Chapter 7 – Analysis of Settlement and Volume Expansion

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7.1. Introduction

7.1.1. Overview

Soil is a non-homogeneous porous material consisting of three phases: solids, fluid (normally water), and air. Soil deformation may occur by change in stress, water content, soil mass, or temperature. Vertical displacements and settlement caused by change in stress and water content are described in this section.

Difficult soils can create serious problems in both settlement and volume expansion. These are discussed in detail in 2.5.

This section excludes settlement caused by the following:

    • Subsidence and undermining by tunnels
    • Subsidence due to buried karst features or cavities
    • Thermal effects of structures on permafrost
    • Effects of frost heave
    • Loss in mass from erosion
    • Loss of ground from rebound and lateral movement in adjacent excavations
    • Loss of support caused by lateral soil movement from landslides, downhill creep, and shifting retaining walls.
    • Horizontal deformation of structures associated with vertical deformations may also occur, but such analysis is complex and beyond the scope of this book.
    • Deep foundations are driven piles and drilled shafts used to transmit foundation loads to deeper strata capable of supporting the applied loads.
    • Settlements of domestic and hazardous landfills are unpredictable and cannot be readily estimated using techniques presented in this book.

Soil movements may be minimized by treating the soil prior to construction by numerous methods such as removal of poor soil and replace with suitable soil, precompression of soft soil, dynamic consolidation of cohesionless soil, and chemical stabilization or wetting of expansive or collapsible soil. Foundations may be designed to tolerate some differential movements. Remedial techniques such as underpinning with piles, grouting, and slabjacking are available to stabilize and repair damaged foundations.

7.1.2. General Considerations and Definitions

Placement of an embankment load or structure on the surface of a soil mass introduces stress in the soil that causes the soil to deform and leads to settlement of the structure. It is frequently necessary to estimate the differential and total vertical soil deformation caused by the applied loads. Differential movement affects the structural integrity and performance of the structure. Total deformation is significant relative to connections of utility lines to buildings, grade and drainage from structures, minimum height specifications of dams (i.e., freeboard), and railroad and highway embankments. Soils and conditions described in Table 2-12 require special considerations to achieve satisfactory design and performance. Early recognition of these problems is essential to allow sufficient time for an adequate field investigation and preparation of an appropriate design. Approach Embankment Settlement

Approach embankment settlement is the most prevalent foundation problem in highway construction. Unlike stability problems, the results are seldom catastrophic but the cost of perpetual maintenance of continuing settlement is immense. The difficulty in preventing these problems is not as much a lack of technical expertise as it is a lack of communication between personnel involved in the roadway design and those involved in the structure design.

The design of a roadway embankment can utilize a wide range of soil materials and permit substantial amounts of settlement without affecting the performance of the highway. Roadway designers necessarily permit such materials to reduce project costs by utilizing cheap locally available soils. Structures are necessarily designed for little or no settlement to maintain specified highway clearances and to insure integrity of structural members. The approach embankment must affect a transition between roadway and structure while providing adequate structural foundation support. In most agencies, the responsibility for approach embankment design is not defined, which results in roadway criteria being used across the structure. This is wrong; the approach embankment requires special materials and placement criteria to prevent internal consolidation and to moderate external consolidation. Sources of Stress

Sources of stress in soil occur from soil weight, surface loads, and environmental factors such as desiccation from drought, wetting from rainfall, and changes in depth to groundwater. Stress in soils is discussed in more detail in § 5. Soil weight

Soil strata with different unit weights alter the stress distribution. Any change in total stress results in changes in effective stress and pore pressure. In a saturated soil, any sudden increase in applied total stress results in a corresponding pore pressure increase, Equation 5-1. This increase may cause a flow of water out of the soil deposit, a decrease in pore pressure, and an increase in effective stress. Changes in pore water pressure such as the raising or lowering of water tables also lead to a reduction or increase in effective stress. Surface loads

