Phase I · Paper 1 · Writing Guide

Bimodal Joint Population Characterisation
at Najd-affected Road Cuts, Makkah Region

Target: Journal of Structural Geology — 3–5 months to submission

Scope

This paper covers

Statistical proof that two distinct joint families co-exist at all five sites
Separation of Najd (NW–SE) and Red Sea (NE–SW) families by orientation and concentration
Site-by-site mean direction, R̄, and κ per family
Geological interpretation of Site 2 overprinting and Site 5 three-way mixture
Rose diagrams and a summary statistics table for all 330 measurements

This paper does not cover

The Najd Intensity Index or any engineering rating — Paper 2
Slope stability, kinematic analysis, or failure modes — Paper 3
Spatial zonation or risk mapping — Papers 4–5
Geotechnical design parameters or support class recommendations

Data at a glance

330

Joint measurements

Granodiorite sites

Joint families

4/5

Sites p < 0.05

Paper sections

Click any section to expand · text scales as the card grows

Abstract

State the problem (no rigorous statistical characterisation of Najd joint fabric at site scale), the data (330 measurements, 5 granodiorite outcrops), the methods (Rayleigh, V-test, von Mises), and the finding (bimodal fabric confirmed at all sites; Site 2 Red Sea overprint; Site 5 three-way mixture). Close with significance: this is the quantitative foundation for the NII in Paper 2.

~150 words

Introduction

Establish why joint fabric matters for road-cut infrastructure in western KSA. Name the gap: the Najd Fault System is invoked qualitatively in nearly every regional engineering study, yet no published work statistically confirms and separates its bimodal joint signature at site scale. State two objectives: (1) confirm non-uniformity at each site; (2) separate and characterise the two families.

~400 words2–3 key references

Geological Setting

Two tectonic episodes. (A) Najd Fault System: Proterozoic sinistral transpression ~600 Ma, NW–SE shear corridor, imprinting the persistent NW-trending joint set. (B) Cenozoic Red Sea rifting ~30 Ma, NE–SW extension, creating the subordinate but locally dominant NE-trending set. Describe the Precambrian granodiorite basement as the host rock at all five sites — lithological uniformity is a strength that isolates structural from lithological variation.

~350 wordsRegional geology map

Study Sites

Brief description of each of the five road-cut outcrops: location, coordinates, exposure length, rock condition. Include a location map (Figure 1). All sites are in granodiorite; note this as a controlled variable that strengthens the structural interpretation.

Table 1 · site summaryFigure 1 · location map

Field Methodology

Describe the scanline survey protocol. For each joint plane: dip angle and dip direction recorded. State total measurements per site. Note whether joint families were separated in the field or post-hoc in analysis. Keep this replicable — a reader must be able to repeat the survey at a new site with the same equipment and protocol.

~250 words

Statistical Methods

Introduce circular statistics as the appropriate framework for directional data. Define: (a) R̄ mean resultant length as a concentration metric; (b) Rayleigh test for non-uniformity — null hypothesis, Z-statistic, p-value threshold; (c) V-test for clustering toward a hypothesised direction; (d) von Mises distribution — μ and κ, fitting procedure; (e) rose diagram construction in 10° bins. Cite Fisher (1993) or Mardia & Jupp.

~400 wordsCite Fisher 1993

Results

Site by site: rose diagram, Rayleigh p-value, and per-family R̄, μ, κ. Call out Site 2 explicitly (Red Sea R̄ exceeds Najd — overprinting evidence) and Site 5 (pooled Rayleigh p=0.228; decomposition yields Najd 39%, Red Sea 18%, unclassified 42%). Close with Table 2 summarising all sites and families.

Table 2 · stats summaryFigures 2a–2e · rose diagrams

Discussion

Three threads. (1) Why bimodal is expected: two tectonic episodes ~600 Ma apart should leave two independent joint sets; the data confirms this. (2) Site 2: argue that stronger Red Sea coherence reflects Cenozoic reactivation or proximity to a rift-related structure. (3) Site 5: interpret the three-way mixture as a structural transition zone, possibly at a shear-zone boundary. Note that Najd R̄ ≈ 0.98–1.00 across sites makes it a reliable input to the NII in Paper 2.

~500 words

Conclusions

Four points: (1) non-uniform distribution confirmed at 4 of 5 sites (p < 0.05); (2) bimodal fabric present at all sites — Najd NW–SE dominant, Red Sea NE–SW subordinate; (3) Site 2 Red Sea overprint, Site 5 structural complexity requiring family decomposition; (4) confirmed families form the quantitative input foundation for the Najd Intensity Index in Paper 2.

~150 words

Statistical methods reference

Rayleigh Test

Non-uniformity · primary test

Tests whether joint azimuths differ from uniform. Statistic Z = n · R̄². A p-value < 0.05 rejects randomness and confirms a preferred direction exists at the site.

Applied to pooled per-site data at all 5 sites

V-test

Directional · targeted test

One-tailed Rayleigh variant that tests clustering toward a specific hypothesised bearing. Use to formally test whether data clusters toward Najd (~135°) or Red Sea (~050°). Strengthens the directional argument beyond Rayleigh alone.

Useful where the Rayleigh test is borderline

Von Mises Fitting

Distribution · per family per site

Circular analogue of the normal distribution. μ = mean direction; κ = concentration (higher = tighter cluster). Fit separately to each family at each site to characterise rather than just detect the preferred direction.

10 fits: 5 sites × 2 families

R̄ Mean Resultant Length

Concentration metric · range 0–1

Length of the mean resultant vector. R̄ ≈ 1.00 = all measurements in the same direction. R̄ ≈ 0.07 = scattered. The Najd family yields R̄ = 0.98–1.00 across sites; this consistency is the key finding that validates the family as a reliable index input.

Core diagnostic separating the two families

Key findings to report

Site	Najd R̄	Najd μ	Red Sea R̄	Rayleigh p	Note
Site 1	~0.99	~135°	Subordinate	< 0.05	—
Site 2	Lower	—	> Najd	< 0.05	Red Sea overprint
Site 3	~0.98	~135°	Subordinate	< 0.05	—
Site 4	~1.00	~135°	Subordinate	< 0.05	—
Site 5	0.99 (39%)	—	0.43 (18%)	0.228 pooled	42% unclassified · 3-way mixture

Figures checklist

Study area location map

Makkah region with the five outcrop locations marked. Inset showing the Najd Fault System corridor (NW–SE) and Red Sea rift axis. The map should convey regional tectonic context at a glance — reviewers will look here first.

Rose diagrams — Sites 1 to 5

One diagram per site in 10° bins, colour-coded by family (teal = Najd, rust = Red Sea). Present as a 2×3 panel or a 1×5 strip. Site 5 should include the three-class decomposition. This is the paper’s core visual.

Summary statistics table (Table 2)

n, R̄, μ, κ, and Rayleigh p-value for each family at each site. Likely a table rather than a figure, but this is the first thing a reviewer will check — values must be internally consistent with the rose diagrams.

Stereonet plot (optional)

Equal-area lower-hemisphere plot of all 330 poles to joint planes, coloured by family. Strong visual for a structural geology journal. Requires Stereonet or OpenStereo software. Include if time allows; skip if it delays submission.

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Bimodal Joint Population Characterisationat Najd-affected Road Cuts, Makkah Region

Bimodal Joint Population Characterisation
at Najd-affected Road Cuts, Makkah Region