Geotechnical Field Exploration, Testing and Uncertainty

Outcomes

After completing this unit the learner should be able to define the governing state variables, calculate representative quantities with correct units, explain when the idealized relation breaks down, interpret the corresponding laboratory models, and defend a field investigation or verification decision.

Core lessons

Lesson 8.1 — Planning a ground investigation

Central question. A useful site investigation links engineering decisions to conceptual ground models rather than collecting isolated test results.

Governing relationships and definitions. Specify investigation objectives, strata continuity, groundwater monitoring, uncertainty and potential design consequences. Choose soundings and boreholes to investigate actual load paths and failure mechanisms.

Worked calculation / observation. A building footprint with possible fill over clay demands different investigation coverage from a long highway embankment crossing an alluvial valley. The depth of interest follows influence, not a universal fixed number.

Why interpretation matters. A borehole log records observations made through a particular sampling window. Drawing continuous layer boundaries between widely spaced boreholes is a geological interpretation, not a direct measurement. Show alternative connections where discontinuous lenses, fill pockets or abrupt contacts remain plausible.

Field case: A small site investigation with sparse borehole coverage. In a small site investigation with sparse borehole coverage, the engineer should first sketch the geometry, state the loading or groundwater history, and identify which of the measured quantities are direct observations. Next identify the controlling stress, volume, hydraulic or strength variable from this lesson. A prediction is only as defensible as the link between the laboratory variable and its field counterpart. For example, the stress relevant to settlement may be an effective stress after excess water pressure dissipates, whereas the load relevant to a temporary wall brace may be a short-term total-stress action. Mixing those questions can produce a plausible-looking but physically inconsistent answer.

From observation to a defensible model. A practical investigation has three stages. Observation: identify the features of a small site investigation with sparse borehole coverage that a field crew can actually record, such as layer thickness, water-table history, moisture state or deformation. Interpretation: select the idealized law described above, explain the chosen signs and units, and identify which soil parameters need independent tests. Prediction: evaluate a baseline and at least two credible alternatives. A single baseline is rarely an adequate basis for choosing a foundation treatment, drainage provision or construction method.

Verification practice. A useful checking sequence is dimensional analysis, limiting behavior and independent arithmetic. Insert the stated units before using a formula; a conductivity given in cm/s cannot be entered as m/s unchanged. Ask whether a computed stress or discharge tends toward zero when its driving load is removed. Then compare with a second hand calculation, a plotted numerical response or a bounding case. A graph from an interactive model provides feedback, not evidence that the assumed governing equation is correct for the site.

Reasoning exercise. Draw the physical control volume or stress path for a small site investigation with sparse borehole coverage. Label the measured variables, the inferred variables and the quantities that could change after construction. Which variable would be the cheapest to measure more accurately? Describe how two alternative assumptions could change the outcome in opposite directions. Finally explain which decision would be postponed until a more representative specimen, groundwater observation or construction-stage measurement becomes available.

Model boundary. Log coordinate, datum, ground elevation, drilling method, sampling depth and groundwater reading date. Record refusals and anomalies rather than deleting them. Present the result with an explicit number of significant digits justified by the inputs; do not confuse that numerical precision with geological certainty. Professional design requires the governing standard, site-specific investigation and independent review.

Lesson 8.2 — Sampling disturbance and laboratory controls

Central question. Sampling may alter water content, fabric, stress state and grain arrangement; laboratory precision cannot undo poor sample representativeness.

Governing relationships and definitions. Distinguish disturbed index samples from high-quality tube samples used for compressibility or strength. Calculate sample recovery and document extrusion, trimming and preservation.

Worked calculation / observation. Two specimens from the same layer may produce different compression indices because one experienced drying or handling disturbance. That discrepancy must prompt investigation rather than averaging blindly.

Why interpretation matters. Groundwater readings made during drilling can be transient. A reliable hydrogeologic model often needs standpipes, repeat readings or piezometers and notes about seasonal conditions. A one-time water level should not automatically become the permanent design water table.

Field case: A coastal project with seasonally high groundwater. In a coastal project with seasonally high groundwater, the engineer should first sketch the geometry, state the loading or groundwater history, and identify which of the measured quantities are direct observations. Next identify the controlling stress, volume, hydraulic or strength variable from this lesson. A prediction is only as defensible as the link between the laboratory variable and its field counterpart. For example, the stress relevant to settlement may be an effective stress after excess water pressure dissipates, whereas the load relevant to a temporary wall brace may be a short-term total-stress action. Mixing those questions can produce a plausible-looking but physically inconsistent answer.

From observation to a defensible model. A practical investigation has three stages. Observation: identify the features of a coastal project with seasonally high groundwater that a field crew can actually record, such as layer thickness, water-table history, moisture state or deformation. Interpretation: select the idealized law described above, explain the chosen signs and units, and identify which soil parameters need independent tests. Prediction: evaluate a baseline and at least two credible alternatives. A single baseline is rarely an adequate basis for choosing a foundation treatment, drainage provision or construction method.

Verification practice. A useful checking sequence is dimensional analysis, limiting behavior and independent arithmetic. Insert the stated units before using a formula; a conductivity given in cm/s cannot be entered as m/s unchanged. Ask whether a computed stress or discharge tends toward zero when its driving load is removed. Then compare with a second hand calculation, a plotted numerical response or a bounding case. A graph from an interactive model provides feedback, not evidence that the assumed governing equation is correct for the site.

Reasoning exercise. Draw the physical control volume or stress path for a coastal project with seasonally high groundwater. Label the measured variables, the inferred variables and the quantities that could change after construction. Which variable would be the cheapest to measure more accurately? Describe how two alternative assumptions could change the outcome in opposite directions. Finally explain which decision would be postponed until a more representative specimen, groundwater observation or construction-stage measurement becomes available.

Model boundary. Sample quality is a continuum and the response is test-specific. A disturbed sample may be suitable for grain-size analysis but not in-situ compressibility. Present the result with an explicit number of significant digits justified by the inputs; do not confuse that numerical precision with geological certainty. Professional design requires the governing standard, site-specific investigation and independent review.

Lesson 8.3 — Reading test data and building a ground model

Central question. Field and laboratory results should be reconciled by depth, geology and credible stress history.

