The characteristic value of subgrade bearing capacity (fak) is the fundamental geotechnical parameter that defines the contact pressure a soil layer can safely sustain without shear failure or excessive settlement, as codified in GB 50007-2011 and related international standards. This article delivers a comprehensive technical analysis of its definition, statistical determination, in-situ and laboratory testing procedures, correction methods, and practical applications in foundation engineering. Engineers, geotechnical consultants, and construction quality supervisors will find actionable guidance on how accredited third-party laboratories evaluate this critical design parameter.
Technical Overview
The characteristic value of subgrade bearing capacity (fak) is defined in GB 50007-2011 (Code for Design of Building Foundation) as the pressure value corresponding to a specified deformation within the linear deformation segment of the pressure-settlement curve obtained from a plate load test, with its maximum value taken as the proportional limit load. Unlike the ultimate bearing capacity, which represents the theoretical collapse load of the soil mass, the characteristic value simultaneously satisfies two design requirements: safety against shear failure of the foundation soil and control of settlement within serviceability limits.
In practice, the characteristic value is governed by a deformation criterion rather than a pure strength criterion. For shallow plate load tests, the governing settlement is typically taken as the load at which the settlement-to-plate-width ratio (s/b) reaches 0.01 to 0.015, provided this load does not exceed the proportional limit on the load-settlement curve. This dual-check approach ensures that foundations designed using the characteristic value will neither undergo bearing failure nor experience differential settlements that damage superstructures.
The analysis of the characteristic value involves three logical stages: determination of the base value (fak) through field testing or empirical correlation, statistical evaluation across multiple test points, and modification to obtain the design value (fa) by applying width and depth corrections. The correction formula specified in GB 50007-2011 is expressed as fa = fak + ηb·γ·(b − 3) + ηd·γm·(d − 0.5), where ηb and ηd are correction factors dependent on soil type, γ is the unit weight of soil below the foundation base, γm is the weighted average unit weight above the base, b is the foundation width (limited to between 3 m and 6 m in the calculation), and d is the embedment depth (taken as no less than 0.5 m).
International frameworks address the same engineering problem through different terminology: Eurocode 7 (EN 1997-1) expresses bearing resistance in terms of characteristic and design values with partial factors, while ASTM D1194 and ASTM D1196 standardize static plate load testing procedures used to derive comparable allowable bearing pressures. Although the parameter systems differ, the underlying mechanics—limit equilibrium analysis of the soil beneath a loaded area combined with settlement verification—remain consistent across all major standards.
Testing Samples
Undisturbed Cohesive Soil Samples
Undisturbed samples of silty clay, clay, and cohesive silt are extracted from boreholes using thin-wall samplers or from trial pits with hand-cut block samples. These specimens preserve the natural fabric, moisture content, and stress history of the soil, allowing laboratory determination of physical indices such as void ratio (e), liquidity index (IL), moisture content, and unconfined compressive strength. These indices are correlated with tabulated characteristic values in GB 50007-2011 to provide an initial estimate of fak, which is subsequently verified by field load testing.
In-Situ Test Positions in Sandy and Gravelly Strata
Cohesionless soils such as fine sand, medium-coarse sand, and gravel are extremely difficult to sample without severe disturbance. For these strata, the "sample" is effectively the in-situ test position itself: the base of an excavated trial pit prepared for plate load testing, or the borehole interval selected for standard penetration testing (SPT) or cone penetration testing (CPT). Test positions must be located within the influential depth of the proposed foundation and must represent the weakest critical stratum identified during site investigation per GB 50021.
Weathered Rock and Rock Core Specimens
For foundations bearing on fully weathered to moderately weathered rock, NX-sized core specimens are retrieved for uniaxial compressive strength testing in accordance with GB/T 50266 or ASTM D7012. Where core recovery is poor, point load index testing on irregular lumps provides an alternative strength index. The characteristic value for rock foundations is derived from the saturated uniaxial compressive strength reduced by a fracturing coefficient that accounts for joint spacing and rock mass integrity.
