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92 the use of load-displacement relations for the tip of a loaded 3.9.2 Experimental Results Using rock socket is analogous to the load-displacement relations a Dual Interface Apparatus (DIA) of a shallow foundation constructed below surface. 4. The scatter of the method is significantly improved when 3.9.2.1 Background measured discontinuity spacing (s) is applied to the Paikowsky et al. (1995) developed a dual interface shear analysis. A COV value of 0.461 for 83 cases is obtained when apparatus to evaluate the distribution and magnitude of friction the spacing is known. A COV value of 0.712 for 36 cases between granular materials and solid inextensible surfaces. was exhibited by the analyses when using a discontinuity The dual interface apparatus (DIA) facilitates the evalua- spacing (s) based on the generic rock description provided tion of boundary conditions (effects) and interfacial shearing by LRFD Bridge Design Specifications Section 10: Foundations modes including unrestricted interfacial shear unaffected by (AASHTO 2007). the boundaries. Such measurements allow comparisons to test 5. A significant reduction in the mean and the bias was results from a modified direct shear (MDS) box commonly systematically observed for foundations (both footings and used for measuring soil-solid interfacial friction (by replacing rock sockets) on fractured rock. This observation is limited, the lower part of the shear box with a solid surface). Ideal and however, to a small number of cases--20 for 9 sites as natural granular materials were sheared along controlled and compared to 99 for 60 sites for all other cases. random solid surface interfaces and compared to direct shear test results. The tests are designed based on a micro-mechanical model 3.9 Uncertainties in the Friction approach describing the interface friction mechanism Along the Soil-Structure Interface (Paikowsky, 1989) and making use of the term "normalized 3.9.1 Overview roughness" (Rn) as defined by Uesugi and Kishida (1986) and illustrated in Figure 81: The solid-soil interfacial friction is an important factor affecting soil-structure interaction. In the context of the Rmax ( L = D50 ) ULS of shallow foundation design, one needs to address the Rn = (111) D50 possibility of shallow foundation sliding when subjected to lateral loading, often encountered in bridge abutments. where Rmax is the maximum surface roughness measured The issue of foundation-rock sliding was not investigated along a distance L equal to the mean grain size of the soil as the state of practice suggested common use of keys and particle D50. dowels and therefore the subject is more related in design Three zones of Rn associated with the interfacial shear mech- to rock or concrete controlled strength. The issue of footings anism reflecting different shear strength levels were identified resting on granular soil is mostly confined to the possibili- and presented (see Figure 82): Zone I for a "smooth" inter- ties of prefabricated versus cast-in-place foundations on soil. face, Zone II for an "intermediate" interface roughness and A general discussion of the soil-structure interfacial friction Zone III for a "rough" interface, respectively. In Zone I, shear is presented. The uncertainties in the interfacial friction angle failure occurs by sliding particles along the soil-solid body of solid-structure interfaces of various "roughness" subjected to inclined loads have been evaluated based on three sources of data: Results of research using a dual interface apparatus to estab- Rmax lish mechanisms and provide a framework (Paikowsky et al., 1995), Results of tests on foundations cast on soil (Horn, 1970), and Results of tests on precast foundations (Vollpracht and particle Weiss, 1975). Additional sources are used to examine the data listed above including friction limits under inclined loads. A practical Figure 81. Solid surface topography summary and appropriate resistance factors are further dis- representation through normalized cussed and presented in Chapter 4. roughness.

