DESIGN OF PIER FOUNDATIONS ON EXPANSIVE SOILS John D. Nelson 1,2, Kuo-Chieh Chao 2 & Daniel D. Overton 2

DESIGN OF PIER FOUNDATIONS ON EXPANSIVE SOILS John D. Nelson 1,2, Kuo-Chieh Chao 2 & Daniel D. Overton 2 1 ) Colorado State University 2 ) Tetra Tech, Inc. Abstract: For sites with high expansion potential the most reliable foundation system is the pier and grade beam foundation. The design of the piers requires careful characterization of the soil profile and appropriate computation of the required pier length. This, in turn, requires prediction of the free-field heave of the foundation soil and/or bedrock. Current design procedure generally considers the maximum ultimate predicted heave that will occur at a site. This is appropriate for sites with low to moderate expansion potential. However, for sites with high to very high expansion potential, it may be impractical to design for the ultimate heave. Therefore, design of foundations for buildings on expansive soils must consider the migration of the wetting front and the associated heave that will occur during the design life of the structure. This paper presents the procedure for predicting free-field heave and heave of straight shaft, belled, and helical piers within the design life of the structure. The effect of overexcavating and replacing the upper few meters of expansive soil in combination with installing piers is discussed. The results of the calculations indicate that the required pier length can be reduced significantly if the rate of heave within the design life of the structure is considered. 1. INTRODUCTION The design of foundations for light structures on expansive soils is perhaps one of the most challenging problems facing foundation engineers. Foundations on expansive soils will cost more than foundations on ordinary soils, and most likely the site investigation and foundation design will cost more as well. Owners of structures demand that the foundations be capable of supporting the structure within tolerable movement limits, and at the same time they are reluctant to spend more than they are accustomed to for ordinary soil sites. The characterization of expansive soil can be done on the basis of the Expansion Potential, EP, which is defined on the basis of percent swell exhibited in a consolidation-swell test and the swelling pressure of the soil (Nelson, et al., 2007). For sites having a low to moderate expansion potential, EP, a variety of foundation systems have been proposed and used. However, for sites with high to very high expansion potential the most reliable method for foundation design is the use of pier and grade beam foundations. For structures that have full depth basements, the basement walls typically serve as the grade beam. If a full depth basement is not used a stiff grade beam supported by the piers and isolated from the underlying soils is used. The geotechnical engineer typically does not perform the structural design, but is called upon to provide the geotechnical input for the design. This includes determination of the soil properties, and computation of soil, and pier movement. In this paper, the important factors to be included in such computations are presented. The movement of water in the subsoils, particularly in the unsaturated zone is discussed as it relates to pier behavior. Pier movement is normalized against free-field heave, and therefore, free-field heave prediction is reviewed. Pier design including methods for both rigid and elastic piers is presented. Required pier lengths for various types of piers within the design life of the structure are compared in this paper. Tensile force in the piers is computed for use in designing the reinforcing steel. 2. FREE-FIELD HEAVE PREDICTION The methodology presented herein computes pier heave as a function of free-field heave. Therefore, it is important to review free-field heave prediction first. Free-field heave is the heave that will occur at the surface of a soil profile if no surcharge or stress is applied. Because the stress imposed by the weight of an unloaded slab-ongrade is small, slab heave is also approximately equal to the free-field heave. Several methods have been proposed for predicting free-field heave. The authors prefer to predict free-field heave using data from the Oedometer test, namely the consolidationswell test. 2.1 Prediction of Free-Field Heave by the Oedometer Method A method for prediction of free-field heave using oedometer test data is outlined in Nelson and

