This paper investigates a method of analysis for the scale effect on shear strength of sands \– a fundamental problem of considerable importance to soil mechanics. The phenomena of scale effect for direct shear box tests and footing bearing capacity tests are briefly described and the available analytical methods are discussed. First, the couple-stress theory is reviewed and its extension to a Drucker\–Prager type is illustrated. Subsequently, material constants are discussed. Attention is then focused on the\ internal length\ of sand, which is shown to be the key parameter for scale effect for granular soil. Then, the predicted results are compared with experimental results on two sands. The main observations of the comparison for the scale effect are sketched and its limitations are discussed.

}, keywords = {bearing capacity, couple stress, direct shear, granular material, scale effect, shear strength}, doi = {10.1080/10298436.2010.488736}, author = {Chang, Ching S. and Cerato, Amy B. and Lutenegger, Alan J.} } @article {11567, title = {Scale effects of shallow foundation bearing capacity on granular material}, journal = {Journal of Geotechnical and Geoenvironmental Engineering, ASCE}, volume = {133}, year = {2007}, month = {10/2007}, pages = {1192-1202}, chapter = {1192}, abstract = {Scale effects of shallow foundation bearing capacity on granular materials were investigated to further evaluate the trend of decreasing bearing capacity factor,\ \ N\γN\γ\ , with increasing footing width,\ \ BB\ , observed by other researchers. Model-scale square and circular footing tests ranging in width from 0.025 to\ \ 0.914m0.914m\ were performed on two compacted sands at three relative densities. Results of the model-scale footing tests show that the bearing capacity factor,\ \ N\γN\γ\ , is dependent on the absolute width of the footing for both square and circular footings. Although this phenomenon is well known, the current study used a large range of footing sizes tested on well-graded sands to show that the previously reported modifications to the bearing capacity factor,\ \ N\γN\γ\ , using grain-size and reference footing width do not sufficiently account for the scale effect seen in the test results from this study. It also shows that behavior of most model-scale footing tests cannot be directly correlated to the behavior of full-scale tests because of differences in mean stresses experienced beneath footings of varying sizes. The relationship of the initial testing conditions (i.e., void ratio) of the sand beds and mean stress experienced beneath the footing (correlated to footing size) to the critical state line controls footing behavior and, therefore, model-scale tests must be performed at a lower density than a corresponding prototype footing in order to correctly predict behavior. Small footings were shown to have low mean stresses but high\ \ N\γN\γ\ values, which indicates high operative friction angles and may be related to the curvature of the Mohr\–Coulomb failure envelope.

}, keywords = {bearing capacity, Granular materials, sand, Scale effects, Shallow foundations}, issn = {1090-0241}, doi = {10.1061/(ASCE)1090-0241(2007)133:10(1192)}, author = {Cerato, Amy B. and Lutenegger, Alan J.} } @article {11575, title = {Bearing capacity of square and circular footings on a finite layer of granular soil underlain by a rigid base}, journal = {Journal of Geotechnical and Geoenvironmental Engineering}, volume = {132}, year = {2006}, month = {11/2006}, pages = {1496-1501}, chapter = {1496}, abstract = {Traditional bearing capacity theories for the ultimate capacity of shallow foundations assume that the thickness of the bearing stratum is infinite. The presence of a hard layer within a certain depth below the foundation can significantly influence the unit load supported by the soil. Therefore the original bearing capacity equations should be modified to account for this condition in determining the ultimate bearing capacity. In order to evaluate this phenomenon further, model square and circular footing tests were performed on a bed of well-graded sand. Test beds were prepared at three different relative densities corresponding to loose, medium, and dense conditions:\ \ Dr=24Dr24\ , 57, and 87\%, using five different sand layer thicknesses,\ \ HH\ ;\ \ H/BHB\ values of 0.5, 1, 2, 3, and 4, where\ \ BB\ is the footing width. Results of the model scale footing tests show that the bearing capacity factor,\ \ N\γN\γ\ , should be modified up to\ \ H/B=3HB3\ , instead of\ \ H/B=1HB1\ , as previously suggested. The footing shape factor,\ \ s\γs\γ\ , should account for both shape and finite layering. This technical note gives a description of the test methods and material used and presents the test results in comparison to previous results.

}, keywords = {bearing capacity, Layered soils, sand, scale effect, Shape, Spread foundations}, issn = {1090-0241}, doi = {10.1061/(ASCE)1090-0241(2006)132:11(1496)}, author = {Cerato, Amy B. and Lutenegger, Alan J.} } @article {11573, title = {Specimen size and scale effects of direct shear box tests of sands}, journal = {Geotechnical Testing Journal}, volume = {29}, year = {2006}, month = {11/2006}, pages = {1-10}, chapter = {1}, abstract = {The direct shear test has survived over the past 50 years in geotechnical engineering applications because of its simplicity and repeatability. Many laboratories perform direct shear box tests on sands to determine the friction angle \φ\′, or shear strength of the sand for engineering design purposes. However, there are different size shear boxes in use today and the effect of the varying specimen size on the resulting friction angle used in foundation deign has never before been investigated thoroughly. Five sands with different properties were tested in three square shear boxes of varying sizes (60 mm, 101.6 mm, and 304.8 mm), each at three relative densities (dense, medium, and loose). Results of the direct shear tests show that the friction angle \φ\′ can be dependent on specimen size and that the influence of specimen size is also a function of sand type and relative density. The tests indicate that for well-graded, angular sands, \φ\′ decreases as box size increases and that the influence of box size is dependent on relative density. The paper provides a description of the test methods and presents the test results.

}, keywords = {Direct shear box, friction angle, Mohr-Coulomb, sand, Scale effects}, issn = {0149-6115}, doi = {10.1520/GTJ100312}, author = {Cerato, Amy B. and Lutenegger, Alan J.} }