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93 Roughness Angle - 5 10 15 30 45 60 90 45 ZONE I ZONE II ZONE III 40 "SMOOTH" "INTERMEDIATE" "ROUGH" 35 30 center ds center 25 20 15 4mm glass beads 10 1mm glass beads #1922 glass beads (washed 5 and sorted) #2429 glass beads (washed) 0 -4 -3 -2 -1 0 1 10 10 10 10 10 10 Normalized Roughness (Rn = Rmax/D50) Figure 82. Interfacial characterization according to zones identified through the relations existing between average unrestricted interfacial friction angles (measured along the central section) of glass beads and normalized roughness (Paikowsky et al., 1995). interface for all granular materials, while in Zone III shear of the friction coefficients, tan(center)/tan(f), were obtained as failure occurs within the granular mass, mobilizing its full shear 0.171 for Zone I, 0.890 for Zone III, and therefore 0.171 to 0.890 strength. In Zone II, the interaction between the solid surface (increasing with Rn) for Zone II. and the soil allows only partial mobilization of the soil's shear strength, depending on normalized roughness and several 3.9.2.3 DIA Results versus MDS Results other factors, primarily the granular material particle shape. The data in Figure 82 relate to tests with glass beads varying Figure 83 presents the relationship between the unrestricted in size from fine to coarse (related to sand) and uniform grain friction angles (center) to friction angles measured using a direct shape (round). The use of natural sand sheared along an inter- shear box modified for interfacial testing with a solid surface face results in the same three-zone characterization, differenti- of the same roughness (MDS). The observations of the results ated only by the absolute magnitude of the friction angles. obtained from the DIA and the MDS tests indicate that if the shearing mechanism takes place along the soil-solid surface interface, the test results are markedly influenced by the resist- 3.9.2.2 Experimental Results Using DIA ing stresses developing on the boundary walls of the direct shear Soil-solid body interfaces with different normalized rough- box (for detailed measurements on the boundary walls, see ness and round particles have been tested. The interface friction Paikowsky and Hajduk, 1997; Paikowsky et al., 1996). The angles along the unrestricted zone at the center of the solid shearing resistances measured over the center interfacial area surfaces, center, were obtained as follows, expressed as the in the DIA tests, which is related to center, represent unrestricted mean (1 standard deviation): friction conditions since this location is not within the bound- aries' zone of influence in the shear box. Paikowsky et al. (1995) Zone I--Smooth interface (14 test results): 6.0 (0.8) found that the ratios of MDS to center for sand and glass beads Zone II--Intermediate interface roughness: center increases in different zones of interface roughness are the following: from about 8 to 25 with an increase in the logarithm of the normalized roughness (Rn) Zone I--1.50, Zone III--Rough interface (6 test results): 28.7 (1.3) Zone II--1.20, and Zone III--1.10. The friction angle of the granular materials used in the experiments was established to be residual f = 31.6 (1.0) These results clearly indicate the inadequacy of the small- from the direct shear tests of 17 samples. As a result, the ratio size direct shear box for interfacial friction measurements and

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94 - Roughness Angle 5 10 15 30 45 60 90 2.50 SMOOTH INTERMEDIATE ROUGH 2.25 (Rn 0.02) (0.02 < Rn < 0.5) (Rn 0.5) 2.00 4mm glass beads 1.75 1mm glass beads MDS Ottawa Sand 1.50 center #1922 glass beads (w/s) 1.25 #2429 glass beads (w) 1.00 0.75 0.50 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 Rn,ave - Average Normalized Roughness Figure 83. The ratio of modified direct shear box to unrestricted (central section) interfacial friction angles versus average normalized roughness (Paikowsky et al., 1995). the need to be aware of the biased measurements. For the porosity of 0.22, and material friction angle f = 33.5 obtained smooth and intermediate zones of normalized roughness, a from direct shear tests. Figure 84 presents the ratio of the significant bias exists when applying direct shear test results, interface friction coefficient (tan s) and the soil's internal namely 0.67 (Zone I) and 0.83 (Zone II). The ranges of the friction coefficient (tan f) as a function of the applied nor- interface friction angles based on center are presented in Table 43, mal stress on the foundation. Both friction angle values were along with the corresponding friction coefficient ratios obtained corrected by Horn, applying the