Cone Penetrating Testing (2007)

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49 CPT is directly suited to evaluating ground response for sup- port of shallow foundations and embankments. According to the results of the study survey (see Figure 5), the top two major uses of CPT by the DOTs include embankment sta- bility and investigations for bridge foundations. In both cases, the CPT is first employed to delineate the subsurface stratigraphy, soil layering, and groundwater regime. Afterwards, the digital data are post-processed to provide numerical values. This chapter addresses the application of CPT penetration data for (1) calculating the magnitudes of BC and settlements of shallow spread footing foundations, and (2) embankment stability, magnitude of consolidation settlements, and time rate of consolidation. As noted previously, CPTu offers an excellent means for profiling the subsurface geostratigraphy to delineate soil strata and detect lenses, thin layers, and sand stringers. Figure 62 provides an example of a piezocone record for an Idaho DOT bridge and embankment construction. This sounding was conducted to an extraordinary final penetra- tion depth of 80 m (262 ft) below grade. The exceptional detailing of the silty clay with interbedded sand layers and small stringers is quite evident. Results from multiple soundings can be combined to form cross-sectional subsurface profiles over the proposed con- struction area. These are needed to evaluate the thickness and extent of compressible soil layers in calculating the magni- tudes of settlements and time duration for completion for embankments and shallow foundation systems. Figure 63 shows a representative cross section derived from four CPT soundings at a test embankment site, clearly indicating the various strata designated A through F with alternating layers of clays, sands, and silts. SHALLOW FOUNDATIONS For shallow spread footings, the CPT results can be used in one of two ways to evaluate bearing capacity: (1) rational (or indirect) CPT methods, or (2) direct CPT methods. CHAPTER SEVEN CONE PENETRATION TESTING FOR SHALLOW FOUNDATIONS AND EMBANKMENTS FIGURE 62 Representative piezocone sounding for soil layering detection at Sandpoint, Idaho.

In the rational (indirect) approach, the measured CPT resistances are used to assess soil engineering parameters (c, , su), which are subsequently input into traditional theoret- ical BC equations. In practice, these BC solutions are based in limit equilibrium analyses, theorems of plasticity, and cav- ity expansion. Most recently, it has become feasible to use numerical modeling simulations by finite elements (e.g., PLAXIS, CRISP, and SIGMA/W) or finite differences (e.g., FLAC) toward this purpose. The CPT data could be post-processed to provide relevant input parameters for these simulations. For the calculation of foundation settlements, the CPT results are post-processed to provide an equivalent soil modulus for use in elastic continuum theory or an alter- nate approach using compressibility parameters in an e-logv framework, also in combination with elastic theory (Bousi- nessq) to provide calculated stress distributions beneath the surface loaded footing. In a direct CPT approach, the CPT readings are employed within a methodology that outputs the ultimate bearing capacity directly. The method may be based either on one of the aforementioned theories or else empirically derived from statistical evaluations of field foundation performance. 50 For both approaches, the allowable bearing stress of the footing (qallow) is obtained by dividing the ultimate bearing capacity (qult) by an adequate factor of safety (FS): qallow  qult/FS. It is normal geotechnical practice to adopt FS  3 for shallow foundations. An alternative to the application of the FS approach is the use of load resistance factored design (LRFD). In simplistic terms, the resistance factor (RF) is used as a reduction term: qallow  RF  qult, where in essence it is the reciprocal of the safety factor, RF  1/FS. However, there are two major improvements offered by LRFD: (1) the RF takes on differing values depending on the quality and source of the data being used in the evaluation, and (2) multiple RF values are utilized on different components of the calculated capac- ity. For instance, assume that the ultimate stress depends on two calculated components: qult  qx  qz. Then, the allowable stress might be ascertained as qallow  RFx  qx  RFz  qz. The assigned RF values are based on risk and reliability indices. Details on the LRFD approach are given by Goble (2000). Rational or Indirect Cone Penetration Testing Approach for Shallow Foundations For the rational CPT approach, the limit plasticity BC solu- tion of Vesic´ (1975) and elastic continuum solutions (Harr FIGURE 63 Subsurface cross section developed from piezocone soundings at Treporti Embankment (Gottardi and Tonni 2004).