Loads applied to the surface of the soil mass increase the stress within the mass. The pressure bulb concept, Figure 5-5, illustrates the change in vertical stress within the soil mass. Placement of a uniform pressure over a foundation with a minimum width much greater than the depth of the soil layer will cause an increase of vertical stress in the soil approximately equal to the applied pressure. Applicability to settlement calculations

The ability to predict settlements using elastic theory depends much more strongly on the in situ nonlinearity and material inhomogeneity than errors in the distribution of stresses. These settlements directly depend on the assumed constitutive material law and on the magnitude of the required soil parameters. Refer to 3.3 for further information on elasticity theory. Rules of thumb for static loads

Preliminary settlement analyses are sometimes performed before the structural engineer and architect are able to furnish the design load conditions.

a) Some rules of thumb for line and column loads for buildings described in Table 7-1 are based on a survey of some engineering firms. Tall multi-storey structures may have column loads exceeding 1000 tons. Column spacings are often 20 to 25 ft or more. The average pressure applied per story of a building often varies from 0.1 to 0.2 tsf.

  1. b)  Vertical pressures from embankments may be estimated from the unit wet weight times height of the fill.
  2. c)  Vertical pressures from locks, dams, and retaining walls may be estimated by dividing the structure into vertical sections of constant height and evaluating the unit weight times the height of each section.

7.2. Limitations of Settlement

7.2.1. General

Significant aspects of settlement from static and dynamic loads are total and differential settlement. Total settlement is the magnitude of downward movement. Differential settlement is the difference in vertical movement between various locations of the structure and distorts the structure. Conditions that cause settlement are described in Table 2-12. Limitations to total and differential settlement depend on the function and type of structure.

7.2.2. Total Settlement

Many structures can tolerate substantial downward movement or settlement without cracking, Table 7-2; however, total settlement should not exceed 2 inches for most facilities. A typical specification of total settlement for commercial buildings is 1 inch. Structures such as solid reinforced concrete foundations supporting smokestacks, silos, and towers can tolerate larger settlements up to 1 ft. Utilities

Total settlement of permanent facilities can harm or sever connections to outside utilities such as water, natural gas, and sewer lines. Water and sewer lines may leak contributing to localized wetting of the soil profile and aggravating differential displacement. Leaking gas from breaks caused by settlement can lead to explosions. Drainage

Total settlement reduces or interferes with drainage of surface water from permanent facilities, contributes to wetting of the soil profile with additional differential movement, and may cause the facility to become temporarily inaccessible. Serviceability

Relative movement between the facility and surrounding soil may interfere with serviceability of entryways. Freeboard

Total settlement of embankments, levees and dams reduces freeboard and volume of water that may be retained. The potential for flooding is greater during periods of heavy rainfall. Such settlement also alters the grade of culverts placed under roadway embankments.

7.2.3. Differential Settlement

Differential settlement, which causes distortion and damages in structures, is a function of the uniformity of the soil, stiffness of the structure, stiffness of the soil, and distribution of loads within the structure. Limitations to differential settlement depend on the application. Differential settlements should not usually exceed 1/2 inch in buildings, otherwise cracking and structural damage may occur. Differential movements between monoliths of dams should not usually exceed 2 inches; otherwise leakage may become a problem. Embankments, dams, one or two story facilities, and multi-storey structures with flexible framing systems are sufficiently flexible such that their stiffness often need not be considered in settlement analysis. Pavements may be assumed to be completely flexible. Types of Damages

Differential settlement may lead to tilting that can interfere with adjacent structures and disrupt the performance of machinery and people. Differential settlement can cause cracking in the structure, distorted and jammed doors and windows, uneven floors and stairways, and other damages to houses and buildings. Differential movement may lead to misalignment of monoliths and reduce the efficiency of water stops. Widespread cracking can impair the structural integrity and lead to collapse of the structure, particularly during earthquakes. The height of a wall for a building that can be constructed on a beam or foundation without cracking is related to the deflection/span length D/L ratio and the angular distortion b described below. Deflection Ratio

The deflection ratio D/L is a measure of the maximum differential movement Din the span length L, Figure 7-1. The span length may be between two adjacent columns, LSAG or LHOG, Figure 7-1a.