Governing relationships and definitions. Use stratigraphic profiles with test depths, water pressure, uncertainty ranges and representative parameters with stated basis; resist false precision from single test points.

Worked calculation / observation. If three sampled pockets show markedly different water contents within a fill, model separate material zones until sampling establishes whether they are continuous. Do not substitute a global mean automatically.

Why interpretation matters. Laboratory errors include instrument calibration, sample identification, moisture loss, volume trimming and calculation transcription. Sampling errors include spatial nonrepresentativeness and disturbance. A well-designed testing plan addresses both; increasing numerical precision does not overcome biased samples.

Field case: A laboratory testing program with chain-of-custody gaps. In a laboratory testing program with chain-of-custody gaps, the engineer should first sketch the geometry, state the loading or groundwater history, and identify which of the measured quantities are direct observations. Next identify the controlling stress, volume, hydraulic or strength variable from this lesson. A prediction is only as defensible as the link between the laboratory variable and its field counterpart. For example, the stress relevant to settlement may be an effective stress after excess water pressure dissipates, whereas the load relevant to a temporary wall brace may be a short-term total-stress action. Mixing those questions can produce a plausible-looking but physically inconsistent answer.

From observation to a defensible model. A practical investigation has three stages. Observation: identify the features of a laboratory testing program with chain-of-custody gaps that a field crew can actually record, such as layer thickness, water-table history, moisture state or deformation. Interpretation: select the idealized law described above, explain the chosen signs and units, and identify which soil parameters need independent tests. Prediction: evaluate a baseline and at least two credible alternatives. A single baseline is rarely an adequate basis for choosing a foundation treatment, drainage provision or construction method.

Verification practice. A useful checking sequence is dimensional analysis, limiting behavior and independent arithmetic. Insert the stated units before using a formula; a conductivity given in cm/s cannot be entered as m/s unchanged. Ask whether a computed stress or discharge tends toward zero when its driving load is removed. Then compare with a second hand calculation, a plotted numerical response or a bounding case. A graph from an interactive model provides feedback, not evidence that the assumed governing equation is correct for the site.

Reasoning exercise. Draw the physical control volume or stress path for a laboratory testing program with chain-of-custody gaps. Label the measured variables, the inferred variables and the quantities that could change after construction. Which variable would be the cheapest to measure more accurately? Describe how two alternative assumptions could change the outcome in opposite directions. Finally explain which decision would be postponed until a more representative specimen, groundwater observation or construction-stage measurement becomes available.

Model boundary. Correlations between SPT and stiffness or between index properties and strength have scatter, equipment corrections and regional bias. State the source and range of applicability. Present the result with an explicit number of significant digits justified by the inputs; do not confuse that numerical precision with geological certainty. Professional design requires the governing standard, site-specific investigation and independent review.

Lesson 8.4 — Uncertainty, decision thresholds and reporting

Central question. Good geotechnical engineering distinguishes measured quantities, derived values and judgmental estimates.

Governing relationships and definitions. Perform transparent sensitivity analysis and, where appropriate, a reproducible simple sampling exercise; the simulated spread reflects the assumed statistical model, not a certified failure probability.

Worked calculation / observation. An estimated k with order-of-magnitude variation can reverse the preferred dewatering method. A simple logarithmic sensitivity may be more informative than reporting average k to four significant digits.

Why interpretation matters. When the cost of a wrong model is high, adaptive investigation can be more effective than immediately increasing design conservatism across the board. A second well-placed sounding, a piezometer or a short monitored trial may discriminate between plausible ground models and reduce design uncertainty substantially.

Field case: A construction design meeting with competing ground models. In a construction design meeting with competing ground models, the engineer should first sketch the geometry, state the loading or groundwater history, and identify which of the measured quantities are direct observations. Next identify the controlling stress, volume, hydraulic or strength variable from this lesson. A prediction is only as defensible as the link between the laboratory variable and its field counterpart. For example, the stress relevant to settlement may be an effective stress after excess water pressure dissipates, whereas the load relevant to a temporary wall brace may be a short-term total-stress action. Mixing those questions can produce a plausible-looking but physically inconsistent answer.

From observation to a defensible model. A practical investigation has three stages. Observation: identify the features of a construction design meeting with competing ground models that a field crew can actually record, such as layer thickness, water-table history, moisture state or deformation. Interpretation: select the idealized law described above, explain the chosen signs and units, and identify which soil parameters need independent tests. Prediction: evaluate a baseline and at least two credible alternatives. A single baseline is rarely an adequate basis for choosing a foundation treatment, drainage provision or construction method.

Verification practice. A useful checking sequence is dimensional analysis, limiting behavior and independent arithmetic. Insert the stated units before using a formula; a conductivity given in cm/s cannot be entered as m/s unchanged. Ask whether a computed stress or discharge tends toward zero when its driving load is removed. Then compare with a second hand calculation, a plotted numerical response or a bounding case. A graph from an interactive model provides feedback, not evidence that the assumed governing equation is correct for the site.

Reasoning exercise. Draw the physical control volume or stress path for a construction design meeting with competing ground models. Label the measured variables, the inferred variables and the quantities that could change after construction. Which variable would be the cheapest to measure more accurately? Describe how two alternative assumptions could change the outcome in opposite directions. Finally explain which decision would be postponed until a more representative specimen, groundwater observation or construction-stage measurement becomes available.

Model boundary. Use an assumptions register; include alternative models, trigger observations, hold points and what new evidence would change the design recommendation. Present the result with an explicit number of significant digits justified by the inputs; do not confuse that numerical precision with geological certainty. Professional design requires the governing standard, site-specific investigation and independent review.

Laboratory activities

Laboratory 15: Sampler Recovery & Disturbance. Recovery ratio and sample handling checks. First predict the direction of change for the output when one control changes. Hold all other controls fixed; record a baseline, two variations, and a short discussion of why the governing assumptions are or are not credible. Navigate to ../labs/lab-15.html. Important: A screening score is pedagogical, not a standard sample quality rating.

Laboratory 16: Parameter Uncertainty Explorer. Reproducible distributions for slope friction angle. First predict the direction of change for the output when one control changes. Hold all other controls fixed; record a baseline, two variations, and a short discussion of why the governing assumptions are or are not credible. Navigate to ../labs/lab-16.html. Important: Assumed normal spread with fixed seed; not a measured reliability distribution.