51 1966; Poulos and Davis 1974) for foundation displacements will be adopted herein. For BC problems, it is common practice to address short-term loading of clays and silts under the assumption of undrained conditions, whereas drained loading condi- tions are adopted for sands and gravels. Technically, how- ever, all soils are geological materials and therefore drained loading will eventually apply to clays, silts, sands, and gravels that are very old. The undrained condition will be the critical case for footings situated over soft clays and silts, because of relatively fast rates of loading relative to the low permeability of these soils; therefore, volumet- ric strains are zero ( V/V0  0). However, for overconsol- idated materials, either drained or undrained conditions may prove to be the critical case; therefore, both should be checked during analysis. For static loading conditions involving sands, the relatively high permeability allows for drained response ( u  0). In the case of seismic loading of sands, however, it is possible for undrained BC to hap- pen during large earthquakes, especially if liquefaction occurs. In all cases, the drained and undrained BC calcula- tions proceed in the same manner. Drained and undrained cases are considered to be extreme boundary conditions; however, it is plausible that intermediate drainage condi- tions can arise (i.e., semi-drained, partly undrained). For undrained loading conditions, the ultimate bearing stress for shallow footings and mats situated on level ground can be calculated as: qult  *Nc su (46) where the bearing factor *Nc  5.15 for a strip foundation and *Nc  6.14 for square and circular foundations. The value of undrained shear strength (su) is taken as an average from the bearing elevation to a depth equal to one footing width (B  smaller dimension) below the base of the foundation. The simple shear mode (suDSS) is appropriate and should be calculated using the three-tiered hierarchy, as dis- cussed previously. For drained BC of shallow foundations where c  0, the appropriate equation is: qult  1⁄2 B * *N (47) where the bearing factor *N is a function of effective stress friction angle () and footing shape (see Figure 64). In the case of rectangular footings, the plan dimensions are length (denoted “c” or “A”) and width (denoted “d” or “B”). The appropriate value of soil unit weight (* ) depends on the depth of the groundwater (zw) relative to the bearing eleva- tion of the footing. If the foundation has a width B and bears at a depth ze below grade, then the operational unit weight may be determined as follows: 1. ze  zw, then: *  sat  w  effective unit weight (also, submerged or buoyant unit weight) 2. zw  (ze  B), then: *  total, where total  dry for sands; yet total  sat in clays with capillarity 3. ze zw (ze  B), then: *  total  w  [1  (zw  ze)/B] FIGURE 64 Bearing factor for shallow foundations under drained loading (Vesic´ Solution).

With the appropriate FS, the applied stress q is determined and used to evaluate the displacement of the foundation at working loads. For the simple case of a flexible rectangular foundation resting on the surface of a homogenous layer (mod- ulus E constant with depth), which has finite thickness, the elastic continuum solution for the centerpoint displacement (sc) is: (48) where the equivalent elastic modulus and Poisson’s ratio are appropriately taken for either undrained conditions (imme- diate distortion) or drained settlements (owing to primary consolidation). That is, the use is synonymous with the e-logv approach within the context of recompression set- tlements owing to the close interrelationship of D and E, plus the standard utilization of elastic theory for calculating stress distributions (Fellenius 1996, updated 2002). Dis- placement influence factors for various distortions of rec- tangles of length “c” and width “d” are given by Harr (1966) and shown in Figure 65 for a compressible layer of thickness “h.” Also, an approximate solution using a spreadsheet integration of the Boussinesq equation is also given by the method described by Mayne and Poulos (1999), with excellent agreement. Additional variables that can be considered in the eval- uation of displacements beneath shallow footings and mats include: (1) soil modulus increase with depth (i.e., “Gibson