Compacted and Improved Fill Materials
When foundations bear on compacted replacement cushions, dynamic-compacted fill, or other ground improvement layers, representative samples of the engineered material are collected for gradation, compaction, and density verification. Plate load tests performed directly on the improved surface serve as the acceptance test, with the measured characteristic value compared against the design target specified by the geotechnical designer.
Testing Items
A complete bearing capacity analysis program typically evaluates the following items, either singly or in combination depending on soil type and project classification:
- Proportional limit load (p0): the load at the end of the linear segment of the pressure-settlement curve.
- Ultimate load (pu): the load producing pronounced continuous settlement, punching failure, or a settlement exceeding 0.06 times the plate width.
- Characteristic value of subgrade bearing capacity (fak): the load at s/b = 0.01 to 0.015, capped at the proportional limit.
- Deformation modulus (E0) and compressed modulus (Es) derived from the load-settlement response for settlement prediction.
- Standard penetration resistance (N63.5) correlated with fak through regional empirical relationships.
- Cone penetration parameters (qc, fs) for continuous stratigraphic profiling and empirical bearing capacity estimation.
- Physical and mechanical indices of undisturbed samples: void ratio, liquidity index, degree of saturation, cohesion, and internal friction angle.
- Corrected design bearing capacity (fa) after width and depth modification per GB 50007-2011.
- Degree of compaction and coefficient of subgrade reaction for improved ground verification.
Testing Methods
Shallow Plate Load Test
The shallow plate load test, standardized in GB 50007-2011 Appendix C, ASTM D1194, and ASTM D1196, is the primary referee method for determining fak. A rigid circular or square steel plate, typically 0.25 m² to 0.5 m² in area, is seated on a leveled and gypsum-cushioned test surface at the proposed foundation level. Load is applied incrementally using a hydraulic jack reacting against a kentledge or anchor system, with each increment held until settlement rate falls below 0.1 mm per hour. Settlement is recorded by four dial gauges or displacement transducers. The characteristic value is read from the p-s curve at the specified settlement ratio, and when obvious shear failure occurs, the ultimate load is divided by a safety factor of no less than 2.0.
Deep Plate Load Test
For deep foundation soils and soils below the groundwater table that cannot be reached by open pits, the deep plate load test (GB 50007-2011 Appendix D) employs a 0.8 m diameter screw-anchor plate installed at depth. Because the confining conditions differ from those at shallow depth, the settlement criterion for deep tests is adjusted, and the results require careful extrapolation before being applied to shallow foundation design.
Standard Penetration Test Correlation
The SPT, performed per GB 50021, ASTM D1586, and ISO 22476-3, provides corrected N63.5 values that are converted to characteristic bearing capacities through regional empirical formulas of the general form fak = a + b·N63.5, calibrated for local stratigraphy. These correlations are widely used for preliminary design of foundations on sandy soils, but GB 50007 requires that final design values for important projects be confirmed by at least one direct plate load test.
Cone Penetration Test Method
The CPT, standardized under ISO 22476-1 and ASTM D3441, continuously measures cone tip resistance and sleeve friction, enabling both stratigraphic interpretation and empirical bearing capacity estimation. Dual-bridge and piezocone variants additionally detect thin weak interlayers that point tests may miss, making CPT particularly valuable for layered alluvial and lacustrine deposits.
Physical Index Correlation Method
For cohesive soils, tabulated characteristic values indexed by void ratio and liquidity index provide a rapid estimation route. The designer enters the codified tables with laboratory-measured indices and interpolates the corresponding fak, which is then subject to statistical reconciliation with field test data before design use.
Statistical Evaluation Procedure
When three or more load tests are performed on the same soil layer, the maximum and minimum values are compared against the mean. If both extremes fall within 30 percent of the mean value, the characteristic value of the layer is taken as the arithmetic mean of all test results. If the spread exceeds 30 percent, the test data must be reviewed for outliers, additional tests conducted, or the characteristic value determined by more conservative statistical treatment, such as discarding extremes in accordance with the applicable data-rejection criteria.