Integrated design conversation

Imagine that the site data are incomplete and construction will begin in phases. Construct two defensible interpretations of the subsurface conditions. For each, state the best estimate of the controlling material parameter and a credible low and high value. Explain how a field observation or laboratory test could reject one interpretation. The deliverable is not only a number but a documented chain from field evidence to calculation, checking, and the resulting construction choice.

Applied dossier: sparse investigation and a misleading average

A proposed light industrial building sits on variable fill over natural clay. Three borings identify fill thicknesses of 1.1, 2.4 and 0.6 m. An average of 1.37 m is easy to compute, but it is not evidence of a uniform layer that is 1.37 m thick beneath every footing. The spatial transitions and origin of the fill are unknown. Before selecting one compressibility or strength parameter, the engineer should plot the borehole locations, encountered materials, sample elevations, groundwater observations and plausible alternative geological sections.

For one tube sample, advance during driving was 0.80 m and recovered length was 0.64 m. Sample recovery ratio is 0.64/0.80×100=80%. With an inside tube diameter of 75 mm and wall thickness 2 mm, the geometric area ratio is [(79²−75²)/75²]×100≈10.95%. These indices are useful descriptions of the sampling operation. Neither number alone proves that undisturbed stress history or fabric has been retained in the tube.

Two oedometer specimens from the same mapped clay unit report quite different compression indexes. Rather than average immediately, compare water content, specimen condition, sampling depth, extrusion notes and tested stress range. A mixed fill, fissured crust and deeper natural clay may have been conflated as one unit. Replicate testing of a critical horizon may be more valuable than a large number of unrelated index tests.

For a sensitivity exercise, assume friction angle measurements are approximately normal with a mean of 32° and standard deviation of 3°, solely for teaching. On a 25° dry cohesionless slope, compute FS=tanφ′/tan25° for each sampled φ′ using a fixed random seed. The resulting histogram or percentile curve tells you what that assumed distribution implies mathematically. It is not an estimate of site failure probability until the assumed statistical model and spatial representativeness have been validated.

A final report should therefore distinguish observed quantities, derived parameters, correlations and judgment. It should list decisions that remain insensitive to uncertainty, decisions that may change and the least expensive additional investigation that resolves each uncertainty. The alternative is false precision: an attractive graph whose narrow confidence band has been invented by unsupported assumptions.

Technical methods notebook: traceability and uncertainty

A field record is a chain of evidence. For each borehole, record coordinates and elevation datum, start and finish date, sampling method, test depths, recovery, weather and temporary or stabilized water readings. An apparent layer boundary in an interpolated profile should be labeled an interpretation between observations, not drawn as a physically measured continuous surface. If a proposed footing crosses a suspect fill-to-clay boundary, a targeted follow-up test may have more value than many additional tests in a well-characterized corner.

Recovery and area ratio. Recovery ratio is recovered sample length divided by advance length and is often reported as a percentage. A recovery over 100% is not impossible in a disturbed sample context, but it flags an inconsistency or special mechanism that should be explained rather than accepted without review. A thin-wall tube geometric area ratio may be defined as (Dout²−Din²)/Din²×100%, provided diameters refer to the cutting geometry being evaluated. Lower ratios generally reduce displacement for an otherwise comparable geometry, but no universal inference about sample quality follows from area ratio alone.

Disturbance is physical, not merely arithmetic. Stress relief during extraction, moisture loss, remolding, vibration, storage and extrusion alter soil structure and measured stress–strain behavior. A sample that is unsuitable for oedometer interpretation may remain useful for moisture or particle-size tests. Specify the data needed before choosing sampling equipment and handling procedures; otherwise tests may be precise but answer the wrong question.

Correlations need context. A field penetration count is affected by energy delivery, equipment, overburden and soil type. It cannot be treated as an intrinsic modulus without procedural corrections and locally relevant correlation evidence. Similar caution applies when predicting hydraulic conductivity from grain size or strength from Atterberg limits. Report estimated values and ranges, and distinguish empirical correlation error from actual subsurface variability.

Deterministic simulations of uncertainty. A fixed-seed Monte Carlo model produces the same sampled numbers for the same input parameters. That is useful for educational reproducibility. Suppose φ′ is assumed to follow a normal distribution with mean 32° and standard deviation 3°, and the slope has β=25°. The simulated spread in tanφ′/tanβ is a transformed spread from the assumed parameter distribution. It does not establish that friction angles are normal at the site, that values are spatially independent, or that the implied proportion below FS=1 estimates real-world landslide frequency.

An uncertainty register. Separate three categories. Measurement uncertainty includes instrument calibration, recovery and test repeatability. Model uncertainty includes simplifications in loading, drainage, stress distribution and failure geometry. Spatial uncertainty includes unobserved lenses and layer changes. A practical mitigation plan identifies which decision depends on which category and chooses follow-up work accordingly. Where outcomes are sensitive to groundwater conditions, a piezometer may outperform a second index test; where outcomes depend on the thickness of weak clay, better stratigraphic coverage may be essential.

Reviewable deliverable. Include a plan of investigation locations, logs, a longitudinal ground profile, groundwater readings by date, a table of chosen parameters with traceable sources, representative calculations, sensitivity plots and unambiguous remaining assumptions. Finish with what additional evidence would change the recommended design approach. The objective is not to remove all uncertainty, which is impossible in earth materials, but to make engineering decisions proportional to the quality and consequences of the available evidence.

Unit 8: Geotechnical methods

Sampling, laboratory practice, data interpretation and uncertainty.

Outcomes

After completing this unit the learner should be able to define the governing state variables, calculate representative quantities with correct units, explain when the idealized relation breaks down, interpret the corresponding laboratory models, and defend a field investigation or verification decision.

Core lessons

Lesson 8.1 — Planning a ground investigation

Central question. A useful site investigation links engineering decisions to conceptual ground models rather than collecting isolated test results.

Governing relationships and definitions. Specify investigation objectives, strata continuity, groundwater monitoring, uncertainty and potential design consequences. Choose soundings and boreholes to investigate actual load paths and failure mechanisms.

Worked calculation / observation. A building footprint with possible fill over clay demands different investigation coverage from a long highway embankment crossing an alluvial valley. The depth of interest follows influence, not a universal fixed number.

