LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures (2010) / Chapter Skim
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From page 3... ...
of the analysis methods; hence, the validity of their assumed effect on the economics of design is questionable. 1.2.2 Limit State Design Demand for more economical design and attempts to improve structural safety have resulted in the re-examination of the entire design process over the past 50 years.
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From 1994 to 2006, the AASHTO LRFD specifications applied to geotechnical engineering utilized the work performed by Barker et al.
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This principle for the strength limit state is expressed in the AASHTO LRFD Bridge Design Specifications (AASHTO, 1994, 1997, 2001, 2006, 2007, 2008) in the following way: R R Qr n i i i= ≥∑φ η γ ( )
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The margin of safety is taken as log R − log Q, when the resistances and load effects follow lognormal distributions. Thus, the limit state function becomes the following: u du− ⎡ ⎣⎢ ⎤ ⎦⎥2 2 exp .
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or standard mathematical tables related to the standard normal probability distribution function. It should be noted, however, that previous AASHTO LRFD calibrations and publications for geotechnical engineering, notably Barker et al.
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. FORM can be used to assess the reliability of a component with respect to specified limit states and provides a means for calculating partial safety factors φ and γi for resistance and loads, respectively, against a target reliability level, β.
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When the desired target reliability index, βT, is achieved, an acceptable set of load and resistance factors has been determined. One unique set of load and resistance factors does not exist; different sets of factors can achieve the same target reliability index (Kulicki et al., 2007)
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Since in the present geotechnical engineering LRFD only one resistance factor is used while keeping the load factors constant, a suitable choice for the resistance factor would shift the limit state function so that Nf T samples fall in the failure region. The resistance factor derived in this study using MCS is based on this concept.
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is provided as a background to the diverse approach of the current research. 1.4.2 Material and Resistance Factor Approach Some of the key issues in developing sound geotechnical design codes based on LSD and LRFD are definition of characteristic values and determination of partial factors together with the formats of design verification (Simpson and Driscoll, 1998; Orr, 2002; Honjo and Kusakabe, 2002; Kulhawy and Phoon, 2002)
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. 0 0.5 1 1.5 2 2.5 3 Ratio of Static Load Test Results over the Pile Capacity Prediction using the α-API/Nordlund/Thurman design method 0 2 4 6 8 10 12 14 16 18 20 22 N um be r o f P ile C as es 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 R el at iv e Fr eq u en cy log normal distribution mlnx = -0.293 σlnx = 0.494 normal distribution mx = 0.835 σx = 0.387 Figure 7.
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Reference: Static Pile Capacity and Resistance Factors for Pile Load Test Program, GTR report submitted to Haley and Aldrich, Inc.
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Reference: Static Pile Capacity and Resistance Factors for Pile Load Test Program, GTR report submitted to Haley and Aldrich, Inc.
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For a general case of centric vertical loading of a rigid strip footing (plain strain problem) on a cohesivefrictional soil surface with a uniform surcharge of q, the ultimate bearing capacity (qu)
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variation of the bias ( ) and uncertainty in the ratio between measured to calculated loads for shallow foundations on granular soils under displacements ranging from 0.25 to 3.00 in.
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Bearing capacity factor N versus friction angle (f ) according to different proposals.
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, and Vesic´ (1973, 1975) to give what is known as the General Bearing Capacity Equation: where si = shape factors, ii = load inclination factors, di = depth factors, and B′ = is the effective (i.e., functional)
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ratios under centric vertical loading and without embedment have been modeled and analyzed. Figures 14 and 15 present the numerical values of the aforementioned shape factors sγ and sq, respectively, versus the foundation width to length ratios, B/L.
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1.5.7 Load Inclination Factors An inclination in the applied load always results in a reduced bearing capacity, often of a considerable magnitude (Brinch Hansen, 1970)
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φf=37° Figure 14. Shape factor s proposed by different authors versus footing side ratio, B/L.
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p fK ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 28 30 32 34 36 38 40 42 44 Soil friction angle, φf (deg) 1 1.1 1.2 1.3 1.4 D ep th fa ct or , d q Brinch Hansen (1970)
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From page 23... ...
