“…Barkan (1962) is the first to use barriers as an in situ method to reduce the vibratory amplitudes of the driving source in the field. Lysmer and Waas (1972), Lysmer and Kuhlemeyer (1969), Dolling (1965), Neumeuer (1963), McNeill et al (1965, Woods (1968), Richart et al (1970) have studied the efficiency of a trench in the reduction of horizontal shear waves arising from a harmonic load. Some numerical studies have also been carried out to evaluate vibration-isolation performances of open or filled trenches (Aboudi, 1973;Ahmad and Al-Hussaini, 1991;AlHussaini andAhmad, 1991, 1996;May and Bolt, 1982;Fuyuki and Matsumoto, 1980;Dasgupta et al 1986Dasgupta et al , 1988Luong, 1994;Kattis et al, 1999a,b;El Naggar and Chehab, 2005;Ahmad and Al-Hussaini, 1991;Yeh et al, 1997).…”