Why interpretation matters. A borehole log records observations made through a particular sampling window. Drawing continuous layer boundaries between widely spaced boreholes is a geological interpretation, not a direct measurement. Show alternative connections where discontinuous lenses, fill pockets or abrupt contacts remain plausible.

Field case: A small site investigation with sparse borehole coverage. In a small site investigation with sparse borehole coverage, the engineer should first sketch the geometry, state the loading or groundwater history, and identify which of the measured quantities are direct observations. Next identify the controlling stress, volume, hydraulic or strength variable from this lesson. A prediction is only as defensible as the link between the laboratory variable and its field counterpart. For example, the stress relevant to settlement may be an effective stress after excess water pressure dissipates, whereas the load relevant to a temporary wall brace may be a short-term total-stress action. Mixing those questions can produce a plausible-looking but physically inconsistent answer.

From observation to a defensible model. A practical investigation has three stages. Observation: identify the features of a small site investigation with sparse borehole coverage that a field crew can actually record, such as layer thickness, water-table history, moisture state or deformation. Interpretation: select the idealized law described above, explain the chosen signs and units, and identify which soil parameters need independent tests. Prediction: evaluate a baseline and at least two credible alternatives. A single baseline is rarely an adequate basis for choosing a foundation treatment, drainage provision or construction method.

Verification practice. A useful checking sequence is dimensional analysis, limiting behavior and independent arithmetic. Insert the stated units before using a formula; a conductivity given in cm/s cannot be entered as m/s unchanged. Ask whether a computed stress or discharge tends toward zero when its driving load is removed. Then compare with a second hand calculation, a plotted numerical response or a bounding case. A graph from an interactive model provides feedback, not evidence that the assumed governing equation is correct for the site.

Reasoning exercise. Draw the physical control volume or stress path for a small site investigation with sparse borehole coverage. Label the measured variables, the inferred variables and the quantities that could change after construction. Which variable would be the cheapest to measure more accurately? Describe how two alternative assumptions could change the outcome in opposite directions. Finally explain which decision would be postponed until a more representative specimen, groundwater observation or construction-stage measurement becomes available.

Model boundary. Log coordinate, datum, ground elevation, drilling method, sampling depth and groundwater reading date. Record refusals and anomalies rather than deleting them. Present the result with an explicit number of significant digits justified by the inputs; do not confuse that numerical precision with geological certainty. Professional design requires the governing standard, site-specific investigation and independent review.

Lesson 8.2 — Sampling disturbance and laboratory controls

Central question. Sampling may alter water content, fabric, stress state and grain arrangement; laboratory precision cannot undo poor sample representativeness.

Governing relationships and definitions. Distinguish disturbed index samples from high-quality tube samples used for compressibility or strength. Calculate sample recovery and document extrusion, trimming and preservation.

Worked calculation / observation. Two specimens from the same layer may produce different compression indices because one experienced drying or handling disturbance. That discrepancy must prompt investigation rather than averaging blindly.

Why interpretation matters. Groundwater readings made during drilling can be transient. A reliable hydrogeologic model often needs standpipes, repeat readings or piezometers and notes about seasonal conditions. A one-time water level should not automatically become the permanent design water table.

Field case: A coastal project with seasonally high groundwater. In a coastal project with seasonally high groundwater, the engineer should first sketch the geometry, state the loading or groundwater history, and identify which of the measured quantities are direct observations. Next identify the controlling stress, volume, hydraulic or strength variable from this lesson. A prediction is only as defensible as the link between the laboratory variable and its field counterpart. For example, the stress relevant to settlement may be an effective stress after excess water pressure dissipates, whereas the load relevant to a temporary wall brace may be a short-term total-stress action. Mixing those questions can produce a plausible-looking but physically inconsistent answer.

From observation to a defensible model. A practical investigation has three stages. Observation: identify the features of a coastal project with seasonally high groundwater that a field crew can actually record, such as layer thickness, water-table history, moisture state or deformation. Interpretation: select the idealized law described above, explain the chosen signs and units, and identify which soil parameters need independent tests. Prediction: evaluate a baseline and at least two credible alternatives. A single baseline is rarely an adequate basis for choosing a foundation treatment, drainage provision or construction method.

Verification practice. A useful checking sequence is dimensional analysis, limiting behavior and independent arithmetic. Insert the stated units before using a formula; a conductivity given in cm/s cannot be entered as m/s unchanged. Ask whether a computed stress or discharge tends toward zero when its driving load is removed. Then compare with a second hand calculation, a plotted numerical response or a bounding case. A graph from an interactive model provides feedback, not evidence that the assumed governing equation is correct for the site.

Reasoning exercise. Draw the physical control volume or stress path for a coastal project with seasonally high groundwater. Label the measured variables, the inferred variables and the quantities that could change after construction. Which variable would be the cheapest to measure more accurately? Describe how two alternative assumptions could change the outcome in opposite directions. Finally explain which decision would be postponed until a more representative specimen, groundwater observation or construction-stage measurement becomes available.

Model boundary. Sample quality is a continuum and the response is test-specific. A disturbed sample may be suitable for grain-size analysis but not in-situ compressibility. Present the result with an explicit number of significant digits justified by the inputs; do not confuse that numerical precision with geological certainty. Professional design requires the governing standard, site-specific investigation and independent review.

Lesson 8.3 — Reading test data and building a ground model

Central question. Field and laboratory results should be reconciled by depth, geology and credible stress history.

Governing relationships and definitions. Use stratigraphic profiles with test depths, water pressure, uncertainty ranges and representative parameters with stated basis; resist false precision from single test points.

Worked calculation / observation. If three sampled pockets show markedly different water contents within a fill, model separate material zones until sampling establishes whether they are continuous. Do not substitute a global mean automatically.

Why interpretation matters. Laboratory errors include instrument calibration, sample identification, moisture loss, volume trimming and calculation transcription. Sampling errors include spatial nonrepresentativeness and disturbance. A well-designed testing plan addresses both; increasing numerical precision does not overcome biased samples.