Load inclination factor iq versus load ratio, H/V, for c = 0, f = 35°, and any Df /B. 0 0.2 0.4 0.6 0.8 1 Load ratio, H/V 0 0.2 0.4 0.6 0.8 1 Lo ad in cl in at io n fa ct or , i γ Brinch Hansen (1970)
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In order to illustrate this problem, Figure 21a shows the bearing capacity limit state and sliding limit state of a shallow foundation under inclined loading as a function of vertical and horizontal loads. In this so-called interaction diagram, the sliding limit state is illustrated as a simple straight line with an inclination tan δS representing the soil foundation interfacial shear resistance accounting for the roughness of the footing's base.
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vertical load possible for certain applied horizontal load VG permanent vertical load VG additional permanent vertical load Vk characteristic vertical load Vd design value of vertical load Vmax bearing capacity under pure vertical loading, i.e., max. vertical load that can be carried by the system V/Vmax degree of utilization of maximum vertical load Figure 21.
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If arbitrary load paths are possible, only additional load components acting within the circles sketched in Figure 23 are admissible. Such a critical load situation is not artificial; it may occur if the wave height is higher than assumed for design, resulting in an increase of the horizontal load along with a decrease of the vertical load due to uplift forces.
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fictitious design loading (V unfavorable) bearing resistance Rv,k sliding resistance Rh,k safety: γR,v = Rv,k/Vd = 2.7 safety: γR,h = Rh,k/Hd = 2.0 Notes: H resultant horizontal load Hd design value of resultant horizontal load Rh,k characteristic value of sliding resistance Rv,k characteristic value of bearing resistance V resultant vertical load V γ γ d design value of resultant vertical load R,h available resistance factor for sliding R,v available resistance factor for bearing resistance safety: γR,v = Rv,k/Vd = 2.0 Figure 23.
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From page 28... ...
. With these input parameters, the failure condition of the general form is defined by the following expression: In Equation 61, all load components are referred to as F10, which is the resistance of a footing under pure vertical loading.
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( ) In the case of footings embedded in the soil, the failure condition according to Equation 61 needs to be extended if the shearing resistance in the embedment zone is taken into account: In Equation 63b, F1,min is the bearing capacity due to pure vertical tension loading resulting from the shearing resistance in the embedment zone, which may be carefully calculated using an earth pressure model.
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b b2/b3 side ratio F10 bearing capacity under pure vertical loading, i.e., maximum vertical load that can be carried by the system M3 bending moment Figure 26. Failure condition for inclined loading (left)
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The bearing capacity defined by the failure condition is qualitatively shown again in the interaction diagram of Figure 30. Each load combination to be checked marks a point in the interaction diagram.
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b b2/b3 side ratio Fk characteristic failure condition Fd design failure condition F1 vertical load F2 horizontal load M3 bending moment F10 bearing capacity under pure vertical loading, i.e., maximum vertical load that can be carried by the system kL characteristic load combination dL design load combination R resistance factor f angle of internal friction φ φ γ φ γ Figure 30. Illustration of the safety concept principle.
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1.7 Bearing Capacity of Shallow Foundations on Rock 1.7.1 Overview The bearing capacity of foundations founded on rock masses depends mostly on the ratio of joint spacing to foundation width, as well as intact and rock mass qualities like joint orientation, joint condition (open or closed) , rock type, and intact and mass rock strengths.
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sinkhole caused by soil erosion into solution cavities (Canadian Geotechnical Society, 2006)
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is equal to the major principal stress of Prism I (σ1-I) such that the bearing capacity is the major principal stress of Prism I and is expressed in Equation 72: where c is cohesion, and φf is friction angle of the rock mass.
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. 1.7.4 The Canadian Foundation Engineering Manual The bearing capacity methods for foundations on rock proposed by the Canadian Foundation Engineering Manual (Canadian Geotechnical Society, 2006)
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may be up to ten times higher. For a more detailed explanation, the Canadian Foundation Engineering Manual (Canadian Geotechnical Society, 2006)
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. Examination of Figure 37 leads to the conclusion that the bearing capacity of a homogeneous, discontinuous rock mass cannot be less than the unconfined compressive strength of the rock mass around the footing, and this can be taken as the lower bound.
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suggested that the Hoek and Brown strength criterion for jointed rock masses (Hoek and Brown, 1980, see also Section 1.8.2.4) can be used in the evaluation of bearing capacity.
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bearing capacity is given by Equations 82a and 82b. The m and s constants are determined by the rock type and the conditions of the rock mass, and selecting an appropriate category is easier if either the Rock Mass Rating (RMR)
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have been successfully used in the past, and (4) are applicable to hard rock masses.