  1. (1)  Table 7-3 provides limiting observed deflection ratios for some buildings.
  2. (2)  Design D/L ratios are often greater than 1/600, but the stiffness contributed by the components of an assembled brick structure, for example, helps maintain actual differential displacement/span length ratios near those required for brick buildings, Table 7-3, to avoid cracking.
  3. (3)  Circular steel tanks can tolerate D/L ratios greater than 1/200 depending on the settlement shape167.

7.3. Evaluation of Settlement for Static Loads

7.3.1. General

This section presents the evaluation of immediate settlement in cohesionless and cohesive soils and consolidation settlement of soil for static loads. Settlement is denoted as a positive value to be consistent with standard practice.

7.3.2. Components of Settlement

Total settlement r in feet, which is the response of stress applied to the soil, may be calculated as the sum of three components

Equation 7-3: r = ri + rc + rs


  • ri = immediate or distortion settlement, ft
  • rc = primary consolidation settlement, ft
  • rs = secondary compression settlement, ftPrimary consolidation and secondary compression settlements are usually small if the effective stress in the foundation soil applied by the structure is less than the maximum effective past pressure of the soil, paragraph 1-5a. Immediate Settlement

Immediate settlement ri is the change in shape or distortion of the soil caused by the applied stress.

  1. (1)  Calculation of immediate settlement in cohesionless soil is complicated by a nonlinear stiffness that depends on the state of stress. Empirical and semi-empirical methods for calculating immediate settlement in cohesionless soils are described in 7.3.3.
  2. (2)  Immediate settlement in cohesive soil may be estimated using elastic theory, particularly for saturated clays, clay shales, and most rocks. Methods for calculating immediate settlement in cohesive soil are described in Primary Consolidation Settlement

Primary consolidation settlement rc occurs in cohesive or compressible soil during dissipation of excess pore fluid pressure, and it is controlled by the gradual expulsion of fluid from voids in the soil leading to the associated compression of the soil skeleton. Excess pore pressure is pressure that exceeds the hydrostatic fluid pressure. The hydrostatic fluid pressure is the product of the unit weight of water and the difference in elevation between the given point and elevation of free water (phreatic surface). The pore fluid is normally water with some dissolved salts. The opposite of consolidation settlement (soil heave) may occur if the excess pore water pressure is initially negative and approaches zero following absorption and adsorption of available fluid.

  1. (1)  Primary consolidation settlement is normally insignificant in cohesionless soil and occurs rapidly because these soils have relatively large permeabilities.
  2. (2)  Primary consolidation takes substantial time in cohesive soils because they have relatively low permeabilities. Time for consolidation increases with thickness of the soil layer squared and is inversely related to the coefficient of permeability of the soil. Consolidation settlement determined from results of one-dimensional consolidation tests includes some immediate settlement ri. Methods for calculating primary consolidation settlement are described in Secondary Compression Settlement

Secondary compression settlement is a form of soil creep that is largely controlled by the rate at which the skeleton of compressible soils, particularly clays, silts, and peats, can yield and compress. Secondary compression is often conveniently identified to follow primary consolidation when excess pore fluid pressure can no longer be measured; however, both processes may occur simultaneously. Methods for calculating secondary compression settlement are described in 7.3.6.

