.

Horizontal and Vertical Planes

A horizontal plane has zero dip and no unique strike or dip direction. A vertical plane has a defined strike line, but either horizontal normal side can be used to describe its 90∘90^\circ dip. State a consistent convention; do not interpret a chosen reference arrow as additional field evidence.

Strike and Dip in Plan and Section

The plan view defines the horizontal directions; a section normal to strike displays true dip. The bearing shown is illustrative, not a field measurement.

Map and section views connect a plane’s strike line, dip direction, and true dip angle

Folds, Faults, and Joints

Folds

Fold

A bend or curvature in originally more continuous rock layers or planar structures produced by deformation.

Antiform and synform

An antiform is an upward-convex bend; a synform is a downward-concave bend. These names describe shape without requiring the relative ages of the layers.

Fold Geometry and Interpretation

  • Anticline: a fold with older strata in its core.
  • Syncline: a fold with younger strata in its core.
  • Monocline: a step-like bend between more gently dipping strata.
  • Dome and basin: approximately circular or elliptical upwarps and downwarps, respectively.

An upright anticline commonly has an antiform shape and an upright syncline a synform shape. Inverted or refolded successions can break that shape/age association. Establish stratigraphic younging from suitable field evidence, such as graded bedding or other reliable facing indicators.

Folded bedding may influence tunnel alignment, slope blocks, groundwater pathways or foundation continuity. A fold label does not establish joint persistence, water pressure, support demand or an inherently favorable alignment.

Fold Shape and Stratigraphic Age

Shape supplies antiform or synform. An established upright succession permits the illustrated anticline/syncline association; inverted successions require separate age interpretation.

An antiform arches upward and a synform curves downward; their age classification requires younging evidence

Faults and Joints

Fault

A fracture or zone of fractures along which relative shear displacement has occurred.

Joint

A fracture with no observable shear displacement parallel to the fracture surface.

Fault Movement and Joint Sets

  • Normal fault: the hanging wall moves down relative to the footwall in the dip direction of the fault.
  • Reverse fault: the hanging wall moves up relative to the footwall. A thrust fault is a low-angle reverse fault; no single angular cutoff applies to every classification scheme.
  • Strike-slip fault: the principal relative motion is horizontal and parallel to the fault strike; state the viewing convention when naming lateral sense.
  • Joint sets: groups of similarly oriented discontinuities. Their spacing, persistence, infill, roughness, aperture, and water conditions help define block size and rock-mass behavior.

Fault cores and surrounding damage zones can affect strength, deformation and groundwater differently. A clay-rich core may impede flow while connected surrounding fractures conduct it. Investigate the actual materials and connectivity; a thrust-fault label does not prove expansive clay, bearing failure or a required treatment.

Joint aperture is opening normal to the surface; observable shear displacement along it supports a fault interpretation. Joint sets group similar orientations, while a joint system can include several sets. A mapped fault's geometry alone does not determine its activity or the timing of its last movement.

Components of Pure Dip Slip

Resolve relative displacement along an inclined fault into horizontal and vertical magnitudes.

H=scos⁡δf,T=ssin⁡δfH=s\cos\delta_f,\qquad T=s\sin\delta_f

Variables

SymbolDescriptionUnit
ssRelative slip magnitude along the faultm
δf\delta_fFault dip below horizontaldegrees
HHHorizontal heave magnitude in the section normal to strikem
TTVertical throw magnitudem

Movement Sense and Observation

The hanging wall lies above an inclined fault surface; the footwall lies below it. For pure dip slip, normal motion lowers the hanging wall and reverse motion raises it. The relative displacement vector lies along the fault, so vertical throw is generally smaller than slip magnitude.

For strike slip, look across the fault: motion of the far block to your right is right-lateral; motion to your left is left-lateral. State the view and correlate displaced features before interpreting sense. Oblique slip combines components and needs a fuller displacement description.

Relative Fault Displacement

The sketches show relative movement senses. Fault geometry, block identity, and strike-slip viewing convention should be stated when mapping a real structure.

Normal and reverse faults show opposite hanging-wall motion while strike-slip motion is horizontal

Explore Shape and Relative Movement

Change fold amplitude and the supplied younging evidence, then compare normal, reverse and lateral fault motion. Set displacement to zero to recover the reference horizons. These are prescribed geometries rather than simulations of tectonic forces or elapsed time.

