Interpreting Results
Two-layer soil models, Annex B curve fitting, and multi-traverse analysis per IEEE 81-2025 §7.6
IEEE 81-2025 §7.6
From Raw Measurements to a Soil Model
A soil resistivity traverse produces a set of apparent resistivity values at different probe spacings. These values are not the actual resistivity of the soil at any specific depth — they are a weighted average of the resistivity of all the soil between the surface and approximately one probe spacing deep. To use these values for grounding design, they must be interpreted into a layered soil model.
IEEE 81-2025 §7.6 describes the process of selecting the appropriate number of layers, fitting the model to the measured data using the Annex B least-squares algorithm, and evaluating the quality of the fit. The STRATIFY™ calculator implements this algorithm directly, producing a two-layer soil model (ρ₁, ρ₂, h₁) from the user's traverse data.
IEEE 81-2025 §7.6.1 caution: Adding more layers to the model always reduces the rms fitting error — but this does not mean the model is more accurate. If the raw data has measurement errors, a three-layer model will fit those errors as if they were real soil layers. Always use the simplest model that adequately fits the data.
Choosing the Number of Layers
§7.6.1
2-Layer Model
Parameters: ρ₁, ρ₂, h₁
Use when: The apparent resistivity curve shows a smooth, monotonic transition from a surface value to a deep asymptote. This is the most common case in practice and covers the majority of grounding design projects.
Strengths
- Requires the fewest parameters — less sensitive to measurement noise
- Directly supported by IEEE Std 80 soil model requirements
- Implemented in STRATIFY™ using the Annex B least-squares algorithm
- Converges reliably with as few as 6–8 well-spaced measurements
Limitations
- Cannot represent a three-layer structure (e.g., frozen surface over moist soil over rock)
- May underfit data with a clear inflection point in the apparent resistivity curve
§7.6.1
3-Layer Model
Parameters: ρ₁, ρ₂, ρ₃, h₁, h₂
Use when: The apparent resistivity curve shows two distinct inflection points — indicating three distinct soil layers. Common in areas with a frozen surface layer over moist soil, or a thin conductive layer over resistive bedrock.
Strengths
- Better fits complex three-layer geology
- Can represent sandwich structures (conductive layer between two resistive layers, or vice versa)
- Reduces rms fitting error for curves with two inflection points
Limitations
- Requires more parameters — much more sensitive to measurement noise
- IEEE 81-2025 §7.6.1 warns that adding more layers reduces rms error but can decrease accuracy if the raw data has errors
- Requires at least 10–12 well-spaced measurements for reliable convergence
- The additional parameters may not be physically meaningful if the data quality is poor
IEEE 81-2025 Annex B
The Annex B Least-Squares Algorithm
The mathematical foundation of the STRATIFY™ two-layer soil model
Compute Apparent Resistivity
Convert each measured resistance R to apparent resistivity ρₐ using the method formula (e.g., ρₐ = 2πaR for Wenner). Plot ρₐ vs. probe spacing a on a log-log scale.
Select Initial Model Parameters
Choose initial estimates for ρ₁, ρ₂, and h₁. A good starting point is: ρ₁ = the apparent resistivity at the smallest spacing, ρ₂ = the apparent resistivity at the largest spacing, and h₁ = the spacing at which the curve shows the most rapid change.
Compute the Theoretical Curve
Using the Sunde (1949) formula or the equivalent Annex B series expansion, compute the theoretical apparent resistivity curve for the current model parameters. This involves an infinite series that converges rapidly for most practical soil models.
Minimize the Weighted Error Function
The algorithm minimizes ψ = Σ [(ρₒ − ρ)² / ρₒ²] — the sum of squared relative errors between the observed (ρₒ) and theoretical (ρ) apparent resistivity values. The relative weighting ensures that all spacings contribute equally regardless of the absolute magnitude of the resistivity.
Iterate to Convergence
The steepest-descent algorithm iteratively adjusts ρ₁, ρ₂, and h₁ to reduce ψ. Convergence is typically achieved in 10–50 iterations. The final model parameters are the best-fit two-layer soil model for the measured data.
Evaluate the Fit Quality
The rms error (√(ψ/N)) should be less than 10–15% for a good fit. If the rms error is higher, consider whether a 3-layer model is warranted, whether there are outlier measurements that should be excluded, or whether the data quality is insufficient for reliable modeling.
Error Function
ψ = Σ [(ρₒ − ρ)² / ρₒ²]
ρₒ = observed apparent resistivity at each spacing · ρ = theoretical apparent resistivity from the model · N = number of measurement points
IEEE 81-2025 §7.6.2
Interpreting Multiple Traverses
When two or more traverses are measured at the same site, IEEE 81-2025 §7.6.2 provides guidance on how to combine or compare them. Differences between traverses may indicate real lateral variation in the soil, or they may indicate measurement errors, interference, or proximity to buried conductors. It is important to distinguish between these cases before selecting the design soil model.
Traverses agree within 20%
Average the two apparent resistivity curves point-by-point and fit a single model to the averaged curve. This is the standard practice for most grounding design projects.
Traverses differ by 20–50%
Fit separate models to each traverse. Use the higher-resistivity model for the grounding design (conservative approach). Document both models in the report and note the variance.
Traverses differ by more than 50%
Investigate the cause before proceeding. Possible causes include: a buried conductor near one traverse, a geological fault, a contamination plume, or a measurement error. Consider adding a third traverse to identify the outlier.
One traverse shows an anomalous low-resistivity zone
This may indicate a buried conductor, a water main, or a contamination plume. Do not average with the other traverse. Report both models and flag the anomaly. The grounding designer must decide which model to use based on the physical layout of the proposed grid.
The STRATIFY™ calculator supports multi-traverse input. When two or more traverses are entered, it plots each curve separately, computes the variance between them, and flags high-variance cases with a warning before curve fitting.
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