Modulus of subgrade reaction that varies with magnitude of displacement of cohesionless soil
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ORIGINAL PAPER
Modulus of subgrade reaction that varies with magnitude of displacement of cohesionless soil Burhan Avci 1 & Ayhan Gurbuz 2 Received: 4 January 2017 / Accepted: 25 June 2018 # Saudi Society for Geosciences 2018
Abstract Modulus of subgrade reaction is one of the required design parameters in any structural analyses of shallow foundations. However, the constant values of modulus of subgrade reaction that are determined from either from literature studies or the results of plate load tests, regardless of magnitude of soil’s displacement under design loads, have been used in structural designs of foundations. In this study, the results of 43 published full-scale field plate load tests in cohesionles soils were gathered to expose any variation in the values of modulus of subgrade reaction as soil’s displacement increases. Extensive finite element (FE) analyses were carried out while the results of FE analyses were compared with actual measured results of field load tests. The results of analyses indicated that both the modulus of subgrade reaction decrease with increase in magnitude of displacement of soils and internal forces of a design of structural frame is higher with the values of modulus of subgrade reaction that are sensitive to soil’s displacement are implemented into analyses. Therefore, structural dimensions of any structure with the constant values of modulus of subgrade reaction would not be a precise engineering solution. Keywords Modulus of subgrade . Finite element method . Plate load test . Foundation . Displacement
Introduction Because of the complexity of soil behavior, any interaction problems between a foundation and subgrade soil have been modelled by a simpler system called subgrade model. One of the most common and simple models in this context is Winkler hypothesis (1867) that represents the soil medium as linearly elastic and closely spaced independent springs. This method also known as modulus of subgrade reaction would be calculated using Eq. (1). k¼
q s
* Ayhan Gurbuz [email protected] 1
Furgo Sial, 06690 Ankara, Turkey
2
Department of Civil Engineering, Gazi University, 06570 Ankara, Turkey
ð1Þ
where, modulus of subgrade reaction (k) is indicated with loads per unit area (q) and vertical deformation (s). Evaluation of the numerical values of k is one of the most complex and sophisticated problems in geotechnical engineering. In other words, this problem yields to inaccuracy in the results of Winkler model. The values of k depend on elastic characteristics of subgrade soil, geometry of foundation, and loading scheme. In the literature, there were numerous studies on k proposed out by Winkler (1867), Biot (1937), Terzaghi (1955), Vesic (1961), Meyerhof and Baike (1963), Selvadurai (1979), and Bowles (1996). The results of these researchers are given in Table 1. The constant values of k, regardless of magnitude of soil’s displacement under a foundation, have been recommended by researchers (Dörken and Dehne 1995; Terzaghi 1955; Zeevaert 1983; Baldouf 1988; Ersoy 199
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