Miller (1992). A refinement of that method is presented in Nelson, et al. (2006) and is discussed below. To predict the heave of a soil profile, the soil is divided into a number of layers, n, of thickness, z. The general equation for heave is (Nelson and Miller, 1992): = n CHzi (1+ eo ) σ f log σ ρ (1) 1 i cv i where: ρ = free-field heave C H = heave index σ f = final effective stress state σ cv = swelling pressure from the constantvolume oedometer test e o = initial void ratio z i = layer thickness 2.2 Determination of Heave Index, C H The heave index, C H, can be determined from consolidation-swell test data along with data from constant-volume tests. Because, the constantvolume test data can be approximated from consolidation-swell test data, as will be described below, all of the needed data can be obtained from that test alone. An example of the consolidation-swell test data is shown in Figure 1. The slope of the loading portion of the curve shown in Figure 1 is the compression index C c, and that of the rebound portion of the curve is the rebound index C s. The volumetric strain experienced during inundation is the percent swell, %S. Figure 2 shows the vertical overburden stress states at three different depths in a soil profile with similar soil throughout. At all points all samples are in a condition of zero lateral strain with a vertical overburden stress equal to σ vo. If a consolidation-swell test is conducted on a sample identical to that at depth, Z A, at an inundation stress, (σ i ) A = (σ vo ) A, the sample will swell by an amount %S A as shown in Figure 3. Similarly for a sample at depth Z B, the sample would be subjected to an inundation stress, (σ i ) B = (σ vo ) B, and the sample would swell by an amount %S B. Obviously, if a sample is tested at an inundation pressure equal to the constant-volume swelling pressure, σ cv, the sample will not swell and the test data would define point C in Figure 3. To arrive at the form of Equation (1), it is convenient to start with the general equation for heave in a soil stratum of thickness, Δz. That is, ρ ε v Δz = %S Δz = (2) GROUND SURFACE Z A (σ vo ) A Z B DEPTH OF (σ vo ) B POTENTIAL HEAVE, Z C Figure 2. Vertical Stress States in Soil Profile. A (σ vo ) C =σ cv C CONSOLIDATION SWELL TEST DATA STRAIN, ε (%) (-) COMPRESSION (+) HEAVE 0 A % SWELL, % S C s C c B D F σ i σ cv σ cs APPLIED STRESS, σ (LOG SCALE) Figure 1. Terminology and Notation for Oedometer Tests. VERTICAL STRAIN % SA CH % SB B (σ i ) A (σ i ) B σcv σcs B σcs A C APPLIED STRESS (LOG SCALE) Figure 3. Hypothetical Oedometer Test Results for Stress States Shown in Figure 2.

For a layer of thickness, Δz, the overburden pressure and applied stress will influence the amount of swell that will occur when that layer becomes wetted. Because that stress varies from layer to layer, it is necessary to define a relationship between the amount of swell that occurs and the imposed stress when the soil is wetted, i.e., the inundation pressure. That relationship is defined by the line ABC in Figure 3. It is important to note that this is not a stress-strain curve obtained by loading or unloading along a stress path. For all practical purposes, the line ABC can be defined by a straight line connecting point A (the point defined by the percent swell in a consolidation-swell test) and point C (the point corresponding to the constant volume swell pressure, σ cv. The slope of that line is denoted by the heave index, C H, where: %S %SA = σcv log (σi ) A C = (3) H logσ cv log(σ i ) A A If values of C H and σ cv are known, the vertical strain, or percent swell, that will occur during inundation at any depth z in a soil profile can be determined from Equation (3). In rewriting Equation (3) as Equation (4), when the soil at depth z is inundated, the stress on the soil is the overburden stress, (σ vo ) z. This value is therefore used for the inundation stress, σ i, in Equation (4). σ cv (ε v ) z = %Sz = CHlog (4) (σ vo ) z Therefore, for a layer of soil of thickness, Δz, that exists at a depth z to its midpoint, the maximum heave that will occur due to expansion of that stratum during complete inundation would be obtained by substituting Equation (4) into Equation (2). Thus, σ cv ρ = CH Δzlog (5) (σvo) z In actual application of Equation (5), a soil profile will be divided into layers of thickness, Δz, the value of heave for each layer will be computed, and the incremental values will be added to determine the total heave. It should be noted that the value of (σ vo ) z to be used in Equation (5) is the stress at the midpoint of the layer at depth z. In a soil with no applied load that value would be the overburden pressure. If a load is applied to the soil, for example, by a footing or stiffened slab, the value of (σ vo ) z to be used in Equation (5), is the overburden plus applied load. The line ABC in Figure 3 and the heave index, C H, can be determined by conducting consolidation-swell and constant volume oedometer tests on samples of the same soil and connecting point A obtained from the consolidation-swell test with point C obtained from the constant volume test. However, to do so is generally not practical, mainly because it is almost impossible to obtain two identical samples from the field. A relationship between σ cv and σ cs has been proposed so that the value of the heave index can be determined from a single consolidation-swell test (Nelson, et al., 2006). 