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Cummings et al., 1982 Mining Numerical F, Functional T Simplified Rock Mass Rating Brook and Dharmaratne, 1985 Mines and tunnels Numerical F, Functional T Modified RMR and MRMR Slope Mass Rating (SMR) Romana, 1985 Spain Slopes Numerical F, Functional T Ramamurthy/Arora Ramamurthy and Arora, 1993 India For intact and jointed rocks Numerical F, Functional T Modified Deere and Miller approach Geological Strength Index (GSI)
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1.8.2.3 Rock Mass Rating (RMR) In 1973, Bieniawski introduced RMR as a basis for geomechanics classification.
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to even multiples of 20 took place, and, in 1979, there was an adoption of the International Society for Rock Mechanics (ISRM) rock mass description.
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. The generalized Hoek-Brown failure criterion is defined as the following: where σ′1 and σ′3 = the principal effective stresses at failure; qu = the unconfined compressive strength of the intact rock pieces; mb = the value of the Hoek-Brown constant m for the rock mass, and mi = the Hoek-Brown constant for the intact rock (see Table 14)
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. D ec re as in g In te rl oc ki ng o f R oc k Pi ec es 10 20 30 40 50 60 70 80 Decreasing Surface Quality Geological Strength Index From the letter codes describing the structure and surface of the rock mass, select the appropriate box in this chart.
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From page 47... ...
The Hoek and Brown criteria can be used to evaluate the shear strength of fractured rock masses in which the shear strength is represented as a curved envelope that is a function of the unconfined compressive strength of the intact rock, qu, and two dimensionless constants, m and s. The values of m and s as defined in Table 19 should be used.
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From page 48... ...
. PARAMETER RANGES OF VALUES Point load strength index >175 ksf 85–175 ksf 45–85 ksf 20–45 ksf For this low range, unconfined co mp ressive test is preferred Strength of intact rock ma terial Unconfined co mp ressive strength >4,320 ksf 2,160– 4,320 ksf 1,080– 2,160 ksf 520– 1,080 ksf 215– 520 ksf 70–215 ksf 20–70 ksf 1 Relative Rating 15 12 7 4 2 1 0 Drill core quality RQD 90% to 100% 75% to 90% 50% to 75% 25% to 50% <25% 2 Relative Rating 20 17 13 8 3 Spacing of joints >10 ft 3–10 ft 1–3 ft 2 in–1 ft <2 in 3 Relative Rating 30 25 20 10 5 Condition of joints Very rough surfaces Not continuous No separation Hard joint wall rock Slightly rough surfaces Separation <0.05 in Hard joint wall rock Slightly rough surfaces Separation <0.05 in Soft joint wall rock Slicken- sided surfaces or Gouge <0.2 in thick or Joints open 0.05–0.2 in Continuous joints Soft gouge >0.2 in thick or Joints open >0.2 in Continuous joints 4 Relative Rating 25 20 12 6 0 Inflow per 30 ft tunnel length None <400 gal/hr 400–2,000 gal/hr >2,000 gal/hr Ratio = joint water pressure/ ma jor principal stress 0 0.0–0.2 0.2–0.5 >0.5 Ground water conditions (use one of the three evaluation criteria as appropriate to the me thod of exploration)
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, m, s = constants from Table 19, σ′n = effective normal stress (ksf) , and φ′i = the instantaneous friction angle of the rock mass (degrees)
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C = Arenaceous rocks with strong crystals and poorly developed crystal cleavage -- sandstone and quartzite D = Fine grained polyminerallic igneous crystalline rocks -- andesite, dolerite, diabase, and rhyolite E = Coarse-grained polyminerallic igneous and metamorphic crystalline rocks -- amphibolite, gabbro, gneiss, granite, norite, quartz-diorite Rock quality Constants A B C D E INTACT ROCK SAMPLES Laboratory size specim ens free from discontinuities. CSIR rating: RM R = 100 m s 7.00 1.00 10.00 1.00 15.00 1.00 17.00 1.00 25.00 1.00 VERY GOOD QUALITY ROCK MASS Tightly interlocking undisturbed rock with unweathered joints at 3–10 ft.
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Closed joints Open joints 100 1.00 0.60 70 0.70 0.10 50 0.15 0.10 20 0.05 0.05 Table 21. Summary of Poisson's Ratio for intact rock (AASHTO, 2008, Table C10.4.6.5-2, modified after Kulhawy, 1978)
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