Soil”), (2) foundation rigidity, (3) embedment, and (4) approximate nonlinear soil stiffness with load level. In a simplified approach, Mayne and Poulos (1999) showed that the first three of these factors could be expressed by: s q d I v Ec H s = ⋅ ⋅ ⋅ −( )1 2 52 (49) where de  diameter of an equivalent circular foundation in plan area [AF  c  d  (0.5de)2], the factor IGH  displace- ment influence factor, IF  modifier for relative foundation flexibility, IE  modifier for foundation embedment, and Eso  soil modulus at the bearing elevation of the foundation base. Relevant terms are defined in Table 5 with the elastic displacement influence factor for homogeneous to Gibson- type soil shown in Figure 66. The analysis can proceed as an equivalent elastic analysis using an appropriate modulus (e.g., D  E from Figure 33) or an approximate nonlinear approach can be taken by adopting s q d I I I v Ec e GH F E so = ⋅ ⋅ ⋅ ⋅ ⋅ −( )1 2 FIGURE 65 Displacement influence factors for flexible rectangular surface loading over finite layer. setoN/skrameR noitauqE rotcaF ro mreT Soil Modulus, Es Es = Eso + kE⋅d Eso = modulus at footing bearing elevation, kE = ΔEs/Δz = rate parameter, d = equivalent diameter, and Homogeneous case: kE = 0 Normalized Gibson Rate βG = Eso/ kE⋅d :esac suoenegomoH βG → ∞ Elastic Displacement Factor 2 )/( 235.0 β 56.0 ]1[][ 1 8.0 ++ ≈ dh GH G I For finite homogeneous to Gibson-type soils where h = thickness of compressible layer Foundation Rigidity Modifier KF KF = footing rigidity factor 3)()( )( a t E E avs FDN ⋅= , EFDN = foundation modulus, t = thickness of foundation, a = ½, and d = footing radius Foundation Embedment Modifier )/6.1)(4.0ν22.1exp(5.3 11 e E zd I +− −≈ ze = depth of embedment F F K I 106.4 1 4 + +≈ π TABLE 5 TERMS FOR CIRCULAR SHALLOW FOUNDATION DISPLACEMENT CALCULATIONS

53 the modified hyperbolic algorithm for modulus reduction with level of loading, as described previously (see Figure 32). Here, the magnitude of mobilized shear stress (/max) can be evaluated as the level of applied loading to ultimate stress from the BC calculations, which is equal to the reciprocal to the cal- culated factor of safety: q/qult  1/FS. Combining this aspect into the generalized equation gives: (50) where the exponent g may be assumed to be on the order of 0.3  0.1 for uncemented sands and fine-grained silts and clays of low to medium sensitivity. This approach has been used successfully in the prediction of footings on sands (e.g., Fahey et al. 1994; Mayne 1994) and clays (e.g., Mayne 2003). Direct Cone Penetrating Testing Approaches for Shallow Foundations The CPT point resistance is a measure of the ultimate strength of the soil medium. Therefore, by means of empirical method- ologies and/or experimental studies, a direct relationship between the measured CPT qt and foundation BC (qult) has been sought (e.g., Sanglerat 1972; Frank and Magnan 1995; Lunne and Keaveny 1995; Eslami 2006). Here, two methods will be presented: one each for sands and clays. For shallow footings on sands, Schmertmann (1978a) pre- sents a direct relationship between qult and qt (shown in Figure 67) as long as the following conditions are met rela- tive to foundation embedment depth (ze) and size (B): • When B  0.9 m (3 ft), embedment ze  1.2 m (4 ft). • When B  0.9 m (3 ft), then embedment ze  0.45 m  1⁄2 B [or ze  1.5  1⁄2 B (ft)]. s q d I I I v E q qc e GH F E g= ⋅ ⋅ ⋅ ⋅ ⋅ − ⋅ − ( ) [ ( / ) ]max 1 1 2 ult For the range of measured cone tip resistances 20  qt  160 tsf, the ultimate BC stresses can be approximated by: Square footings: qult  0.55 atm (qt/atm)0.785 (51) Strip footings: qult  0.36 atm (qt/atm)0.785 (52) where atm  reference stress equal to one atmosphere (1 atm  100 kPa  1 tsf). For shallow footings on clays, Tand et al. (1986) defined a parameter Rk as follows: (53) which is obtained from Figure 68. The term Rk depends on the embedment ratio (He/B), where He  depth of embed- ment and B  foundation width, as well as whether the clay is intact (upper curve) or fissured (lower curve). R q qk t vo t vo = − − ul   FIGURE 66 Displacement influence factor for finite homogeneous to Gibson-type soil for shallow circular footings and mat foundations. FIGURE 67 Direct relationship for ultimate bearing stress and CPT measured tip stress in sands (after Schmertmann 1978a).