2.3 Relationship Between σ cv and σ cs A relationship between σ cv and σ cs exists that is of the form. σ cv = σ + λ(σ σ ) (6) i cs i The rationale behind this equation is that the value of σ i must be less than σ cv, otherwise heave would not have occurred. Also as noted previously, it is reasonable to expect that σ cv will be less than σ cs. Equation (6) proposes that the value of σ cv falls between σ i and σ cs by the proportionality defined by the value of λ. The authors experience has indicated that a reasonable value for λ is 0.6 for the clay soil in the Front Range area of Colorado, USA. Since the value of λ is dependent upon mineralogy of the clay soil, the λ value should be determined for soil on a regional basis. 2.4 Depth of Heaving The depth of soil that is contributing to heave at any instant of time depends on two factors. These are the depth to which water contents in the soil have increased since the time of construction, and the expansion potential of the various soil strata. As water migrates through a soil profile different strata become wetted, some of which may have more swell potential than others. Consequently, the zone of soil that is contributing to heave varies with time. The amount of heave that will occur at a particular time depends on the manner in which the

groundwater migrates in the soil and the expansion potential of the soil at depth. Movement of the soil surface will begin almost immediately after construction, whereas some time will be required for the soil at deeper depths to become wetted. Thus, a slab-on-grade will begin to heave almost immediately, but movement of piers will be delayed sometimes for several years. The term Active Zone has been in common usage in the field of expansive soils. However, the usage of that term has taken different meaning at different times and in different places. Therefore, for purposes of clarity and consistency, the following four definitions have been put forth (Nelson, et al., 2001). 1. Active Zone is that zone of soil that is contributing to heave due to soil expansion at a particular point in time. The depth of the active zone will vary as heave progresses, and therefore varies with time. 2. Zone of Seasonal Moisture Fluctuation is that zone of soil in which water contents change due to climatic changes. 3. Depth of Wetting is the depth to which water contents have increased due to external factors. Such factors could include capillary rise after the elimination of evapo-transpiration from the surface, infiltration due to irrigation or precipitation, or introduction of water from offsite. Underground sources may include broken water lines, perched water tables, flow through more permeable strata that are recharged at distant locations, or a number of other factors. 4. Depth of Potential Heave is the depth to which the overburden vertical stress equals or exceeds the swelling pressure of the soil. This represents the maximum depth of Active Zone that could occur. 3. PIER DESIGN Figure 4 shows a typical detail of a type of drilled pier and grade beam foundation system. A void space must be maintained between the grade beam and the soil to prevent uplift forces from being transmitted directly to the grade beam as the soil heaves. Typically a structural floor is supported on the grade beam. Slab-on-grade floor systems will not function well because of intolerable movements due to heave of the subsoils. Piers can be of different types. They may be straight shaft drilled piers, they may be drilled piers with belled ends, they may be steel piles that are driven or pushed, or they may be helical piers. The principle on which the piers are designed is to found them in a sound stratum at sufficient depth so as to provide sufficient anchorage to minimize movement under the uplift forces exerted by the expansive soil. Figure 4. Typical Pier and Grade Beam Foundation System. If a stable non-expansive stratum exists sufficiently near the surface, the pier may be designed as a rigid member anchored in that stratum so as to prevent movement. However, if the depth of potential heave is large, the design length of a pier designed as a rigid pier may be too long to be practical. The pier should then be designed as an elastic member in an elastic medium. In this case, the required length of a pier that will not heave more than the allowable amount is computed. The discussion below will briefly present the procedures for design of a rigid pier, and then present procedures for predicting heave of an elastic pier. 3.1 Rigid Pier Design The forces acting on a pier in expansive soil are shown in Figure 5. The principle of the design is that the negative skin friction below the depth of potential heave plus the dead load, P, must resist the uplift pressures produced by the swelling pressures exerted on the pier above that point.