Field case: A laboratory testing program with chain-of-custody gaps. In a laboratory testing program with chain-of-custody gaps, the engineer should first sketch the geometry, state the loading or groundwater history, and identify which of the measured quantities are direct observations. Next identify the controlling stress, volume, hydraulic or strength variable from this lesson. A prediction is only as defensible as the link between the laboratory variable and its field counterpart. For example, the stress relevant to settlement may be an effective stress after excess water pressure dissipates, whereas the load relevant to a temporary wall brace may be a short-term total-stress action. Mixing those questions can produce a plausible-looking but physically inconsistent answer.

From observation to a defensible model. A practical investigation has three stages. Observation: identify the features of a laboratory testing program with chain-of-custody gaps that a field crew can actually record, such as layer thickness, water-table history, moisture state or deformation. Interpretation: select the idealized law described above, explain the chosen signs and units, and identify which soil parameters need independent tests. Prediction: evaluate a baseline and at least two credible alternatives. A single baseline is rarely an adequate basis for choosing a foundation treatment, drainage provision or construction method.

Verification practice. A useful checking sequence is dimensional analysis, limiting behavior and independent arithmetic. Insert the stated units before using a formula; a conductivity given in cm/s cannot be entered as m/s unchanged. Ask whether a computed stress or discharge tends toward zero when its driving load is removed. Then compare with a second hand calculation, a plotted numerical response or a bounding case. A graph from an interactive model provides feedback, not evidence that the assumed governing equation is correct for the site.

Reasoning exercise. Draw the physical control volume or stress path for a laboratory testing program with chain-of-custody gaps. Label the measured variables, the inferred variables and the quantities that could change after construction. Which variable would be the cheapest to measure more accurately? Describe how two alternative assumptions could change the outcome in opposite directions. Finally explain which decision would be postponed until a more representative specimen, groundwater observation or construction-stage measurement becomes available.

Model boundary. Correlations between SPT and stiffness or between index properties and strength have scatter, equipment corrections and regional bias. State the source and range of applicability. Present the result with an explicit number of significant digits justified by the inputs; do not confuse that numerical precision with geological certainty. Professional design requires the governing standard, site-specific investigation and independent review.

Lesson 8.4 — Uncertainty, decision thresholds and reporting

Central question. Good geotechnical engineering distinguishes measured quantities, derived values and judgmental estimates.

Governing relationships and definitions. Perform transparent sensitivity analysis and, where appropriate, a reproducible simple sampling exercise; the simulated spread reflects the assumed statistical model, not a certified failure probability.

Worked calculation / observation. An estimated k with order-of-magnitude variation can reverse the preferred dewatering method. A simple logarithmic sensitivity may be more informative than reporting average k to four significant digits.

Why interpretation matters. When the cost of a wrong model is high, adaptive investigation can be more effective than immediately increasing design conservatism across the board. A second well-placed sounding, a piezometer or a short monitored trial may discriminate between plausible ground models and reduce design uncertainty substantially.

Field case: A construction design meeting with competing ground models. In a construction design meeting with competing ground models, the engineer should first sketch the geometry, state the loading or groundwater history, and identify which of the measured quantities are direct observations. Next identify the controlling stress, volume, hydraulic or strength variable from this lesson. A prediction is only as defensible as the link between the laboratory variable and its field counterpart. For example, the stress relevant to settlement may be an effective stress after excess water pressure dissipates, whereas the load relevant to a temporary wall brace may be a short-term total-stress action. Mixing those questions can produce a plausible-looking but physically inconsistent answer.

From observation to a defensible model. A practical investigation has three stages. Observation: identify the features of a construction design meeting with competing ground models that a field crew can actually record, such as layer thickness, water-table history, moisture state or deformation. Interpretation: select the idealized law described above, explain the chosen signs and units, and identify which soil parameters need independent tests. Prediction: evaluate a baseline and at least two credible alternatives. A single baseline is rarely an adequate basis for choosing a foundation treatment, drainage provision or construction method.

Verification practice. A useful checking sequence is dimensional analysis, limiting behavior and independent arithmetic. Insert the stated units before using a formula; a conductivity given in cm/s cannot be entered as m/s unchanged. Ask whether a computed stress or discharge tends toward zero when its driving load is removed. Then compare with a second hand calculation, a plotted numerical response or a bounding case. A graph from an interactive model provides feedback, not evidence that the assumed governing equation is correct for the site.

Reasoning exercise. Draw the physical control volume or stress path for a construction design meeting with competing ground models. Label the measured variables, the inferred variables and the quantities that could change after construction. Which variable would be the cheapest to measure more accurately? Describe how two alternative assumptions could change the outcome in opposite directions. Finally explain which decision would be postponed until a more representative specimen, groundwater observation or construction-stage measurement becomes available.

Model boundary. Use an assumptions register; include alternative models, trigger observations, hold points and what new evidence would change the design recommendation. Present the result with an explicit number of significant digits justified by the inputs; do not confuse that numerical precision with geological certainty. Professional design requires the governing standard, site-specific investigation and independent review.

Laboratory activities

Laboratory 15: Sampler Recovery & Disturbance. Recovery ratio and sample handling checks. First predict the direction of change for the output when one control changes. Hold all other controls fixed; record a baseline, two variations, and a short discussion of why the governing assumptions are or are not credible. Navigate to ../labs/lab-15.html. Important: A screening score is pedagogical, not a standard sample quality rating.

Laboratory 16: Parameter Uncertainty Explorer. Reproducible distributions for slope friction angle. First predict the direction of change for the output when one control changes. Hold all other controls fixed; record a baseline, two variations, and a short discussion of why the governing assumptions are or are not credible. Navigate to ../labs/lab-16.html. Important: Assumed normal spread with fixed seed; not a measured reliability distribution.

Integrated design conversation

Imagine that the site data are incomplete and construction will begin in phases. Construct two defensible interpretations of the subsurface conditions. For each, state the best estimate of the controlling material parameter and a credible low and high value. Explain how a field observation or laboratory test could reject one interpretation. The deliverable is not only a number but a documented chain from field evidence to calculation, checking, and the resulting construction choice.

Applied dossier: sparse investigation and a misleading average

A proposed light industrial building sits on variable fill over natural clay. Three borings identify fill thicknesses of 1.1, 2.4 and 0.6 m. An average of 1.37 m is easy to compute, but it is not evidence of a uniform layer that is 1.37 m thick beneath every footing. The spatial transitions and origin of the fill are unknown. Before selecting one compressibility or strength parameter, the engineer should plot the borehole locations, encountered materials, sample elevations, groundwater observations and plausible alternative geological sections.

