Estimating Settlement of Shallow Foundations on Granular Soils

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One aspect of the effective design and long-term stability of any structure is considering the need to construct the foundation on suitable subsurface conditions. During the design phase, structural engineers evaluate various combinations of dead and live loads for the design of beams, girders, and columns and their connections and joints within a structure. They analyze how these forces and moments are transmitted through the structure and into the foundation elements. Often, structural engineers collaborate with geotechnical engineers who characterize subsurface soil and bedrock conditions and provide recommendations on allowable bearing pressures for appropriately sizing the foundation elements. The design process considers the allowable bearing pressure and potential settlement under design loads. Estimating settlements involves understanding soil behavior under load and using data from soil borings to predict vertical displacement of foundations. This article focuses on quantifying the potential settlement of shallow foundation elements, such as spread footings and isolated footings, which bear on granular soils (primarily sandy or gravelly).

Before structural analyses begin, the geotechnical engineer coordinates a subsurface exploration at the construction site. This exploration may involve various methods to determine the soil and bedrock present, including soil borings with Standard Penetration Testing (SPT) per ASTM Standard D1586, undisturbed soil sampling of soft and loose soils per ASTM Standard D1587, and rock coring to retrieve physical samples of the underlying bedrock per ASTM Standard D2113. Other methods might include test pits to evaluate subsurface conditions along adjacent property lines (especially for excavation support or underpinning) or cone penetrometer testing (CPT) for deep foundations or specific subsurface soil properties needed for seismic evaluation. However, most reports received by structural engineers for straightforward sites include soil borings and their associated logs. These boring logs provide essential information for estimating settlement. While log formats may vary, they should include basic information such as:

Soil Descriptions: These can range from the concise Group Name in the Unified Soil Classification System (e.g., Silty Sand, SM) to the detailed description system developed by Donald Burmister of Columbia University in the 1940s (e.g., Brown coarse to fine SAND, some (+) Silt, little (-) medium to fine (+) Gravel). Note the difference in these descriptions, even though they refer to the same soil sample.

Depth to Groundwater: This may be based on fluid level observations in the completed borehole, descriptions of encountered soil materials (dry, moist, or wet/saturated), or a temporary observation well or wellpoint installed upon boring completion. This information is used to evaluate neutral stresses from water in the soil mass and for subsequent computations requiring effective or buoyant unit weights for geotechnical analyses.

The SPT N-Value (N): This value may be noted separately but often needs to be computed from field boring logs. Most logs indicate the number of hammer blows on the split spoon soil sampler in 6-inch intervals. A 2-foot-long soil sampling interval typically will have four consecutive numbers listed, sometimes separated by slashes or dashes. According to ASTM Standard D1586, N is the sum of the second and third blow count numbers (i.e., the number of blows needed to drive the soil sampler from a depth of 6 inches to 18 inches below the testing depth).

N correlates with the relative density of a soil; for sands, this can indicate loose sands (N < 10 blows per foot), medium dense sands (N between 10 and 30 blows per foot), dense sands (N between 30 and 50 blows per foot), or very dense sands (N > 50 blows per foot). Subsequent corrections to N can be made based on sampling method (depth of sample below ground surface, borehole size, use of a liner within the sampler, and sampling hammer efficiency) and overburden soil pressure (including consideration for effective stresses from groundwater). For the following discussion on estimating foundation settlement, N is a key component, requiring some correction based on sampling methods and overburden pressure.

Numerous methods are given in published texts, scholarly articles, and professional journals to estimate the magnitude of settlement of shallow foundations. Many of these methods consider the same fundamental information. These include:

Footing Dimensions. While it is basic information, some earlier formulas only considered the width of the foundation or estimated the footing to be circular (for allowing stress calculations that developed radially from the center of the footing. With additional data from actual field testing and measurement of settlement, more recent methods can consider the shape of a footing, whether it is square, circular, rectangular, long (usually the ratio of length to width is greater than 10), or strip footings.

Existing Overburden Pressure. Before any new construction begins, the ground is in its own “happy place,” at equilibrium with the forces and pressures acting on it. The addition of a new footing will increase the stress to the underlying soil. To identify the increase in the new stress, information about the existing stresses at the subgrade level of the footing need to be evaluated. For example, in New York City, footing depths for buildings are governed by Section 1809.5 of the NYC Building Code, requiring a minimum depth of 4 feet below finished exterior grade. If the ground surface remains the same, the effective overburden pressure at the frost depth may be between 400 and 500 pounds per square foot (based on a unit weight that ranges between 100 and 125 pounds per cubic foot). If a new footing designed by the structural engineer is intended to impart a contact pressure of 2,000 pounds per square foot at the same depth, the net increase in pressure that the soil would experience would be the difference of the contact pressure and the effective overburden pressure (in this case, 1,500 or 1,600 pounds per square foot). This net increase in pressure would be considered for estimating the magnitude of settlement.