Z p DEPTH OF POTENTIAL HEAVE P dl UPLIFT SKIN FRICTION approximately twice the depth of potential heave. In such cases the design rigid pier length is generally not practical for a light structure, and it would be appropriate to use a shorter pier if the predicted heave of the shorter pier is within tolerable limits. In that case an elastic pier design would be appropriate. L (L - Z p ) f s Figure 5. Forces Acting on a Rigid Pier. d f u NEGATIVE SKIN FRICTION PROVIDING ANCHORAGE The equation for required length of a rigid straight shaft pier is, L = z p + where: 1 f s α 1σ cvz p Pdl πd z p = the depth of potential heave f s = the negative skin friction below the depth of potential heave α 1 = a coefficient of uplift between the pier and the soil σ cv = the swelling pressure from the constant volume pressure P dl = minimum dead load on the pier d = diameter of the pier The maximum tensile force generated in the pier, P max, would occur at the bottom of the depth of potential heave and would be equal to P max = P f z πd (8) dl u p where, f u = the uplift skin friction on the pier = α 1 σ cv and all other terms were defined in Equation (7). A more complete treatment of rigid pier design is presented in Nelson and Miller (1992). Rigid pier design works well if the stratum of expansive soil is not thick and is underlain by a stable non-expansive stratum. However, in a deep deposit of expansive soil, the required pier length is (7) 3.2 Elastic Pier Design Elastic pier design is presented in Nelson and Miller (1992). The heave prediction methodology presented therein, is based on a theoretical treatment of pier heave in an elastic medium developed by Poulos and Davis (1980). The material presented by Poulos and Davis was modified somewhat by Nelson and Miller (1992) to make it more easily usable by the design engineer. The material below is also somewhat modified from Nelson and Miller (1992), to further facilitate its use by the design engineer. The uplift skin friction along the side of the pier may be considered to be uniform along the length of the pier or may increase with depth. A case for the uniform distribution would be the situation where the soil within the depth of potential heave has generally the same swelling pressure throughout. A case for the linearly increasing distribution would be where several strata of soils exist with the deeper soils having a higher Expansion Potential. Another case would be where the soundness of a claystone stratum increases with depth as a result of weathering of the upper material, such that the swelling pressure increases with depth. Figure 6 shows normalized pier heave plotted as a function of the ratio of pier length to depth of potential heave for a straight shaft pier. The two curves presented in that figure are for the two cases where the soil-pier skin friction is constant with depth and where it varies linearly with depth. Similar curves are presented in Figure 7 for belled piers having a bell diameter twice that of the shaft. Figures 8 and 9 show the normalized maximum tensile force in straight shaft and belled piers plotted as a function of the ratio of pier length to depth of potential heave. The maximum force is normalized to a force, P FS, computed by applying the uplift friction over the entire length of the pier.

For the case where the skin friction varies linearly with depth, this force, P FS, is equal to, P FS = 0.5f Lπd (9) um For the case where the skin friction is uniform with depth, this force, P FS, is equal to, P FS = f Lπd (10) um Figure 6. Normalized Straight Shaft Pier Heave vs. L/z p. Figure 7. Normalized Belled Pier Heave vs. L/z p. Figure 8. Normalized Force in Straight Shaft Piers vs. L/z p. Figure 9. Normalized Force in Belled Piers vs. L/z p. 3.3 Accuracy of Drilled Pier Heave Prediction There is not much data available with which to verify the pier movement predictions. One reason is that pier movement is smaller and occurs more slowly than free-field heave (slab movement). Also, in most cases, there is not a stable benchmark against which to measure pier movement. The authors have had experience with two cases in which reliable data has been available. One is a commercial, relatively heavy masonry building, located in Loveland, Colorado. It is located on the Pierre Shale that is dipping to the east at about 20 at that location. The building has a deep basement with a crawl space below. The piers are 7.0 meters long with the top being 6.4 meters below finished grade. Piers are 457 to 1067 mm in diameter with dead loads varying from 270 to 1,110 kn. The depth of wetting at the time of the investigation was about 10.7 meters. Piers in one corner of the building had heaved 279 mm. Calculations indicated that maximum heave would be about 380 mm. Considering that additional heave will occur after the time of investigation, the predicted heave is very reasonable. The other building is located on the flat-lying Denver formation claystones, east of Colorado, USA. This also is a relatively heavy building supported on piers. The ground floor is a slab-ongrade and has heaved as much as 127 mm in places. The piers are 457, 610, or 762 mm in diameter and are 7.6 or 8.5 meters deep. The grade beams supported on the piers are relatively shallow, so that the tops of the piers are only 0.8 to 0.9 meters below finished grade. Deep benchmarks have been established that are founded well below the depth of potential heave to allow for accurate monitoring of pier movement (Chao, et al., 2006). The maximum pier movement to date (12 years after construction) is 102 mm. Analyses have been conducted to predict pier heave as a function of time. Comparison of the predicted pier movement

