## 4 Water Table Correction Factor for Settlement Analysis of Footings on Granular Soils  
According to the literature, when the water table rises into the influence zone of footings, it reduces the soil stiffness, and thus additional settlement is induced. Several researchers attempted to quantify this phenomenon, suggesting a suitable water table correction factor, Cw [2; 32; 33; 34; 35; 36; 37; 38]; in these studies, \(C_{w}\) is related to the depth of the water table measured from the foundation level (this depth defines the unsaturated zone), the embedment depth of footing and the footing width. A critical review of these approaches is out of the scope of the present paper; besides, this has already been done by [PERSON] et al. [39]. Very recently, based on laboratory model tests in sands and numerical modeling, the same authors [40; 41] concluded to the following expression for \(C_{w}\):  
\[C_{w}=1+(C_{w,\max}-1)(A_{w}/A_{t})^{n}, \tag{11}\]  
where \(n\) and \(C_{w,max}\) are site-specific parameters depending on the relative density of sand and the shape of footing, whilst \(A_{w}\) and \(A_{t}\) are areas on the influence factor diagram corresponding to the \"submerged\" and total area, respectively (apparently up to the influence depth of footing). [PERSON] et al. [40] suggested that \(C_{w,max}\) be determined by model tests, measuring the additional settlement induced after inundating the entire sand; generally, the \(C_{w,max}\) is greater in loose sands. \(n\), also according to [PERSON] et al. [40], can be assumed as unity for all practical purposes, especially as a first estimate. [PERSON] [42] suggests that Equation (11) be simplified as follows:  
\[C_{w}=1+A_{w}/A_{t}. \tag{12}\]  
Adopting either Equation (11) or Equation (12), the strain influence factor charts presented herein can be used for determining the areas \(A_{w}\) and \(A_{t}\). The updated settlement value derives, finally, from the multiplication of \(\rho\) given by Equation (8) with \(C_{w}\).  
It is noted that this correction is not necessary if the soils' elastic modulus is taken from relations with the probing test data (e.g., CPT, SPT). However, if for any reason the water table were to rise into or above the zone of influence \(z_{l}\) after the penetration tests were conducted, this correction is necessary for the soil layers, being between the initial and new water table level (see also [2; 43; 44]).  
At this point, the author would like to mention that various researchers express the opinion that the degree of saturation has only a minor effect on the \(q_{c}\) value of the CPT test [45; 46; 47; 48; 49] and in turn, on the elastic modulus of soil and the settlement of footing. Other researchers (e.g., [50]) observed that \(q_{c}\) is influenced to a great extent by the water table depth (due to suction), so that \(q_{c}\) increases.  
Figure 10: (a) \(\rho_{R}\)_E/B_ values for rigid footings vs. \(\rho_{Chr}\)_E/\(q\)B_ values for the characteristic point of the respective flexible footings (chart drawn based on 210 different cases); (b) \(\rho\)_E/\(q\)B_ vs. \(\
u\) chart for \(L\)/B = 1 and \(H\)/B = 2 (the maximum \(\
u\) value for the rigid footing considered was 0.499).  
Figure 11: \(I_{z}\) versus normalized depth charts for various \(v\) values of soil ((**a–f**) for \(v=0\) to \(0.5\) with \(0.1\) interval), comparing the case of rigid circular footing with the respective flexible footing at the characteristic point.  
Figure 12: \(I_{z}\) versus normalized depth charts for various \(v\) values of soil ((**a–f**) for \(v=0\) to \(0.5\) with \(0.1\) interval), comparing the case of rigid strip footing with the respective flexible strip footing at the characteristic point.