7.3.3. Immediate Settlement of Cohesionless Soil for Static Loads

Settlement in cohesionless soil (see 5.2.7 for definition) is normally small and occurs quickly with little additional long-term compression. Six methods described below for estimating settlement in cohesionless soil are based on data from field tests (i.e., Standard Penetration Test (SPT), Cone Penetration Test (CPT), Dilatometer Test (DMT) and Pressuremeter Test (PMT). Undisturbed samples of cohesionless soil are normally not obtainable for laboratory tests. The first four empirical and semi-empirical methods – Alpan, Schultze and Sherif, Modified Terzaghi and Peck, and Schmertmann approximations – were shown to provide estimates from about 1/4 to 2 times the measured settlement for 90% confidence based on the  results of a statistical analysis171. Penetration tests may not be capable of sensing effects of prestress or over consolidation and can underestimate the stiffness that may lead to overestimated settlements. Accuracy of Settlement Predictions

Experience shows that predictions of settlement are reasonable and within 50% of actual settlements for many soil types. Time rates of settlement based on laboratory tests and empirical correlations may not be representative of the field because time rates are influenced by in situ fissures, existence of high permeable sand or low permeable bentonite seams, impervious boundaries, and nonuniform soil parameters as well as the rate of construction. Preconsolidation Stress

Soil disturbance of laboratory samples used for one-dimensional consolidation tests decreases the apparent preconsolidation stress. Virgin Compression Index

Soil disturbance decreases the compression index. Swelling and Recompression Indices

Soil disturbance increases the swelling and recompression indices. Coefficient of Consolidation

Soil disturbance decreases the coefficient of consolidation for virgin compression and recompression, Figure 7-20, in the vicinity of initial overburden and preconsolidation stresses. The value of cv decreases abruptly at the preconsolidation stress for good undisturbed samples. Field Test Embankment

A field test embankment may be constructed for significant projects to estimate field values of soil parameters such as Cc and cv. Installation of elevation markers, inclinometers, and piezometers allow the measurement of settlement, lateral movement, and pore pressures as a function of time. These field soil parameters may subsequently be applied to full-scale structures.

7.3.6. Secondary Compression and Creep Description

Secondary compression and creep are time-dependent deformations that appear to occur at essentially constant effective stress with negligible change in pore water pressure. Secondary compression and creep may be a dispersion process in the soil structure causing particle movement and may be associated with electrochemical reactions and flocculation. Although creep is caused by the same mechanism as secondary compression, they differ in the geometry of confinement. Creep is associated with deformation without volume and pore water pressure changes in soil subject to shear; whereas, secondary compression is associated with volume reduction without significant pore water pressure changes. Model

Secondary compression and creep may be modelled by empirical or semi-empirical visco-elastic processes in which hardening (strengthening) or softening (weakening) of the soil occurs. Hardening is dominant at low stress levels; whereas, weakening is dominant at high stress levels. Deformation in soil subject to a constant applied stress can be understood to consist of three stages. The first stage is characterized by a change in rate of deformation that decreases to zero. The second or steady state stage occurs at a constant rate of deformation. A third stage may also occur at sufficiently large loads in which the rate of deformation increases ending in failure because of weakening in the soil. Soil subject to secondary compression in which the volume decreases as during a one dimensional consolidometer test may gain strength or harden with time leading to deformation that eventually ceases, and, therefore, the second (steady state) and third (failure states) may never occur.

7.5.3. Collapsible Soil General

Many collapsible soils are mudflows or windblown silt deposits of loess often found in arid or semiarid climates such as deserts, but dry climates are not necessary for collapsible soil. Loess deposits cover parts of the Western, Midwestern, and Southern United States, Europe, South America, Asia including large areas of Russia and China, and Southern Africa. A collapsible soil at natural water content may support a given foundation load with negligible settlement, but when water is added to this soil the volume can decrease significantly and cause substantial settlement of the foundation, even at relatively low applied stress or at the overburden pressure. The amount of settlement depends on the initial void ratio, stress history of the soil, thickness of the collapsible soil layer, and magnitude of the applied foundation pressure. Collapsible soils exposed to perimeter watering of vegetation around structures or leaking utility lines are most likely to settle. Collapse may be initiated beneath the ground surface and propagate toward the surface leading to sudden and nonuniform settlement of overlying facilities. Structure

Soils subject to collapse have a honeycombed structure of bulky shaped particles or grains held in place by a bonding material or force illustrated in Figure 7-35. Common bonding agents include soluble compounds such as calcareous or ferrous cementation that can be weakened or partly dissolved by water, especially acidic water. Removal of the supporting material or force occurs when water is added enabling the soil grains to slide or shear and move into voids.