“Stiffness” of the Soil. The stiffness of the soil can be correlated to the N-Value. Some formulas use the N-value—either corrected for overburden or the uncorrected field value—in the direct calculation of settlement. More recent methods consider the Modulus of Elasticity of the soil (E), which is based on the theory of elasticity and considers the soil to be an elastic material that shortens or compresses under loading like a spring. The Modulus of Elasticity can be obtained by testing of soils in the laboratory setting, by use of correlations with SPT N-Values, or by use of correlations with CPT data.

To perform a settlement analysis, guidance using the many formulae available is not simple, or using a “one formula fits all” may not be suitable. Designers may consider one method to use for certain soil types (for which they were expressly developed), but may choose multiple methods to determine whether the overall magnitude of settlement is in the same range. If the results of one method are greatly different than other approaches used, it may be a sign that the parameters may be incorrect, the wrong units of measurement were considered, or an assumption used for a correlation for strength or stiffness parameters may need to be reevaluated.

As an example, consider three different methods currently in use and compare their results. These three methods are as follows:

Terzaghi and Peck (1948), with adjustments from Teng (1962). While the study of modern geotechnical engineering dates to the early 1900s, most significant advancements in analysis occurred between the late 1920s and the 1940s. Terzaghi and Peck’s first edition of Soil Mechanics in Engineering Practice in 1948 introduced an empirical method for computing settlement by comparing it to a reference settlement of 1 inch. Their original formula and procedure included graphs based on their observations and empirical data for footings of various sizes, with footing width plotted along the x-axis. In 1962, Teng revised these graphs and the original formula to include a component for footing width, as well as corrections for groundwater depth and embedment depth.

Bazaraa (1967, 1969). This method resulted from the doctorate dissertation of Bazaraa while studying at the University of Illinois under Dr. Peck—the same Peck mentioned in the previous method. The formula for this method considers values of N corrected for overburden only and considers the lowest weighted average of the corrected values of N for this formula to a depth of B below the foundation (where B is the width of the footing). Additional corrections for the depth of groundwater and embedment depth are also included, which are intended to incorporate effective overburden pressures and changes to the unit weights being evaluated based on the presence of groundwater below the subgrade level of the footing.

Schmertmann (1978). Building on the research and developments of academics and scholars in geotechnical engineering, Schmertmann devised a method for estimating foundation settlement on sand and gravel. This method is based on field observations, laboratory models, finite element analyses, and the theory of elasticity. Schmertmann’s equation, initially developed in 1970 and refined by 1978, includes several enhancements: a semi-empirical strain influence factor that varies with depth and footing dimensions, a correction factor for the effective overburden pressure at the foundation depth, a correction factor for soil creep over time (e.g., the design life of the structure), and the Elastic Modulus (or Young’s Modulus) for estimating soil stiffness beneath the foundation.

Assume a 10-foot-wide square footing is built 5 feet below the existing ground surface, supporting a load of 200 tons (including the self-weight of the column and footing). The groundwater table is approximately 8 feet below the ground surface. The soil consists of a medium to fine sand deposit, consistent with depth, with an overburden-corrected SPT N-Value of 28 blows per foot (indicating medium dense soils). This soil was sampled using drilling equipment with a safety hammer (60% efficiency). The soil has a moist unit weight of 120 pounds per cubic foot above the groundwater table and a saturated unit weight of 125 pounds per cubic foot below the groundwater table. Estimate the footing settlement after one year.

Considering the three methods presented, the settlement range varied between 0.37 inches and 0.87 inches, giving a range of about 0.5 inches between the highest and lowest estimated values. While these settlements may fall within acceptable limits, the results are highly dependent on the values used in the analyses. The first two methods rely on a weighted average of an overburden-corrected SPT N-value, whereas the third method (Schmertmann) can vary based on the correlation used for the Modulus of Elasticity, the number of discrete soil layers considered, variations in N values, and the timeframe considered for evaluating long-term settlement. For this example, variations of the Modulus of Elasticity selected for the soil could result in the magnitude of settlement ranging between 0.74 inches and 1.05 inches, a difference of 0.31 inches. Due to this variability, designers may need to consider variations in the correlation between the Modulus of Elasticity and the SPT N-Value (or CPT data, if used) to evaluate the sensitivity of the analysis and potential variations in stresses and moments in connections, joints, and structural members. Although all three methods yielded different settlement estimates, the overall settlement can be assessed by using multiple methods to ensure the estimates are within an acceptable range.

Like financial investing, diversifying methods is better than relying on a single method for settlement estimation. This approach will add to developing a range of settlement estimates that a designer may need to consider to best identify movements that the structure may experience during its design life. If additional guidance is needed, the project’s geotechnical engineer may also be able to suggest methods which are suitable for the type of foundation and in-situ site soils. ■

About the Author

Gary Marcus, PE, F.ASCE, BC.GE, is a geotechnical engineer with 27 years of experience, which includes the evaluation of soil and bedrock properties for the design of structures and infrastructure. He is currently a VP and Director of Geotechnical Engineering in NV5’s New York City Office and is also an adjunct assistant professor at Cooper Union in New York City and SUNY Farmingdale State College on Long Island. (gary.marcus@nv5.com)