Fold shape and fault displacement

Concept and model scope

Choose a structure and control its geometry. Use younging evidence to distinguish shape from age class, or resolve prescribed fault slip into its components.

Model and limits: Synthetic geometry, not a stress, strain, earthquake-time or stability model. Fold horizons are vertical offsets of a cosine and do not preserve bed thickness or arc length. Faults show rigid relative motion within a stationary observation window; the other block is fixed. Fault dip 15–75°; slip and amplitude 0–20 m; wavelength 40–100 m, all in 1-unit steps.

Controls

Structure type

Antiform and synform describe upward and downward bends. Normal/reverse identify hanging-wall motion on an inclined fault. Strike-slip sense is the motion of the far block when looking across the fault, shown here looking east from the fixed west block.

10 m

Slip magnitude

Prescribed relative displacement along the fault, not a vertical offset by itself. The open marker stays at its reference position; the filled marker and correlated horizons move with the selected block.

Range: 0–20 m. Step: 1 m.

60 °

Fault dip

Inclination of the illustrated fault below the positive horizontal axis. The hanging wall lies above the fault. Slip stays tangent to that plane; changing dip changes horizontal heave and vertical throw.

Range: 15–75 °. Step: 1 °.

Vertical section: horizontal and up axes
Footwall (fixed)Hanging wall−40040Horizontal position (m)200−20Up position (m) ↑

Normal fault; prescribed relative slip 10.0 m.

Hanging-wall up displacement: -8.66 m

Horizontal displacement: 5.00 m

Negative up displacement is downward throw. Slip and the fault trace are parallel; horizontal displacement is the signed heave.

Open circle: reference marker. Filled amber circle: moved marker. The rectangle is a fixed observation window, not a moving ground surface.

Stereographic Projection and Kinematic Screening

Stereographic projection

A method for representing the orientations of lines and planes in three dimensions on a two-dimensional circular net. A plane is commonly plotted as a great-circle trace; its pole is the line normal to that plane.

Trend and plunge

Trend is a line's horizontal azimuth, and plunge is its downward inclination from horizontal. Together they describe a directed line, subject to the chosen hemisphere convention.

Reading a Stereonet

Use a stated projection and hemisphere consistently. The great circle represents the plane; the pole represents its normal. Equal-angle stereographic and equal-area nets use different radial scales. The figure here is lower-hemisphere, equal-angle stereographic.

For a nonhorizontal plane dipping toward azimuth DD, the lower-hemisphere pole trends opposite to DD and plunges 90∘−δ90^\circ-\delta. Thus a plane dipping 45∘45^\circ toward 135∘135^\circ has pole trend 315∘315^\circ and plunge 45∘45^\circ. A horizontal plane's pole is vertical, with no unique trend. A vertical plane's poles lie on opposite rim points; state the selected convention.

Plotting discontinuity sets with the slope-face orientation supports geometric comparison. It does not supply missing persistence, release surfaces, shear strength or groundwater data.

Radius on the Stated Stereographic Net

Relate a lower-hemisphere line's plunge to radial distance on a unit-radius equal-angle net.

ρ=tan⁡(45∘−p2)\rho=\tan\left(45^\circ-\frac{p}{2}\right)

Variables

SymbolDescriptionUnit
ppDownward line plunge, from 0° to 90°degrees
ρ\rhoRadial distance divided by the net radius; horizontal lines are on the rim and a vertical line is at the center1
Plane Great Circle and Pole

The lower-hemisphere stereographic net uses a synthetic plane to distinguish the great circle from its pole. It is an orientation illustration, not a site kinematic result.

An illustrative 45 degree plane dipping toward azimuth 135 degrees appears as a great circle with its normal plotted as a pole

Rock-Slope Failure Mechanisms

Geometric Failure Modes

  • Planar sliding: a persistent discontinuity dips toward and daylights in the slope face; its orientation must be compatible with the direction of possible sliding.
  • Wedge sliding: two discontinuities intersect, and their line of intersection may daylight through the face.
  • Toppling: steep discontinuities dip into the slope and may form columns or blocks that rotate outward.