For one tube sample, advance during driving was 0.80 m and recovered length was 0.64 m. Sample recovery ratio is 0.64/0.80×100=80%. With an inside tube diameter of 75 mm and wall thickness 2 mm, the geometric area ratio is [(79²−75²)/75²]×100≈10.95%. These indices are useful descriptions of the sampling operation. Neither number alone proves that undisturbed stress history or fabric has been retained in the tube.

Two oedometer specimens from the same mapped clay unit report quite different compression indexes. Rather than average immediately, compare water content, specimen condition, sampling depth, extrusion notes and tested stress range. A mixed fill, fissured crust and deeper natural clay may have been conflated as one unit. Replicate testing of a critical horizon may be more valuable than a large number of unrelated index tests.

For a sensitivity exercise, assume friction angle measurements are approximately normal with a mean of 32° and standard deviation of 3°, solely for teaching. On a 25° dry cohesionless slope, compute FS=tanφ′/tan25° for each sampled φ′ using a fixed random seed. The resulting histogram or percentile curve tells you what that assumed distribution implies mathematically. It is not an estimate of site failure probability until the assumed statistical model and spatial representativeness have been validated.

A final report should therefore distinguish observed quantities, derived parameters, correlations and judgment. It should list decisions that remain insensitive to uncertainty, decisions that may change and the least expensive additional investigation that resolves each uncertainty. The alternative is false precision: an attractive graph whose narrow confidence band has been invented by unsupported assumptions.

Technical methods notebook: traceability and uncertainty

A field record is a chain of evidence. For each borehole, record coordinates and elevation datum, start and finish date, sampling method, test depths, recovery, weather and temporary or stabilized water readings. An apparent layer boundary in an interpolated profile should be labeled an interpretation between observations, not drawn as a physically measured continuous surface. If a proposed footing crosses a suspect fill-to-clay boundary, a targeted follow-up test may have more value than many additional tests in a well-characterized corner.

Recovery and area ratio. Recovery ratio is recovered sample length divided by advance length and is often reported as a percentage. A recovery over 100% is not impossible in a disturbed sample context, but it flags an inconsistency or special mechanism that should be explained rather than accepted without review. A thin-wall tube geometric area ratio may be defined as (Dout²−Din²)/Din²×100%, provided diameters refer to the cutting geometry being evaluated. Lower ratios generally reduce displacement for an otherwise comparable geometry, but no universal inference about sample quality follows from area ratio alone.

Disturbance is physical, not merely arithmetic. Stress relief during extraction, moisture loss, remolding, vibration, storage and extrusion alter soil structure and measured stress–strain behavior. A sample that is unsuitable for oedometer interpretation may remain useful for moisture or particle-size tests. Specify the data needed before choosing sampling equipment and handling procedures; otherwise tests may be precise but answer the wrong question.

Correlations need context. A field penetration count is affected by energy delivery, equipment, overburden and soil type. It cannot be treated as an intrinsic modulus without procedural corrections and locally relevant correlation evidence. Similar caution applies when predicting hydraulic conductivity from grain size or strength from Atterberg limits. Report estimated values and ranges, and distinguish empirical correlation error from actual subsurface variability.

Deterministic simulations of uncertainty. A fixed-seed Monte Carlo model produces the same sampled numbers for the same input parameters. That is useful for educational reproducibility. Suppose φ′ is assumed to follow a normal distribution with mean 32° and standard deviation 3°, and the slope has β=25°. The simulated spread in tanφ′/tanβ is a transformed spread from the assumed parameter distribution. It does not establish that friction angles are normal at the site, that values are spatially independent, or that the implied proportion below FS=1 estimates real-world landslide frequency.

An uncertainty register. Separate three categories. Measurement uncertainty includes instrument calibration, recovery and test repeatability. Model uncertainty includes simplifications in loading, drainage, stress distribution and failure geometry. Spatial uncertainty includes unobserved lenses and layer changes. A practical mitigation plan identifies which decision depends on which category and chooses follow-up work accordingly. Where outcomes are sensitive to groundwater conditions, a piezometer may outperform a second index test; where outcomes depend on the thickness of weak clay, better stratigraphic coverage may be essential.

Reviewable deliverable. Include a plan of investigation locations, logs, a longitudinal ground profile, groundwater readings by date, a table of chosen parameters with traceable sources, representative calculations, sensitivity plots and unambiguous remaining assumptions. Finish with what additional evidence would change the recommended design approach. The objective is not to remove all uncertainty, which is impossible in earth materials, but to make engineering decisions proportional to the quality and consequences of the available evidence.

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Integrated project 1: A mixed-grain subgrade

Problem setting. Develop a complete phase diagram for two compacted samples; plot their saturation curves; reconcile measured mass, moisture, specific gravity and volume; classify the materials with explicit evidence rather than assuming density determines grading.

Deliverable. Explain why similar measured water contents do not imply similar saturation; propose at least two follow-up tests before a subgrade material selection.

Part A — Evidence table. Produce a two-column table distinguishing quantities directly measured from those computed or adopted through judgment. For each reported number include its units, the method or source, the measurement volume or location, and a plausible uncertainty range. Data that contradict the assumed stratigraphy must be explained, not discarded.

Part B — Reproducible calculations. Perform calculations by hand for a baseline. Then use both interactive laboratory models in Unit 1 to generate a response curve. Export one CSV file and annotate the inputs that lead to every plotted point. Check a limiting case in which the physical driver becomes small or the sample becomes saturated or unloaded, as appropriate.

Part C — Interpretation. Compare at least two plausible ground models. Explain how changes in the governing parameter alter the decision and why the graph alone cannot choose the correct model. Report an action supported by current evidence and identify a low-cost field or laboratory test whose result could materially reverse that action.

Part D — Review. Create a one-page engineering memo with purpose, physical assumptions, schematic section, measurements, computations, model limitations, uncertainties and recommended next investigation. A reviewer should be able to reproduce calculations without contacting the author.

Assessment rubric. Physical model and correct units (25%), evidence traceability (20%), independent numerical checking (20%), uncertainty and alternative scenarios (20%), clear decision and professional documentation (15%). This project is educational, not an authorized construction document.