to date and extrapolation to the ultimate heave has indicated that the difference between the predicted pier movement and the actual measured heave is approximately 15 to 20%. These two cases indicate that with careful sampling and testing, and with accurate definition of the subsoil profile, pier heave can be predicted with good accuracy. 3.4 Prediction of Helical Pier Heave A number of different configurations of helical piers are available commercially. Figure 10 shows an installation of helical pier at a test site. Figure 11 shows a schematic of a helical pier to use for describing the heave prediction methodology. In predicting heave of a helical pier, it is assumed that the skin friction along the shaft is very low. This is considered a reasonable assumption, because as the pier is advanced into the soil, the material in the annulus space above the helix, in which the shaft is centered, is disturbed. It is not recompacted and the swell potential in this area is reduced greatly. Thus, the heave of the top of the pier is limited by the amount by which the helix can move. The helix will move by the amount that the soil at the depth, L HP, will heave. This value can be determined from the calculations of free-field heave. Figure 11. Schematic of Helical Pier. 4. EXAMPLE FOUNDATION DESIGN For purposes of illustrating the above design procedures, a hypothetical subsoil profile has been defined. It consists of a site with 3 meters of native clay over claystone. The values of EP for the high expansive native clay and claystone are 1.1 and 2.0, respectively. Table 1 shows the material properties used in the calculations. Table 1. Material Properties Used in the Heave Calculations. Consolidation-Swell Soil Type Water Total Test (1) Content Density Percent Swelling Swell Pressure (%) (Mg/m 3 ) (%) (kpa) Native Clay 15.0 1.84 2.0 240 Claystone 10.0 1.94 3.0 335 (1) Inundation Pressure = 48 kpa Figure 10. Photo of Installation of Helical Pier. For simplicity, the example structure was assumed to have no basement and grade beam. The piers were assumed to be constructed starting from the ground surface. The piers will have a diameter of 254 mm. The minimum dead load on the piers will be 50 kn. The example will calculate the following.

1. Free-field heave at the bottom of the grade beam. 2. Required length of a rigid straight shaft pier with no movement. 3. Required reinforcement steel for the rigid pier. 4. Required length of an elastic straight shaft pier with 50 mm of movement. 5. Required reinforcement steel for the straight shaft pier with 50 mm of movement. 6. Required length of an elastic belled pier with 50 mm of movement. 7. Required reinforcement steel for the belled pier with 50 mm of movement. 8. Required length of a helical pier with 50 mm of movement. For purpose of illustration in the design example, the maximum tolerable movement of the foundation was assumed to be 50 mm. It should be noted that this is the assumed total movement at that pier location. Our experience shows that a differential movement between adjacent piers is usually half to one times of the predicted total heave. Therefore, the assumption of 50 mm of the total movement could result in a differential movement of 25 to 50 mm. Normally, the maximum tolerable differential movement ranges from 25 to 50 mm depending on the type and configuration of the pier and grade beam foundation. Sometimes, an adjustable collar might be needed to be placed on the top of the pier if the predicted total movement is greater than the tolerable heave. The actual maximum tolerable differential movement should be discussed with a structural engineer. CALCULATIONS Step 1: The swelling pressure for a constant volume oedometer test is estimated using Equation (6). Thus, σ cv = 48 + 0.6 (240 48) = 163 kpa for clay σ cv = 48 + 0.6 (335 48) = 220 kpa for claystone C H can be determined from Equation (3): C H = 2% / log(163 / 48) = 0.038 for clay C H = 3% / log(220 / 48) = 0.045 for claystone The depth of potential heave, z p, is computed by equating the overburden pressure to the swelling pressure. Thus, (1.84 9.81 3) + [1.94 9.81 (z p 3)] = 220 kpa z p = 11.7 m In computing heave, the depth of potential heave is divided into several layers and the heave of each layer is computed. The total heave is the sum of heave over all layers. For this example, the soil was divided into 35 layers. Therefore, each layer is then (11.7 m / 35) or 0.33 m thick. The midpoint of the first layer is 0.17 meters below the ground surface. The effective stress at that depth is, σ vo = 1.84 9.81 0.17 = 3.1 kpa From Equation (5), the heave of that layer is ρ 1 = 0.038 0.33 log (163 / 3.1) = 0.022 m = 22 mm This computation is then repeated for all layers and the increments of heave are summed. These computations lend themselves well to computation by simple spreadsheets. The total free-field heave is computed to be 193 mm. Step 2: The required length of a rigid pier is calculated by equating the uplift forces shown in Figure 5 to the sum of the negative (anchorage) skin friction forces and the dead load. The uplift skin friction is equal to, f u = α 1 σ cv where α 1 is a coefficient of uplift between the pier and the soil. The value of α 1 can reasonably be assumed to be between 0.10 and 0.25 (Nelson and Miller, 1992). A value of 0.2 was assumed here. The uplift skin friction forces are, F u = f u z p π d F u1 = (0.2 163) 3 π (254 / 1000) = 78 kn from clay F u2 = (0.2 220) (11.7 3) π (254 / 1000) = 305 kn from claystone Total F u = F u1 + F u2 = 383 kn The negative (anchorage) skin friction can be calculated by f s = α s σ h where α s is a coefficient of negative friction between the pier and the soil, and σ h is the lateral stress acting on the pier in the anchorage zone.