A simple kinematic screen compares orientation and daylighting geometry. Friction, cohesion, persistence, water pressure, loads, block release, and the selected analysis method govern whether a geometrically possible mechanism is stable.

For an oblique intersection line, compare its plunge with the apparent slope-face dip in that line's trend, not automatically with the face's larger true dip. The line must point out of the face and satisfy the actual spatial release conditions. A friction-cone shortcut is not a complete two-plane wedge force analysis.

Any lateral direction window used in a simplified planar screen must be stated as an assumption or method criterion. Do not invent a universal angular tolerance or factor-of-safety requirement. A negative screen for one mechanism also leaves other mechanisms and uncertainty to be assessed.

Planar, Wedge, and Toppling Geometry

The panels identify possible release geometries only. They do not establish failure likelihood or replace strength, groundwater, and stability analyses.

Planar, wedge, and toppling mechanisms are shown as distinct possible rock-slope geometries
Rock-Slope Kinematic Screening

Use measured discontinuity geometry to screen planar, wedge, and toppling release mechanisms. A geometric screen identifies mechanisms that need analysis; it does not establish stability or a factor of safety.

Record the slope face and discontinuity sets in a consistent orientation convention. Include persistence, condition, groundwater, and uncertainty in the subsequent stability analysis. Apply only project-defined criteria; hold the decision when required data or criteria are unresolved.

Rock-Slope Kinematic ScreeningUse measured discontinuity geometry to screen planar, wedge, and toppling release mechanisms. A geometric screen identifies mechanisms that need analysis; it does not establish stability or a factor of safety.. Record the slope face and discontinuity sets in a consistent orientation convention. Include persistence, condition, groundwater, and uncertainty in the subsequent stability analysis. Apply only project-defined criteria; hold the decision when required data or criteria are unresolved.. Start → Define slope face and map discontinuity sets; Define slope face and map discontinuity sets → Orientation data and scope adequate?; Orientation data and scope adequate? — Yes → Screen planar, wedge, and toppling geometry; Orientation data and scope adequate? — No → Hold: resolve missing data or scope; Hold: resolve missing data or scope → End; Screen planar, wedge, and toppling geometry → Any mechanism is geometrically feasible?; Any mechanism is geometrically feasible? — Yes → Analyze feasible modes using strength, water, and loads; Any mechanism is geometrically feasible? — No → Document screen; assess other failure modes; Document screen; assess other failure modes → End; Analyze feasible modes using strength, water, and loads → Project-specific analysis criteria defined?; Project-specific analysis criteria defined? — Yes → Analysis meets the defined criteria?; Project-specific analysis criteria defined? — No → Hold: establish governing criteria; Hold: establish governing criteria → End; Analysis meets the defined criteria? — Yes → Document basis, limitations, and monitoring; Analysis meets the defined criteria? — No → Revise geometry or support; reanalyze; Document basis, limitations, and monitoring → End; Revise geometry or support; reanalyze → Analyze feasible modes using strength, water, and loads

Start → Define slope face and map discontinuity sets; Define slope face and map discontinuity sets → Orientation data and scope adequate?; Orientation data and scope adequate? — Yes → Screen planar, wedge, and toppling geometry; Orientation data and scope adequate? — No → Hold: resolve missing data or scope; Hold: resolve missing data or scope → End; Screen planar, wedge, and toppling geometry → Any mechanism is geometrically feasible?; Any mechanism is geometrically feasible? — Yes → Analyze feasible modes using strength, water, and loads; Any mechanism is geometrically feasible? — No → Document screen; assess other failure modes; Document screen; assess other failure modes → End; Analyze feasible modes using strength, water, and loads → Project-specific analysis criteria defined?; Project-specific analysis criteria defined? — Yes → Analysis meets the defined criteria?; Project-specific analysis criteria defined? — No → Hold: establish governing criteria; Hold: establish governing criteria → End; Analysis meets the defined criteria? — Yes → Document basis, limitations, and monitoring; Analysis meets the defined criteria? — No → Revise geometry or support; reanalyze; Document basis, limitations, and monitoring → End; Revise geometry or support; reanalyze → Analyze feasible modes using strength, water, and loads