so-called energy correction from the DIA tests. The ratio of MDS to center is represented by proposed by Hvorslev (1937) as reported in Schofield and the multiplier m. The bias of the typical measured (by a direct Wroth (1968).The mean and COV of the friction coefficient shear box) interfacial friction angle (MDS) is 1/m. The values ratio, tan(center)/tan(f), of the 44 tests were found to be 0.99 of m are used to obtain the converted friction coefficient ratios, and 0.091, respectively. The mean of the friction coefficient tan /tan , resulting in 0.25 for Zone I, 1.00 for Zone III, and ratio and the corresponding range of interface friction angles increasing from 0.25 to 1.00 for Zone II. of 33.3 3.5 correspond to those for Zone III (rough interface) in Table 43. 3.9.3 Experimental Results of Footings Cast in Place (Horn, 1970) 3.9.4 Uncertainties in the Interface Friction Coefficient Ratio Horn (1970) presented experimental results of sliding resist- ance tests for 44 concrete footings of 3.3 ft 3.3 ft 1.6 ft (H) The uncertainties in the interface friction coefficient ratio (1 m 1 m 0.5 m [H]) cast in place on sandy-gravel fill. (tan s /tan f) are directly related to the uncertainties in the The soil contained 15% gravel with stones greater than 2.5 in. interface friction and the soil friction angles. If the uncertainties (63 mm) and maximum stone size (dmax) of 7.9 in. (200 mm), in these angles are known, the statistics of the friction coefficient Table 43. Ranges of soil-solid body interface friction angles for different interface roughness zones, based on DIA tests (based on Paikowsky et al., 1995). Friction coefficient Multiplier m MDS Converted friction Roughness zone center ratio from DIA (= MDS/ center) (= center m) coefficient ratio Zone I 6.0 0.8 0.17 1.50 9.0 0.25 Zone II 8.0 to 25.0 0.17 to 0.90 1.20 9.5 to 30.0 0.25 to 1.00 Zone III 28.7 0.90 1.10 31.5 1.00 Note: Material friction angle obtained from direct shear test = 31.6 (1.0)

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95 ksf Table 44. Variations in the estimated 0 5 10 15 20 25 1.4 soil friction angle (f ). 1.2 f for Granular soils Obtained D'Appolonia & University tan s, corrected / tan f, corrected f Used for study 1.0 from of Michigan, 20041 Bias COV Bias COV 0.8 SPT 1.00 to 1.20 0.15 to 0.20 1.00 0.20 CPT 1.00 to 1.15 0.10 to 0.15 1.00 0.15 0.6 Lab test 1.00 to 1.13 0.05 to 0.10 1.00 0.10 1 0.4 Unpublished material based on Phoon et al., 1995. Horn (1970) 44 Tests 0.2 mean = 0.99 s.d. = 0.091 0.0 Table 44 presents the uncertainties in the estimation of 0 200 400 600 800 1000 1200 Normal Stress n (kN/m ) 2 the soil friction angle (based on Phoon et al., 1995; NCHRP Project 12-55, 2004). Hence, for a given soil friction angle, Figure 84. Ratio of measured friction coefficients say 31.6, obtained from correlations to SPT N counts, the of cast-in-place footings (rough base) to the soil's standard deviation is 6.32. Using Equation 112, the COV of internal friction coefficient versus applied normal the friction coefficient ratio is 0.444 for Zone I and 0.201 for stress (Horn, 1970). Zone III. The friction coefficient ratio uncertainties in Zones I and III are presented in Table 45 for material friction angles obtained from various tests. ratio can be computed as follows. If the distributions followed Comparing the results for Zone III (rough interface) in by both friction angles are normal, the corresponding friction Table 45 with the experimental results by Horn (1970), it coefficients and, thereby, the friction coefficient ratio, also can be seen that the COV of the friction coefficient ratio in follow normal distributions. For simplicity in notation, let Table 45 corresponds to that obtained by Horn for Zone III the interface and material friction coefficients be X1 and X2, and f from lab tests. It can thus be concluded that for respectively. a rough foundation base (e.g., resulting from a direct Hence, for mean mXi and standard deviation Xi, pour on the soil), the interface roughness in Zone III is rel- evant and, further, that the uncertainties in the sliding X1 ) X1 N ( m X 1 , 2 friction coefficient ratio (tan s /tan f) directly correspond X2 ) X 2 N (m X 2 , 2 to those existing in the method by which the soil friction angle is being defined (i.e., lab test, SPT, and so forth). If the friction coefficient ratio is g, then Based on these observations, the uncertainties in the inter- face friction coefficient ratio to be used for calibration g = X1 X 2 ln ( g ) = ln ( X1 ) - ln ( X 2 ) purposes can be recommended as presented in Table 46, i.e., mln( g ) = mln( X1 ) - mln( X 2 ) , and 2 ln( g ) = ln( X1 ) + ln( X 2 ) 2 2 Table 45. Uncertainties in friction where the mean and the variance of ln(Xi) are given by coefficient ratio obtained using Equation 112, based on data in mln( Xi ) = ln (mXi ) - 0.5 2 ln( Xi ) Tables 43 and 44. Friction coefficient ratio 2 X 2 ln( Xi ) = ln 1 + 2 i (tan s/tan f) mXi f Obtained Zone I Zone III (Smooth) (Rough) from tan s/tan f = tan s/tan f = Then the mean and variance of g, mg and 2 g are given by 0.25 1.00 COV COV mg = exp mln( g ) + 0.5 2 ( ln( g ) ) SPT CPT 0.444 0.374 0.201 0.158 (112) 2 g = m ( exp ( ( ) ) - 1) g 2 ln g Lab test 0.312 0.109