The value of α s should be similar to that of α 1. Whereas that is most likely true in most soils, tests at Colorado State University have shown that it may be somewhat higher in the stiff and, sometimes sandy, claystone in Colorado. Therefore, a value of 0.25 will be used here. The lateral pressure will be taken as being equal to the swelling pressure of the claystone. Thus, F s = f s (L z p ) π d = (0.25 220) (L 11.7) π (254 / 1000) = 43.9L 513.6 kn Summing all forces including the dead load, 43.9L 513.6 + 50 = 383 kn L reqd = 19.3 meters Step 3: The maximum tensile force in the straight shaft pier is, P max = 50 383 = 333 kn The negative sign indicates that the force is tensile. If conventional Grade 60 steel reinforcement, with an allowable design stress of 40 ksi is used, the required area of steel is, (A s ) reqd = 333 (0.23 kips / 1 kn) / 40 = 1.91 in 2 = 1,323 mm 2 Step 4: Figure 6 will be used to compute the required length of an elastic straight shaft pier with 50 mm of movement. Because the claystone is stiff and has a high swelling pressure, the pier-soil interaction is considered to be uniform with depth. This corresponds to case A in Figure 6. ρ p / ρ = 50 / 193 = 0.26 Using case A in Figure 6, L /z p = 1.43 The depth of potential heave, z p, was previously calculated to be 11.7 meters. Thus, the required pier length, L reqd, is, L reqd = 1.43 11.7 = 16.7 meters Step 5: Figure 8 will be used to compute the maximum force in the pier, for use in computing the required amount of reinforcing steel. From Equation (10), the value of P FS is calculated to be, P FS = f u L π d P FS1 = (0.2 163) 3 π (254 / 1000) = 78 kn from clay P FS2 = (0.2 220) (16.7 3) π (254 / 1000) = 481 kn from claystone Total P FS = P FS1 + P FS2 = 805 kn Again, the minus sign indicates that the force is tensile. From Figure 8, P max / P FS = 0.48 for L /z p = 1.43 P max = 0.48 805 = 386 kn For Grade 60 steel, (A s ) reqd = 386 (0.23 kips / 1 kn) / 40 = 2.2 in 2 = 1,419 mm 2 Step 6: Figure 7 will be used to compute the required length of an elastic belled pier with 50 mm of movement. Again, the pier-soil interaction is considered to be uniform with depth. This corresponds to case A in Figure 7. Using case A in Figure 7, L /z p = 0.85 for ρ p / ρ = 50 / 193 = 0.26 Thus, the required pier length, L reqd, is, L reqd = 0.85 11.7 = 9.9 meters Step 7: Figure 9 will be used to compute the maximum force in the pier, for use in computing the required amount of reinforcing steel. From Equation (10), the value of P FS is equal to -805 kn, as calculated in Step 5. From Figure 9, P max / P FS = 0.90 for L /z p = 0.85 P max = 0.90 805 = 725 kn For Grade 60 steel,

(A s ) reqd = 725 (0.23 kips / 1 kn) / 40 = 4.2 in 2 = 2,709 mm 2 Step 8: As discussed in Section 3.4, the helix will move by the amount that the soil at the depth, L HP, will heave. This value can be determined from the calculations of free-field heave. A spreadsheet calculation of the free-field heave was conducted using the free-field heave procedure discussed in Step 1. From that spreadsheet, it is predicted that the soil at a depth of 5.2 meters will heave by the amount of 50 mm. Therefore, the required length of a helical pier with 50 mm of movement is 5.2 meters. 5. REQUIRED PIER LENGTH FOR DESIGN LIFE OF STRUCTURE The rate of heave of the piers will depend on the rate at which subsoil become wetted. Analyses of rate of wetting front movement, for a typical case where there is a constant source of water at the ground surface, have shown that to move downward a distance of 10 meters can require 20 to 30 years or more (Durkee, 2000). As time progresses, the depth of wetting, and hence, distress to the building, will continue. Figure 12 shows slab and pier heave as a function of time for the rate of wetting front movement. Data for only the first ten years after development of a wetting front are shown. It is particularly interesting to note that, whereas slab movement begins almost immediately after a wetting front has begun to develop, pier movement does not begin until several years later. Furthermore, the length of the pier influences both the time at which pier movement begins and the amount of pier movement (Nelson, et al., 2001). HEAVE & PIER MOVEMENT ( MM) 350 300 250 200 150 100 50 SLAB HEAVE 6 M (20 FT) PIER 0 0 0 2 4 6 8 10 TIME ( YEARS ) 11 M (35 FT) PIER Figure 12. Heave and Pier Movement for Hypothetical Site, First Ten Years. 