Chapter 18: Groundwater and Seepage - Free

Groundwater and Seepage 18-23A′ B′ABC hD(b)g m ′RWatercolumnLMaterialArea, AScreen(c)g m ′Riγ wiγ w(a)FIGURE 18.23 Piping.isDividing by the volume AL, the resultant force per unit volume acting at a point within the flow regionR = g ¢ m– ig w(18.44)where i is the hydraulic gradient. The quantity i g w is the seepage force (force per unit volume). In general,Eq. (18.44) is a vector equation, with the seepage force acting in the direction of flow [Fig. 18.23(b)]. Ofcourse, for the flow condition shown in Fig. 18.23(a), the seepage force will be directed vertically upward[Fig. 18.23(c)].If the head h is increased, the resultant force R in Eq. (18.44) is seen to decrease. Evidently, should hbe increased to the point at which R = 0, the material would be at the point of being washed upward.Such a state is said to produce a quick (meaning alive) condition. From Eq. (18.44) it is evident that aquick condition is incipient ifgi m¢cr = ----- =g wG – 1------------1 + e(18.45)Substituting typical values of G = 2.65 (quartz sand) and e = 0.65 (for sand, 0.57 £ e £ 0.95), we seethat as an average value the critical gradient can be taken asi cr ª 1(18.46)When information is lacking as to the specific gravity and void ratio of the material, the critical gradientis generally taken as unity.At the critical gradient, there is no interparticle contact (R = 0); the medium possesses no intrinsicstrength, and will exhibit the properties of liquid of unit weightG+eg q = Ê------------ˆ gË1 + e ¯ l(18.47)Substituting the above values for G, e, and g l = g w , g q = 124.8 lb/ft 3 . Hence, contrary to popular belief,a person caught in quicksand would not be sucked down but would find it almost impossible to avoidfloating.© 2003 by CRC Press LLC