Rearranging, the BC for shallow foundations on clay becomes: (54) For the direct assessment of footing settlements at working loads by CPT, a number of methods have been proposed (e.g., Meyerhof 1965; Schmertmann 1970; Lunne and Keaveny 1995). Many of these approaches are a form of the elastic the- ory solution described earlier where the CPT resistance is used to provide a direct evaluation of modulus through: D E   qt (55) or alternate form: D  c (qt  vo), as discussed previ- ously. Notably, since qt is actually a measure of strength, the use of the same measurement for estimating stiffness has noted a wide range in  values from as low as 0.4 for q R q vo k t voult = + ⋅ − ( ) 54 organic clays (Frank and Magnan 1995), 1  10 for clays and sands (Mitchell and Gardner 1975), to   40 for OC sands at low relative densities (Kulhawy and Mayne 1990). The use of Gmax to obtain a relevant stiffness may therefore be more justifiable (e.g., Fahey et al. 1994). Footing Case Study A case study can be presented to show the approximate nonlinear load-displacement-capacity response from Eq. 50. Results are taken from the load test program involving large square footings on sand as reported by Briaud and Gibbens (1994). The large north footing (B  3 m) can be used with data from SCPT conducted by the Louisiana Transportation Research Center, as reported by Tumay (1997) and pre- sented in Figure 69. The site is located at Texas A&M Uni- versity and underlain by clean sands to about 5 to 6 m, whereby the sands become slightly silty and clayey with depth. The groundwater table lies about 5.5 m deep. Re- sults from the seismic cone testing indicate a representa- tive mean value of cone tip resistance qc (ave)  7.2 MPa (72 tsf) and mean shear wave velocity Vs (ave) at approxi- mately 250 m/s. The calculation procedure is detailed in Figure 70. Using the direct Schmertmann CPT approach from Eq. 51, the ulti- mate bearing stress is calculated as qult  1.6 MPa (16.6 tsf). Alternatively, the CPT data can be post-processed to deter- mine an effective stress friction angle   40.1º, which determines qult  1.7 MPa (17.7 tsf) from Vesic BC solution from Eq. 47. The initial stiffness Emax is obtained from the shear wave velocity measurements and can be used in Eq. 50 to generate the curve in Figure 70. Good agreement is shown in comparison to the measured load-displacement response of the footing. FIGURE 68 Direct CPT method for determination of ultimate bearing stresses on clay (Tand et al. 1986). FIGURE 69 Results from seismic cone tests at Texas A&M experimental test site.