  • Start: terminator
  • Define slope face and map discontinuity sets: process
  • Orientation data and scope adequate?: decision
  • Hold: resolve missing data or scope: process
  • Screen planar, wedge, and toppling geometry: process
  • Any mechanism is geometrically feasible?: decision
  • Document screen; assess other failure modes: process
  • Analyze feasible modes using strength, water, and loads: process
  • Project-specific analysis criteria defined?: decision
  • Hold: establish governing criteria: process
  • Analysis meets the defined criteria?: decision
  • Document basis, limitations, and monitoring: process
  • Revise geometry or support; reanalyze: process
  • End: terminator

A Kinematic Screen Is Not a Stability Check

Geometric feasibility does not establish a factor of safety or justify a slope design. If a mechanism is feasible, proceed to a suitable analysis using site-specific strength, groundwater, loads, and project-defined criteria. Keep the conclusion on hold when required data or criteria are unresolved.

Apparent Dip

Apparent dip

The inclination of a planar feature's intersection trace in a specified vertical section. Its magnitude is no greater than the true dip when a unique trace is defined.

Section Orientation

Let β\beta be the acute horizontal angle from the strike line to the section direction. The section perpendicular to strike shows true dip; an oblique section shows apparent dip. Use the measured section azimuth and the same strike convention when reconstructing a geologic section.

The equation below gives a magnitude for a nonvertical plane. For a directed section, a trace descending toward its chosen azimuth has positive signed apparent dip; reversing the section direction reverses that sign. Treat strike as a line when finding acute β\beta, including bearings that wrap through north.

Apparent Dip Relationship

Relates the apparent dip in an oblique section to the true dip and horizontal section angle.

tan⁡δ′=tan⁡δ sin⁡β\tan \delta' = \tan \delta \, \sin \beta

Variables

SymbolDescriptionUnit
δ\deltaTrue dip of the planedegrees
δ′\delta'Dip measured in the oblique sectiondegrees
β\betaAcute horizontal angle from strike to section directiondegrees
True Dip and Apparent Dip

The plan view defines the angle beta; the sections show the corresponding dip angles. The equation uses the acute angle from strike to section direction.

A section oblique to strike records a shallower apparent dip than a section normal to strike

Recovering True Dip

Invert a measured apparent-dip magnitude when the nonzero angle from strike is known.

tan⁡δ=tan⁡δ′sin⁡β,0∘<β≤90∘\tan\delta=\frac{\tan\delta'}{\sin\beta},\qquad 0^\circ<\beta\leq90^\circ

Variables

SymbolDescriptionUnit
δ\deltaRecovered true-dip magnitudedegrees
δ′\delta'Measured apparent-dip magnitudedegrees
β\betaKnown acute horizontal angle from strike to the sectiondegrees

Non-Unique and Limiting Sections

For a nonvertical plane, a section parallel to strike has zero apparent dip regardless of the true dip. A zero trace with β=0∘\beta=0^\circ therefore cannot determine the true dip. Small β\beta also makes inversion sensitive to orientation and angle errors.

A vertical plane intersects any nonparallel vertical section in a vertical line. If the vertical section is coincident with that plane, their intersection is the entire plane and there is no unique apparent-dip trace. The tangent formula is not a substitute for checking that geometry.

Explore the Section Response

Keep a plane fixed and rotate the section through north and through the opposite direction. Compare signed apparent dip, the actual section trace and the response curve. Test zero dip, a strike-parallel section and the vertical-plane limit.

Strike, dip and section direction

Concept and model scope

Keep north fixed, change the right-hand-rule strike and dip, then rotate the vertical section. Compare the section trace with the signed apparent-dip curve.

Model and limits: A single planar surface. Azimuth is clockwise from north; positive apparent dip descends toward the selected section azimuth. At zero dip strike is only a reference. A vertical plane has two equivalent normal sides, and a section coincident with it has no unique intersection trace. Controls: strike and section 0–359° in 1° steps; dip 0–90° in 1° steps.

Controls
45 °

RHR strike

A directed horizontal bearing used by the right-hand rule. For a dipping, nonvertical plane, the down-dip side is 90° clockwise from this bearing. Reversing only this bearing selects the opposite dipping plane.

Range: 0–359 °. Step: 1 °.