Width and Depth Correction
The measured fak reflects the conditions of the test plate, not the actual foundation. Because larger foundations mobilize deeper and wider soil zones, and because embedment provides confining overburden, GB 50007-2011 requires correction using the formula fa = fak + ηb·γ·(b − 3) + ηd·γm·(d − 0.5). Correction coefficients ηb and ηd are selected from codified tables according to soil classification and the values of porosity and consistency indices. For foundations on soft plastic or flowing plastic clays, the depth correction coefficient is reduced, and for mud-type soils, corrections may be restricted altogether to preserve conservatism.
Applications
The characteristic value of subgrade bearing capacity is applied across the full lifecycle of geotechnical and structural engineering projects:
- Natural shallow foundation design: sizing independent footings, strip footings, and raft foundations for residential, commercial, and public buildings under the GB 50007 framework.
- Ground improvement verification: confirming that dynamic compaction, replacement cushions, vibro-flotation, and CFG pile composite foundations achieve the specified post-improvement bearing capacity.
- High-rise and heavy industrial structures: validating bearing strata beneath towers, silos, boiler foundations, and equipment pedestals where differential settlement tolerances are stringent.
- Transportation infrastructure: evaluating subgrade strength for highway pavements, railway embankments, and airfield runways, often expressed alongside the modulus of subgrade reaction.
- Port and marine works: assessing reclaimed fill and marine deposits prior to construction of quay walls, container yards, and crane rails.
- Forensic and renovation engineering: re-evaluating bearing capacity of existing strata when buildings are upgraded, additional stories are added, or adjacent deep excavation may have altered ground conditions.
- Seismic and special loading review: re-verifying bearing capacity under seismic load combinations, wind uplift and overturning cases, and machine-induced dynamic loads.
FAQ
What is the difference between fak and fa?
The value fak is the characteristic value obtained directly from plate load tests or empirical correlations, reflecting the soil itself under test conditions. The value fa is the corrected design value obtained after applying the width and depth correction formula of GB 50007-2011, accounting for the actual foundation geometry and embedment. Only fa may be used in the final foundation bearing verification calculation.
How many plate load tests are required for a reliable characteristic value?
GB 50007-2011 requires that when the characteristic value is based on statistical analysis, no fewer than three load tests should be conducted on the same soil layer. If the extreme values deviate from the mean by no more than 30 percent, the mean is adopted as the characteristic value of the layer; otherwise the dataset must be supplemented or treated conservatively.
Why is the settlement criterion s/b = 0.01 to 0.015 used instead of the failure load?
Most foundations on medium-strength and compressible soils reach serviceability problems—cracking, tilting, or architectural damage—long before the soil approaches shear failure. Reading the load at a settlement ratio of 1.0 to 1.5 percent of plate width ties the characteristic value to realistic deformation control, while the safety factor of at least 2.0 against the ultimate load covers strength margin.
Can the characteristic value be determined without plate load testing?
Yes, for preliminary design and for lower-importance structures, SPT correlations, CPT correlations, and physical-index tables provide acceptable estimates. However, for important projects, foundations on unusual or variable strata, and all ground improvement acceptance testing, direct plate load testing performed by accredited third-party laboratories remains the mandatory referee method.
How does the Chinese characteristic value system compare with Eurocode 7?
Both systems separate a characteristic soil property from a design value, but Eurocode 7 applies statistical partial factors to characteristic values of soil parameters and computes bearing resistance from theoretical models, whereas GB 50007 anchors the characteristic value in measured load-settlement behavior and applies explicit geometric corrections. When projects cross both frameworks, accredited third-party laboratories map the parameters so that consistent safety levels are demonstrated under either code.
Does the characteristic value change with groundwater conditions?
Yes. Effective unit weight must be used below the water table in the correction formula, and submerged conditions reduce the confining contribution of embedment. Rising groundwater after construction can therefore reduce the effective design bearing capacity, which is why hydrogeological conditions are always assessed as part of the overall bearing capacity analysis.