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96 Table 46. Uncertainties in interface friction where the bias of the friction coefficient ratio estimation is coefficient ratio according to interface roughness assumed to be that of the direct shear test interfacial testing and the determination of the soil friction angle. (bias = 1/m) and that of Table 44 for the estimation of f (bias = 1.0). Friction coefficient ratio (tan s/tan f) The interpretation of smooth, intermediate, and rough f Obtained Smooth Intermediate Rough from interfaces has been illustrated in Table 47, based on friction Bias = 0.67 Bias = 0.83 Bias = 0.91 angles provided by the NAVFAC (1986) for different dis- COV COV COV SPT 0.45 0.45 to 0.20 0.20 similar materials used in geotechnical construction. The CPT 0.38 0.38 to 0.15 0.15 COV to be used depends on the range of roughness (as defined Lab test 0.31 0.31 to 0.10 0.10 in Table 47). The resistance factors associated with the un- certainties discussed above and a rationale for their use is discussed in Chapter 4. Table 47. Friction coefficients (NAVFAC, 1986b) and interface roughness of dissimilar materials. Friction Interface Materials tan s (degrees) Interface roughness Clean sound rock 0.70 35 Rough Clean gravel, gravel-sand 0.55 to 0.60 29 to 31 Intermediate-Rough mixtures, coarse sand Clean fine to medium sand, silty medium to coarse sand, silty or 0.45 to 0.55 24 to 29 Intermediate-Rough clayey gravel Mass concrete on the Clean fine sand, silty or clayey 0.35 to 0.45 19 to 24 Intermediate following foundation fine to medium sand materials: Fine sandy silt, nonplastic silt 0.30 to 0.35 17 to 19 Intermediate Very stiff and hard residual or 0.40 to 0.50 22 to 26 Intermediate-Rough preconsolidated clay Medium stiff and stiff clay and silty clay (Masonry on 0.30 to 0.35 17 to 19 Intermediate foundation materials has same friction factors.) Clean gravel, gravel-sand mixtures, well-graded rock fill 0.40 22 Intermediate with spalls Steel sheet piles against the following Clean sand, silty sand-gravel 0.30 17 Intermediate soils: mixture, single size hard rock fill Silty sand, gravel or sand mixed 0.25 14 Intermediate-Smooth with silt or clay Fine sandy silt, nonplastic silt 0.20 11 Intermediate-Smooth Clean gravel, gravel-sand mixture, well-graded rock fill 0.40 to 0.50 22 to 26 Intermediate-Rough Formed concrete or with spalls concrete sheet piling Clean sand, silty sand-gravel 0.30 to 0.40 17 to 22 Intermediate against the following mixture, single size hard rock fill soils: Silty sand, gravel or sand mixed 0.30 17 Intermediate with silt or clay Fine sandy silt, nonplastic silt 0.25 14 Intermediate Dressed soft rock on dressed 0.70 35 Rough Masonry on soft rock masonry, Dressed hard igneous and rock on dressed 0.65 33 Rough Various structural metamorphic soft rock materials: rocks: Dressed hard rock on dressed 0.55 29 Intermediate-Rough hard rock Masonry on wood (cross grain) 0.50 26 Intermediate-Rough Steel on steel at sheet pile 0.30 17 Intermediate interlocks

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97 3.9.5 Experimental Results of Precast Table 48. Uncertainties in interface friction Footings (Vollpracht and Weiss, 1975) coefficients of foundations on granular soils according to the foundation's construction Vollpracht and Weiss (1975) presented experimental results method and the determination of the soil of sliding resistance tests for 10 precast concrete footings of friction angle. 1.6 ft 6.6 ft 2.6 ft (H) (0.5 m 2.0 m 0.8 m [H]) on sandy gravel fill. The soil interfacial friction angle was 39, void ratio Friction coefficient ratio (tan s/tan f) e was 0.395, and relative density was 61%. The mean soil- f Obtained Cast in place Prefabricated foundation interface friction angle of the 10 tests was found from Bias = 0.91 Bias = 0.53 to be 23.2 (4.08). Figure 85 presents the ratio of the inter- COV COV face friction coefficient (tan s) and the soil's internal friction SPT 0.20 0.34 coefficient (tan f) as a function of the applied normal stress CPT 0.15 0.30 on the foundation. The mean of the 10 tests was found to be Lab test 0.10 0.26 0.530.102 ( 1 standard deviation). This range clearly iden- tified the precast concretesand interfacial shear as having the intermediate roughness of Zone II. The scatter of the data can be attributed to the different ratios of horizontal to vertical were analyzed in Sections 3.6 and 3.7 for bearing capacity loads, as will be further discussed below. purposes, and some tests are re-evaluated here for interfacial friction purposes. 