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Integrated project 2: Groundwater drawdown near an excavation

Problem setting. Set a conceptual two-layer profile; evaluate kh and kv, a one-dimensional discharge and effective-stress profiles before and after hypothetical water-level changes; compare against monitoring.

Deliverable. Identify potential seepage exits and explain why a simple layered model cannot establish piping resistance or excavation stability.

Part A — Evidence table. Produce a two-column table distinguishing quantities directly measured from those computed or adopted through judgment. For each reported number include its units, the method or source, the measurement volume or location, and a plausible uncertainty range. Data that contradict the assumed stratigraphy must be explained, not discarded.

Part B — Reproducible calculations. Perform calculations by hand for a baseline. Then use both interactive laboratory models in Unit 2 to generate a response curve. Export one CSV file and annotate the inputs that lead to every plotted point. Check a limiting case in which the physical driver becomes small or the sample becomes saturated or unloaded, as appropriate.

Part C — Interpretation. Compare at least two plausible ground models. Explain how changes in the governing parameter alter the decision and why the graph alone cannot choose the correct model. Report an action supported by current evidence and identify a low-cost field or laboratory test whose result could materially reverse that action.

Part D — Review. Create a one-page engineering memo with purpose, physical assumptions, schematic section, measurements, computations, model limitations, uncertainties and recommended next investigation. A reviewer should be able to reproduce calculations without contacting the author.

Assessment rubric. Physical model and correct units (25%), evidence traceability (20%), independent numerical checking (20%), uncertainty and alternative scenarios (20%), clear decision and professional documentation (15%). This project is educational, not an authorized construction document.

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Integrated project 3: Field fill acceptance case

Problem setting. Create a laboratory moisture-density dataset and field dry-density table; calculate relative compaction; classify observations under an explicitly stated hypothetical contract limit; recommend retesting where evidence is marginal.

Deliverable. Discuss what could change with altered moisture conditioning, different compactive effort and field test uncertainty.

Part A — Evidence table. Produce a two-column table distinguishing quantities directly measured from those computed or adopted through judgment. For each reported number include its units, the method or source, the measurement volume or location, and a plausible uncertainty range. Data that contradict the assumed stratigraphy must be explained, not discarded.

Part B — Reproducible calculations. Perform calculations by hand for a baseline. Then use both interactive laboratory models in Unit 3 to generate a response curve. Export one CSV file and annotate the inputs that lead to every plotted point. Check a limiting case in which the physical driver becomes small or the sample becomes saturated or unloaded, as appropriate.

Part C — Interpretation. Compare at least two plausible ground models. Explain how changes in the governing parameter alter the decision and why the graph alone cannot choose the correct model. Report an action supported by current evidence and identify a low-cost field or laboratory test whose result could materially reverse that action.

Part D — Review. Create a one-page engineering memo with purpose, physical assumptions, schematic section, measurements, computations, model limitations, uncertainties and recommended next investigation. A reviewer should be able to reproduce calculations without contacting the author.

Assessment rubric. Physical model and correct units (25%), evidence traceability (20%), independent numerical checking (20%), uncertainty and alternative scenarios (20%), clear decision and professional documentation (15%). This project is educational, not an authorized construction document.

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Integrated project 4: Settlement and staging strategy

Problem setting. Construct a synthetic oedometer e–log stress path, calculate compression through the preconsolidation breakpoint, then predict U(t) for single and double drainage.

Deliverable. Plot three plausible consolidation coefficients and recommend an observation program that distinguishes the curves before the next construction stage.

Part A — Evidence table. Produce a two-column table distinguishing quantities directly measured from those computed or adopted through judgment. For each reported number include its units, the method or source, the measurement volume or location, and a plausible uncertainty range. Data that contradict the assumed stratigraphy must be explained, not discarded.

Part B — Reproducible calculations. Perform calculations by hand for a baseline. Then use both interactive laboratory models in Unit 4 to generate a response curve. Export one CSV file and annotate the inputs that lead to every plotted point. Check a limiting case in which the physical driver becomes small or the sample becomes saturated or unloaded, as appropriate.

Part C — Interpretation. Compare at least two plausible ground models. Explain how changes in the governing parameter alter the decision and why the graph alone cannot choose the correct model. Report an action supported by current evidence and identify a low-cost field or laboratory test whose result could materially reverse that action.

Part D — Review. Create a one-page engineering memo with purpose, physical assumptions, schematic section, measurements, computations, model limitations, uncertainties and recommended next investigation. A reviewer should be able to reproduce calculations without contacting the author.

Assessment rubric. Physical model and correct units (25%), evidence traceability (20%), independent numerical checking (20%), uncertainty and alternative scenarios (20%), clear decision and professional documentation (15%). This project is educational, not an authorized construction document.

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Integrated project 5: Strength parameter selection

Problem setting. Compare direct shear and triaxial test records for the same hypothetical soil; calculate effective stress envelopes, q and p′ paths; describe the different meaning of su and c′–φ′.

Deliverable. Report which analysis needs short-term undrained and which needs long-term effective stress parameters. Explain what experiment would settle a disagreement.

Part A — Evidence table. Produce a two-column table distinguishing quantities directly measured from those computed or adopted through judgment. For each reported number include its units, the method or source, the measurement volume or location, and a plausible uncertainty range. Data that contradict the assumed stratigraphy must be explained, not discarded.

Part B — Reproducible calculations. Perform calculations by hand for a baseline. Then use both interactive laboratory models in Unit 5 to generate a response curve. Export one CSV file and annotate the inputs that lead to every plotted point. Check a limiting case in which the physical driver becomes small or the sample becomes saturated or unloaded, as appropriate.

Part C — Interpretation. Compare at least two plausible ground models. Explain how changes in the governing parameter alter the decision and why the graph alone cannot choose the correct model. Report an action supported by current evidence and identify a low-cost field or laboratory test whose result could materially reverse that action.

Part D — Review. Create a one-page engineering memo with purpose, physical assumptions, schematic section, measurements, computations, model limitations, uncertainties and recommended next investigation. A reviewer should be able to reproduce calculations without contacting the author.

Assessment rubric. Physical model and correct units (25%), evidence traceability (20%), independent numerical checking (20%), uncertainty and alternative scenarios (20%), clear decision and professional documentation (15%). This project is educational, not an authorized construction document.