30 °

True dip

Maximum inclination below horizontal. Zero is a horizontal plane with no unique strike; 90° is vertical. The plan and section axes use fixed, stated conventions.

Range: 0–90 °. Step: 1 °.

90 °

Section azimuth

The positive horizontal direction in a vertical section. Reverse it by 180° to reverse the sign of a nonvertical apparent dip without changing its magnitude.

Range: 0–359 °. Step: 1 °.

Plan: north stays up
N · 000°SEW

Solid brown: strike line. Amber arrow: selected normal side. Dashed blue: section, arrow toward 090°.

Vertical section toward 090°
+hupOne scale on both axes

Blue is the intersection trace. Positive dip falls to the right; negative dip rises to the right. No vertical exaggeration.

Signed apparent dip (°) versus section azimuth (°)
+90°0°−90°0°90°180°270°360°

Dip direction: 135°

Acute angle from strike: 45.0°

Signed apparent dip: 22.21°

True dip magnitude: 30.0°

Plane-Following Inclination and Grade

Convert inclination to percentage grade and find a direction limit for a straight alignment constrained to a nonvertical plane.

G=100tan⁡∣δ′∣,βmax⁡=arcsin⁡(tan⁡δlimtan⁡δ)G=100\tan|\delta'|,\qquad \beta_{\max}=\arcsin\left(\frac{\tan\delta_{\mathrm{lim}}}{\tan\delta}\right)

Variables

SymbolDescriptionUnit
GGAbsolute percentage grade: 100 times vertical change divided by horizontal distance%
δlim\delta_{\mathrm{lim}}Permitted apparent-dip magnitude, below the nonzero true dip for this inversedegrees
δ\deltaTrue dip of the plane; 0° < dip < 90° for the stated inversedegrees
βmax⁡\beta_{\max}Maximum acute deviation from the strike line; there are bands around both strike bearingsdegrees

Scope of a Direction Constraint

The direction-limit formula assumes a straight alignment actually follows the plane, so its grade is the section trace's grade. It is not a general tunnel-design rule. If the permitted inclination equals or exceeds true dip, every direction meets that inclination constraint. A horizontal plane also meets any nonnegative inclination limit. Excavation, drainage, access, support and operating requirements still need independent assessment.

Recovering a Plane from Two Sections

Two Orthogonal Signed Dips

Two nonparallel section observations can supply information that a single exposure cannot. For the special case of sections directed east and north, define positive angles as descending east and north, respectively. The plane's downward gradients in those directions are the tangents of the measured angles. Their vector sum gives the steepest descent.

This construction assumes both measurements belong to the same planar feature and use a common horizontal datum, north reference and sign convention. It is not valid for combining unrelated joints or curved bedding. A horizontal plane has zero gradient in both sections and no unique dip direction.

Orthogonal Section Reconstruction

Recover dip and dip direction from signed east and north apparent dips on one nonvertical plane.

gE=tan⁡αE,gN=tan⁡αNg_E=\tan\alpha_E,\qquad g_N=\tan\alpha_Nδ=arctan⁡gE2+gN2,D=atan2⁡(gE,gN)(mod360∘)\delta=\arctan\sqrt{g_E^2+g_N^2},\qquad D=\operatorname{atan2}(g_E,g_N)\pmod{360^\circ}

Variables

SymbolDescriptionUnit
αE,αN\alpha_E,\alpha_NSigned apparent dips toward east and north; positive means descendingdegrees
gE,gNg_E,g_NDownward vertical change per unit horizontal distance in the two directions1
DDDip-direction azimuth clockwise from north; atan2 takes east then north components heredegrees
δ\deltaTrue dip; RHR strike is D − 90° reduced to the 0–360° rangedegrees
Key Takeaways
  • Strike, dip, and dip direction define a plane’s orientation when the convention is stated.
  • Fold shape gives antiform/synform; anticline/syncline require the stratigraphic age relation.
  • Faults have displacement; joints do not show observable shear displacement along the fracture.
  • Stereonets support orientation comparison and kinematic screening, not proof of slope stability.
  • An oblique section shows apparent dip, which is no greater than true dip.
  • An along-strike zero trace cannot uniquely recover true dip; coincident vertical planes have no unique trace.
  • Resolve fault displacement along its plane and assess daylighting in the direction of the possible movement.

References