55 EMBANKMENT STABILITY AND SETTLEMENTS In geotechnical practice, stability analyses of embank- ments are handled by limit equilibrium analyses, usually by trial and error search routines within computer software codes, such as UTEXAS4, GeoSlope, STABL, and others. Settlements resulting from the primary consolidation of the underlying soft ground are calculated using one-dimensional consolidation theory to evaluate both their magnitudes and time rate behavior. The key advantages of using CPTu for embankment settlement calculations include: (1) the ability to obtain a continuous profile of OCR in soft ground, and (2) in situ assessment of cvh from dissipation testing. Displacements Beneath Embankments For embankments on soft ground it is common practice to use elastic theory to calculate the magnitudes of undrained distortion (immediate displacements), as detailed by Foott and Ladd (1981). These displacements are determined in the same manner as described previously for shallow footings, but apply displacement influence factors that account for the side slopes and height of the embankment. The stiffness is assessed in terms of an undrained soil modulus (Eu) and cor- responding u  0.5. The calculation of consolidation settlements can proceed in a similar manner using elastic theory with the appropriate displacement influence factors (Poulos and Davis 1974) and a drained stiffness (E) and drained Poisson’s ratio (), pro- vided that the applied embankment stresses do not exceed the natural preconsolidation stresses: vo  v p. At the centerpoint of the embankment, the total vertical displace- ments for undrained distortion and drained primary consoli- dation settlements, plus additional displacements resulting from long-term creep, are then given by: [undrained distortion] [drained settlements] [secondary compression] (56) The calculation of long-term displacements caused by creep can be assessed from: (57) where z  thickness of layer undergoing creep, t  time, and Ce  coefficient of secondary consolidation. Extensive lab testing on various soils has shown the ratio of Ce/Cc is constant for a given NC soil (Mesri 1994; Leroueil and Hight 2003), including Ce/Cc  0.025  0.01 for sands, Ce/Cc  0.04  0.01 for inorganic clays and silts, and up to Ce/Cc  0.06  0.01 for organic materials. The same constant also applies to that soil in overconsolidated states, but uses the recompression index in the ratio; that is, Ce/Cr  0.04 for inorganic clays. In the case of embankment loadings where the imposed earth loadings exceed the preconsolidation stresses, either the special method described by Schmertmann (1986) can be used, or else the conventional calculations for one- dimensional consolidation owing to primary settlements: Drained settlements: (58) The CPTu is particularly suited to the in situ and continu- ous profiling of the effective preconsolidation stress (p) and corresponding OCRs with depth, thus aiding in a more defin- itive calculation of settlements. In contrast, determining OCRs from oedometer and/or consolidometer testing are rather restricted, as only discrete points are obtained in limited num- bers because of high costs in sampling, time, and laboratory s C e z C e zc r o c p vf= + ⋅ ⋅ + + ⋅ ⋅( ) log( ) ( ) log(1 1 OCR   / ) p s C e z te o creep = + ⋅ ⋅  ( ) log( )1 s q d I v E q d I v E sc H u u H = ⋅ ⋅ ⋅ − + ⋅ ⋅ ⋅ − +     ( ) ( )1 12 2 creep FIGURE 70 Calculated and measured response of large 3-m square footing at Texas A&M University sand site.

testing budgets. In addition, sample disturbance effects tend to lower and flatten the e-logv curves and imply yield values that are lower than true in situ p profiles (Davie et al. 1994). Embankment Stability Stability analyses of embankments include: (1) the evalua- tion of the soft ground conditions beneath large fills, and (2) the constructed embankment itself, with adequate side slopes and use of suitable soil fill materials. For the underlying nat- ural soft ground, the CPTu can provide the profile of pre- consolidation stress that controls the undrained shear strength for the stability analysis: suDSS  0.22 p (59) that applies for OCRs 2, as described previously. For control of constructed fills, the CPTu can be used as a measure of quality control and quality assurance. This is perhaps advantageous when large fills are made using the hydraulic fill process (e.g., Yilmaz and Horsnell 1986). Time Rate Behavior Large areal fills and embankments constructed over soft ground may require long times for completion of primary 56 consolidation, ranging from months to tens of years, depending on the thickness of the consolidating layer, coef- ficient of consolidation, and available drainage paths. Results from CPTu soundings can provide information on layer thickness, presence of lower sand drainage layers, and the detection of sand lenses or stringers that may promote consolidation. Dissipation testing by CPTù helps assess cvh needed in the one-dimensional rate of consolidation analy- sis, as well as the calculated spacing of vertical wick drains, sand drains, or stone columns that may be required by the geotechnical engineer to expedite the consolidation process. The time for completion of one-dimensional consolida- tion for a doubly drained soil layer (top and bottom) can be estimated from: t  Tv hp2/cv (60) where Tv  1.2  time factor (assuming 96% consolidation is essentially “complete”) from one-dimensional vertical consolidation and hp  drainage path length ( one-half layer thickness for double drainage). Time factors for other percentage degrees of consolidation are given by Holtz and Kovacs (1981) with approximations cited as: U 60%: Tv  0.785(U%/100)2 (61a) U  60%: Tv  1.781  0.933 log(100  U%) (61b)