14 12 10 8 6 4 2 HEAVE & PIER MOVEMENT ( IN.) Table 2 summarizes the required pier lengths for the cases computed in Section 4 of this paper. The required pier length ranges from 5.2 to 19.3 meters. Table 2 indicates that the length of the straight shaft pier was reduced by approximately 13% if a tolerable movement of 50 mm is acceptable for the structure. Using a belled pier reduced the pier length by approximately 41% compared to the length for the straight shaft pier. The helical pier is the most effective technique in terms of the required pier length for structures on expansive soils. Table 2. Summary of Pier Length Calculations for the Ulitimate Heave Cases. Required Case Design Pier Type Pier No. Method Length (m) 1 Straight Shaft Pier with No Movement Rigid Pier 19.3 2 Straight Shaft Pier with 50 mm of Movement Elastic Pier 16.7 3 Belled Pier with 50 mm of Movement Elastic Pier 9.9 4 Helical Pier with 50 mm of Movement -- 5.2 The required pier lengths shown in Table 2 were computed considering the amount of predicted heave that will ultimately occur at a site. Design of foundations for extreme ultimate conditions is not always practical and economical in engineering practice. When large values of heave are predicted, the depth of potential heave may be very deep, and the time required for the wetting front to reach large depths of potential heave may exceed the design life of the structure. In that case, it is important to consider the rate of water migration in the vadose zone. Thus, design of foundations for buildings on expansive soils must consider the migration of the wetting front that will occur during the design life of the structure, and the amount of expected heave that such wetting will produce. Overton, et al. (2006) conducted water migration analyses for the hypothetical subsoil profile (3 meters of native clay over claystone) described in Section 4 of this paper using the computer program VADOSE/W Version 6.16 (GEO-SLOPE, 2005). Consideration was given to the time period of analysis. The Housing Facts, Figures, and Trends published by National Association of Home Builders (1997) indicated that the design life for residential foundations should be 200 years. The

minimum design life for residential foundations as presented by the U.S. Department of Housing and Urban Development (2002) and Schmatz and Stiemer (1995) is 100 years for foundations. Consequently, the VADOSE/W analysis was conducted considering 100 years of the design life of the structure. The results of the water migration analysis are presented in Figure 13. Figure 13 indicates that water will continue to migrate down into the subsoil to a depth of approximately 15 meters in 100 years for this particular case. It should be noted that neither the clay nor claystone is completely saturated at the end of design life of the structure in 100 years. This means that the heave prediction method using the consolidation-swell test results and assuming the entire depth of potential heave will be wetted could be conservative for certain circumstances. The required pier length for the design life of the structure analyzed using the water content profiles shown in Figure 13, the total free-field heave calculated in Section 4 of this paper, and the relationship between heave and volumetric water content for a typical claystone in the Front Range area (Overton, et al., 2006). The results of these analyses are shown in Table 3. In addition to the example cases presented in Table 2, the effect of overexcavation and replacement method in combination with a pier and grade beam foundation was evaluated in this paper. Table 3 presents the results of the required pier lengths with various design conditions. Table 3 shows the required pier lengths for Cases 1, 3, and 5 at the end of the design life of the structure are 9.1, 6.1, and 1.8 meters, respectively. Comparing these results to those shown in Table 2 indicates that by considering rate of heave for the site at the end of design life of the structure, the required pier length can be reduced by 38 to 65%. Cases 2 and 4 shown in Table 3 indicate that if the 3 meters of overexcavation and replacement method is adopted, no pier is