3.9.6 Summary of Relevant Results Tests were carried out by Foik (1984) on foundations under inclined loads ranging in size from 2.9 in. 5.4 in. (7.4 cm Table 48 summarizes the uncertainties in interface 13.7 cm) to 46 in. 26 in. (117 cm 65 cm). The foundations' friction coefficient ratios according to type of foundation construction--cast-in-place or precast concrete--utilizing base had a rough contact surface made of glued coarse sand or the aforementioned data. fine gravel. Figure 86 presents the relationship between the soil's unit weight and the internal friction angle. Figure 87 presents the relationship between the soil's unit weight and the measured 3.9.7 Examination of Load Inclination friction coefficient ratios of the footings. Figure 88 presents the and Other Factors Influencing relationship between the load inclination (expressed as inter- Footings Interfacial Friction facial friction coefficient, tan s) and the internal friction angle Different tests were carried out to examine the bearing coefficient (expressed as internal friction coefficient, tan f), capacity of foundations under inclined loading. These tests and Figure 89 presents the relationship between the load ksf 0 1 2 3 4 5 lb/ft3 0.8 106 107 108 109 110 48.0 0.7 0.6 Internal Friction Angle f(o) 44.0 tan s / tan f 0.5 0.4 40.0 0.3 0.2 Vollpracht and Weiss (1975) 10 Tests Foik (1984) mean = 0.53 36.0 75 data points 0.1 s.d. = 0.102 f = 5.083 d - 42.900 2 R = 0.997 0.0 0 50 100 150 200 250 32.0 Normal Stress n (kN/m2) 16.6 16.8 17.0 17.2 17.4 Unit Weight of Soil d (kN/m3) Figure 85. Ratio of measured friction coefficients of precast footings to the soil's internal friction Figure 86. Relationship of soil unit weight and coefficient versus applied normal stress the internal friction angle used by Foik (1984) (Vollpracht and Weiss, 1975). in test results interpretation.

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98 tan phi tan delta (a/b = 12cm/8.6cm) tan delta (a/b = 12cm/8.3cm) tan delta (a/b = 8.3cm/12cm) tan delta (a/b = 13.7cm/7.4cm) tan delta (a/b = 7.4cm/13.7cm) tan delta (a/b = 9cm/16.4cm) tan delta (a/b = 20cm/5cm) tan delta (a/b = 26.5cm/6.5cm) tan delta (a/b = 5cm/20cm) tan delta (a/b = 63cm/35cm) tan delta (a/b = 50cm/150cm) tan delta (a/b = 117cm/65cm) 1.20 1.00 0.80 tan s/ tan f 0.60 0.40 0.20 0.00 16.6 16.7 16.8 16.9 17 17.1 17.2 17.3 17.4 Unit Weight of Soil d [kN/m3] Figure 87. Ratio of measured footing friction coefficient ratios to the soil's internal friction coefficient versus soil unit weight (Foik, 1984). 1.0 psi Foik (1984) 75 data points 0 10 20 30 40 50 60 70 99.6 area (cm ) 169 2 1.0 2205 area (cm2) 7605 0.8 Foik (1984) 75 data points Load Inclination (tan s) Trendline for Large Foundations 99.6 area (cm2) 169 0.8 Load Inclination (tan s) 2205 area (cm2) 7605 0.6 Trendline for Large Foundations 0.6 0.4 0.4 0.2 0.2 0.0 0.88 0.90 0.92 0.94 0.96 0.98 1.00 0.0 Internal Friction Angle Coefficient (tan f) 0 100 200 300 400 500 Figure 88. Load inclination (tan s ) versus Vertical Applied Stress at time of Failure (kPa) the internal friction angle coefficient (tan f ) Figure 89. Load inclination (tan s ) versus vertical (Foik, 1984). applied stress at the time of failure (VB /a b) (Foik, 1984).

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99 inclination (tan s) and the vertical applied stress at the time and the vertical applied stress (respectively) suggest that the of failure (VB/a b). scatter in the data is significantly smaller for the larger foot- The data in Figures 86 to 89 suggest the following: ing sizes. This may be explained by the physical difficulties of applying loads and conducting tests on small footings. 1. Large variation exists in the ratio of the foundation's friction 3. The interface friction coefficient (equal to the load inclina- coefficient to the soil's internal friction coefficient. The data tion at failure) is clearly affected by the size of the vertical in Figure 87 do not indicate on a clear factor that controls load, as shown in Figure 89. The sliding of the footing under this variation, but in all cases tan s < tan f. small vertical loads is eliminated and large loads can be 2. Figures 88 and 89, which show the interface friction coeffi- applied, which, again, seems to be associated with the phys- cient as a function of the soil's internal friction coefficient ical limitations of conducting tests.