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Integrated project 6: Foundation and wall stress concepts

Problem setting. Plot point-load stress decay, approximate finite footing influence and evaluate Rankine ideal thrust with surcharge. Create a diagram showing where the assumptions about boundary movement and groundwater enter.

Deliverable. Identify the first three site characteristics that would cause the simple solution to be rejected for professional structural design.

Part A — Evidence table. Produce a two-column table distinguishing quantities directly measured from those computed or adopted through judgment. For each reported number include its units, the method or source, the measurement volume or location, and a plausible uncertainty range. Data that contradict the assumed stratigraphy must be explained, not discarded.

Part B — Reproducible calculations. Perform calculations by hand for a baseline. Then use both interactive laboratory models in Unit 6 to generate a response curve. Export one CSV file and annotate the inputs that lead to every plotted point. Check a limiting case in which the physical driver becomes small or the sample becomes saturated or unloaded, as appropriate.

Part C — Interpretation. Compare at least two plausible ground models. Explain how changes in the governing parameter alter the decision and why the graph alone cannot choose the correct model. Report an action supported by current evidence and identify a low-cost field or laboratory test whose result could materially reverse that action.

Part D — Review. Create a one-page engineering memo with purpose, physical assumptions, schematic section, measurements, computations, model limitations, uncertainties and recommended next investigation. A reviewer should be able to reproduce calculations without contacting the author.

Assessment rubric. Physical model and correct units (25%), evidence traceability (20%), independent numerical checking (20%), uncertainty and alternative scenarios (20%), clear decision and professional documentation (15%). This project is educational, not an authorized construction document.

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Integrated project 7: Rainfall-sensitive shallow slope

Problem setting. Calculate infinite-slope FS for dry and pore-pressure-affected conditions, vary friction angle and slope geometry, compare a φ=0 strip-bearing illustration for a nearby footing.

Deliverable. Treat all results as screening: identify credible alternative failure surfaces and monitoring triggers, and specify a next analysis.

Part A — Evidence table. Produce a two-column table distinguishing quantities directly measured from those computed or adopted through judgment. For each reported number include its units, the method or source, the measurement volume or location, and a plausible uncertainty range. Data that contradict the assumed stratigraphy must be explained, not discarded.

Part B — Reproducible calculations. Perform calculations by hand for a baseline. Then use both interactive laboratory models in Unit 7 to generate a response curve. Export one CSV file and annotate the inputs that lead to every plotted point. Check a limiting case in which the physical driver becomes small or the sample becomes saturated or unloaded, as appropriate.

Part C — Interpretation. Compare at least two plausible ground models. Explain how changes in the governing parameter alter the decision and why the graph alone cannot choose the correct model. Report an action supported by current evidence and identify a low-cost field or laboratory test whose result could materially reverse that action.

Part D — Review. Create a one-page engineering memo with purpose, physical assumptions, schematic section, measurements, computations, model limitations, uncertainties and recommended next investigation. A reviewer should be able to reproduce calculations without contacting the author.

Assessment rubric. Physical model and correct units (25%), evidence traceability (20%), independent numerical checking (20%), uncertainty and alternative scenarios (20%), clear decision and professional documentation (15%). This project is educational, not an authorized construction document.

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Integrated project 8: A defensible geotechnical report

Problem setting. Build a fictional borehole and sampling log, document an uncertainty register, compare recovery and tube ratios, and run a fixed-seed parameter sensitivity experiment.

Deliverable. Deliver a ground model profile, test plan, two alternative interpretations, a decision table and a section on what cannot be concluded from the existing evidence.

Part A — Evidence table. Produce a two-column table distinguishing quantities directly measured from those computed or adopted through judgment. For each reported number include its units, the method or source, the measurement volume or location, and a plausible uncertainty range. Data that contradict the assumed stratigraphy must be explained, not discarded.

Part B — Reproducible calculations. Perform calculations by hand for a baseline. Then use both interactive laboratory models in Unit 8 to generate a response curve. Export one CSV file and annotate the inputs that lead to every plotted point. Check a limiting case in which the physical driver becomes small or the sample becomes saturated or unloaded, as appropriate.

Part C — Interpretation. Compare at least two plausible ground models. Explain how changes in the governing parameter alter the decision and why the graph alone cannot choose the correct model. Report an action supported by current evidence and identify a low-cost field or laboratory test whose result could materially reverse that action.

Part D — Review. Create a one-page engineering memo with purpose, physical assumptions, schematic section, measurements, computations, model limitations, uncertainties and recommended next investigation. A reviewer should be able to reproduce calculations without contacting the author.

Assessment rubric. Physical model and correct units (25%), evidence traceability (20%), independent numerical checking (20%), uncertainty and alternative scenarios (20%), clear decision and professional documentation (15%). This project is educational, not an authorized construction document.

Technical reading and source guide

These sources support engineering context and terminology. The numerical simulation code was authored for this educational project and is not a licensed implementation of a design standard.

• Federal Highway Administration, Geotechnical Technical Guidance Manual (2024): https://highways.dot.gov/federal-lands/pddm/geotechnical-technical-guidance-manual
• Washington State Department of Transportation, Geotechnical Design Manual M 46-03 (2022): https://apps.wsdot.wa.gov/engineering-standards/all-manuals-and-standards/manuals/geotechnical-design-manual
• U.S. Geological Survey, Introduction to Ground-Water Hydraulics (Darcy relationship): https://water.usgs.gov/ogw/pubs/TWRI3-B2/TWRI3-B2-with-links.pdf
• USDA Natural Resources Conservation Service, Soil Survey Manual (2017): https://www.nrcs.usda.gov/resources/guides-and-instructions/soil-survey-manual
• USDA NRCS, Field Book for Describing and Sampling Soils, Version 4.0 (2024): https://nrcs-prod.azureedge.us/resources/guides-and-instructions/field-book-for-describing-and-sampling-soils

Limitations

• USDA texture, USDA Soil Taxonomy and the Unified Soil Classification System are not identical classification systems.
• Illustrative values and simplified models are clearly labeled and are not construction design recommendations.
• Governing national codes, project specifications and laboratory methods must be verified for every jurisdiction and application.
• Site-specific engineering decisions require licensed professional review, investigation and quality assurance.