7.7.3. Calibration of Equipment

In the consolidation test, it is desired to measure only the volume change of the specimen; therefore, corrections must be applied for any significant deformation due to the compressibility of the apparatus itself. In sandy and stiff soils, an appreciable proportion of the total deformation may be caused by this factor. Therefore, a calibration curve should be prepared for each consolidometer when testing such soils. This is done by placing the consolidometer with submerged porous stones and filter papers in the loading device, applying the load increments to be used in the consolidation test, and reading the dial indicator for each load. After the maximum load has been applied, the loads are decreased in the same order as that in which they were applied, and the dial indicator reading is again recorded. Since the deformations are almost instantaneous, the effect of time can be ignored. The total change in dial reading for each load is the correction to be applied to the dial reading recorded during the consolidation test under that same load. Generally, a single cycle will be sufficient for the calibration.

7.7.4. Preparation of Specimens

Specimens shall be prepared in a humid room to prevent evaporation of soil moisture. Extreme care shall be taken in preparing specimens of sensitive soils to prevent disturbance of their natural structure. Specimens of relatively soft soils may be prepared by progressive trimming in front of a calibrated, ring- shaped specimen cutter as shown in Figure 3-10. More commonly, specimens are prepared using the trimming turntable shown in Figure 7-49 herein; the procedure, based on the use of this equipment, shall be as described in the following subparagraphs. Preferably, specimens of compacted soil should be compacted to the desired density and water content directly into the consolidation ring, in thin (1/4 to 3/8”) layers, using a pressing or kneading action of a tamper having an area less than one-sixth the area of the specimen and thoroughly scarifying the surface of each layer before placing the next. Alternatively, specimens may be trimmed from samples compacted in a compaction mould by a similar kneading action.

  1. Using a wire saw, knives, or other tools, trim the specimen into approximately cylindrical shape with a diameter about 1/2” greater than the inside diameter of the specimen ring. Care should be taken to disturb the specimen as little as possible during trimming. Chamfer the lower edge of the specimen until the bottom will fit exactly into the specimen ring.
  2. Place the specimen ring on the rotating wheel and the specimen on the ring, starting the bottom into the ring as shown in Figure 7-49. Use a cutting tool to trim the specimen to accurate dimensions, place a glass plate on top of the specimen, and gently force the specimen down during the trimming operation. The specimen shou1d fit snugly in the consolidation ring.
  3. Cut off the portion of the specimen remaining above the ring with a wire saw or knife (or other convenient tool for harder specimens). Extreme care must be taken for many soils, especially fissured clays, in cutting off this portion. Carefully true the surface flush with the specimen ring with a straight edge. If a pebble is encountered in the surface, remove it and fill the void with soil. Place a glass plate (previously weighed) over the ring and turn the specimen over.226 Cut off the soil extending beyond the bottom of the ring in the same manner as that described for the surface portion. Place another glass plate on this surface, and again invert the specimen to an upright position, removing the metal disk if one was used.

7.7.5. Procedure

The procedure shall consist of the following steps:

  1. Record all identifying information for the specimen, such as project number, boring number, and other pertinent data, on the data sheet (Figure 11-23 is a suggested form); note any difficulties encountered in preparation of the specimen. Measure and record the height and cross-sectional area of the specimen. Record weight of specimen ring and glass plates. After specimen is prepared, record the weight of the specimen plus tare (ring and glass plates), and from the soil trimmings, obtain 200 g of material for specific gravity227 and water content determinations. Record the wet weight of the material used for the water content determination on the data sheet.
  2. Fill the grooves in the base of the consolidometer with water. Fit the porous stone (previously saturated with water) into the base of the consolidometer. Add sufficient water so that the water level is at the top of the porous stone. Place a moist filter paper (Whatman No. 1 or equal) over the porous stone. (Be very careful to avoid entrapping any air during the assembly operations.) Place the ring with the specimen therein on top of the porous stone. If the fixed-ring consolidometer is used, secure the ring to the base by means of clamps and screws.
  3. Place a moist filter paper on top of the specimen, and then place the previously saturated top porous stone and the loading plate in position.
  4. Place the consolidometer containing the specimen in the loading device.
  5. Attach the dial indicator support to the consolidometer, and adjust it so that the stem of the dial indicator is centred with respect to the specimen. Adjust the dial indicator to permit the approximate maximum travel of the gage but still allow measurement of any swelling.
  6. Adjust the loading device until it just makes contact with the specimen. The seating load should not exceed about 0.02 ksf.
  7. Read the dial indicator, and record the reading on a data sheet (Figure 11-24 is a suggested form). This is the initial reading of the dial indicator.
  8. With the specimen assembled in the loading device, apply a load of 0.5 ksf to the specimen and immediately inundate the specimen by filling the volume within the inundation ring or the chamber surrounding the specimen with water. If a fixed-ring device is used, a low head of water should be applied to the base of the specimen and maintained during the test by means of the standpipe. Place a thermometer in the water, and record the temperature at 2-hour intervals. To obtain reliable time- consolidation curves the temperature should not vary more than ± 2o C during the test. For most fine- grained soils a load of 0.5 ksf is usually enough to prevent swelling, but if swelling occurs apply additional load increments until swelling ceases. Were the specimen permitted to swell, the resulting void ratio-pressure curve would have a more gradual curvature and the preconsolidation pressure would not be well defined. Alternatively to applying a large initial load increment, swelling can be prevented by not inundating the specimen until the load on the specimen has reached such a level that consolidation is obviously occurring along the straight-line portion of the void ratio pressure curve, During the stages before water is added, the humidity around the specimen should be maintained at 100% to prevent evaporation; a moist paper towel, cotton batting, or other cellular material wrapped around the specimen is usually adequate. This alternative procedure permits an initial load increment less than 0.5 kips/ft_ to be applied to the specimen.
    1. Continue consolidation of the specimen by applying the next load increment. The following loading schedule is considered satisfactory for routine tests: 0.5, 1.0, 2.0, 4.0, 8.0, and 16.0 and 32.0 ksf, the total load being doubled by each load increment. The maximum load should be great enough to establish the straight-line portion of the void ratio-pressure curve, subsequently described. The designer may modify the loading schedule to simulate the loading sequence anticipated in the field.
    2. Observe and record on the data sheet (Figure 11-24) the deformation as determined from dial indicator readings after various elapsed times. Readings at 0.1, 0.2, 0.5, 1.0, 2.0, 4.0, 8.0, 15.0, and 30.0 minutes, and 1, 2, 4, 8, and 24 hours for each load increment are usually satisfactory. A timing device should be located near the consolidometer to insure accurately timed measurements. Allow each load increment to remain on the specimen for a minimum of 24 hours until it is determined that the primary consolidation is completed. For most plastic, fine-grained soils, a time interval of 24 hours will be sufficient. It is desirable that the duration of all load increments be the same. During the course of the test, plot the dial le reading versus time data for each load increment on a semilogarithmic plot as shown in Figure 11-25. Plot the dial reading on an arithmetic scale (ordinate) and the corresponding elapsed time on a logarithmic scale (abscissa) as shown in Figure 11-25. For saturated fine -grained soils, the dial reading versus time curve will generally be similar to the curve shown in Figure 11-25 and can be converted into a time-consolidation curve using the theory of consolidation. The 100% consolidation or the completion of the primary consolidation is arbitrarily defined as the intersection of the tangent to the curve at the point of inflection, with the tangent to the straight-line portion representing the secondary time effect. The construction necessary for determination of the coordinates representing 100% consolidation and other degrees of consolidation is shown in Figure 11-25.

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