needed within the design life of the structure if 50 mm of movement can be tolerated. For these cases, a spread footing foundation could be used for the structure. Comparison of the required helical pier lengths shown in Table 3 indicates that the helical pier is the most efficient foundation system in terms of the length consideration for the structure. Depth Below Ground Surface (m) Volumetric Water Content (%) 10 20 30 40 50 0 5 10 15 20 25 30 Initial Conditions 2 yrs 10 yrs 20 yrs 100 yrs Figure 13. Migration of Water Content Profiles for Soil Profile with 3 meters of Clay over Claystone. Table 3. Summary of Pier Length Calculations for the Design Life of the Strcuture Cases. Required Case Design Pier Type Pier No. Method Length (m) 1 Straight Shaft Pier with 50 mm of Movement Elastic Pier 9.1 2 Straight Shaft Pier and 3-m Overexcavation with 50 mm of Elastic Pier 0 Movement 3 Belled Pier with 50 mm of Movement Elastic Pier 6.1 4 Belled Pier and 3-m Overexcavation with Elastic Pier 0 50 mm of Movement 5 Helical Pier with 50 mm of Movement -- 1.8 6. DISCUSSION AND CONCLUSIONS It is shown that for design of foundations on expansive soils, it is essential to compute free-field heave and predicted foundation movement. Pier foundations can be either straight shaft, belled, helical piers, or some version thereof. In soil profiles with high EP, the required length of a straight shaft pier may not be practical. The use of belled piers or helical piers may be very effective in those cases. Clay CS

Another means of mitigating the effects of heave is to overexcavate and replace the upper few meters of expansive soil with non-expansive soil. For sites with low to moderate EP the overexcavation and replacement procedure may even negate the need for piers and spread footings may be used. It is essential that heave calculations be performed to verify if that can be done. The use of helical piers or overexcavation and replacement method in combination with piers can be very effective in mitigation effects of expansive soils. For sites with low to moderate EP, it is likely that the entire depth of potential heave will be wetted. However, for sites with high to very high EP, it becomes impractical to design a foundation system for that case. Consequently, design of foundations for structures on expansive soils must consider the migration of the wetting front that will occur and the associated heave that such wetting will produce during the design life of the structure Expansive Clay Soils and Vegetative Influence on Shallow Foundations, ASCE, Houston, Texas, USA: pp. 95-109. Overton, D.D., Chao, K.C. and Nelson, J.D. 2006. Time Rate of Heave Prediction in Expansive Soils. GeoCongress 2006 Conference, Atlanta, USA. Poulos, H.G. and Davis, E.H. 1980. Pile Foundation Analysis and Design. New York: John Wiley. Schmalz, T.C, and Stiemer, S.F. 1995. Consideration of Design Life of Structures. Journal of Performance of Constructed Facilities, ASCE 9(3): pp. 206-219. U.S. Department of Housing and Urban Development. 2002. Durability by Design, A Guide for Residential Builders and Designers. Washington, D.C., USA. REFERENCES Chao, K.C., Overton, D.D. and Nelson, J.D. 2006. Design and Installation of Deep Benchmarks in Expansive Soil. Journal of Surveying Engineering 132(3): pp. 124-131. Durkee, D.B. 2000. Active Zone and Edge Moisture Variation Distance in Expansive Soils. Ph.D. Thesis, Colorado State University, Fort Collins, Colorado. USA. GEO-SLOPE International, Ltd. 2005. GEO- STUDIO VADOSE/W Software Package for Seepage Analysis, Version 6.16. Calgary, Alberta, Canada. National Association of Home Builders 1997. Housing Facts, Figures, & Trends. Washington, D.C., USA. Nelson, J.D. and Miller, D.J. 1992. Expansive Soils: Problems and Practice in Foundation and Pavement Design. New York: John Wiley and Sons. Nelson, J.D., Chao, K.C. and Overton, D.D. 2007. Definition of Expansion Potential for Expansive Soils. Proceedings of the Third Asian Conference on Unsaturated Soils, Nanjing, China. Nelson, J.D., Reichler, D.K. and Cumbers, J.M. 2006. Parameters for Heave Prediction by Oedometer Tests. Proceedings of the Fourth International Conference on Unsaturated Soils. Carefree, Arizona, USA. Nelson, J.D., Overton, D.D. and Durkee, D.B. 2001. Depth of Wetting and the Active Zone.