 
          1277
        
        
          Technical Committee 202 /
        
        
          
            Comité technique 202
          
        
        
          roadbeds, which can be explained by the limited distribution of
        
        
          stress applied by the footing with a width of 48 mm.
        
        
          Except for the cases in which
        
        
          
            H
          
        
        
          b
        
        
          = 80 mm, residual settling
        
        
          of the footing was attributed to total compression of crushed
        
        
          stones and roadbed materials. In general, stress concentration in
        
        
          roadbeds should be higher in the
        
        
          
            H
          
        
        
          b
        
        
          = 20 mm cases than those
        
        
          in the
        
        
          
            H
          
        
        
          b
        
        
          = 50 mm cases. Therefore, owing to the plastic
        
        
          deformation of roadbeds, the highest
        
        
          
        
        
          value was observed in
        
        
          Case 4, in which
        
        
          
            H
          
        
        
          b
        
        
          = 20 mm, as shown in Fig. 4.
        
        
          Figure 5. Distribution of maximum shear strain generated before tie-
        
        
          tamper implementation (Case 1)
        
        
          Figure 6. Distribution of maximum shear strain generated before tie-
        
        
          tamper implementation (Case 2)
        
        
          Case3-1
        
        
          Case3-2
        
        
          Case1-1
        
        
          Case3-3
        
        
          Case1-2
        
        
          Case1-3
        
        
          Figure 7. Distribution of maximum shear strain generated before tie-
        
        
          tamper implementation (Case 3)
        
        
          Conversely, the compression of crushed stones was higher in
        
        
          the
        
        
          
            H
          
        
        
          b
        
        
          = 50 mm cases than those in the
        
        
          
            H
          
        
        
          b
        
        
          = 20 mm cases. If
        
        
          nonlinear compression of roadbeds is relatively moderate, the
        
        
          deformation modulus of the roadbeds changes slightly through
        
        
          the change in stress levels. In this situation,
        
        
          
        
        
          can be higher in
        
        
          the
        
        
          
            H
          
        
        
          b
        
        
          = 50 mm cases compared to that when
        
        
          
            H
          
        
        
          b
        
        
          = 20 mm.
        
        
          
            3.2 Effects of tie-tamper implementation
          
        
        
          Case2-1
        
        
          Figure 8 shows typical relationships between footing settlement
        
        
          and applied stress, represented by convex curves, in Case 1-1
        
        
          when the 1
        
        
          st
        
        
          , 10
        
        
          th
        
        
          , and 100
        
        
          th
        
        
          cyclic loadings were applied before
        
        
          tie-tamper implementation. In this research, the curves were
        
        
          fitted by bilinear lines, and the slopes of the two lines were
        
        
          estimated as
        
        
          
            k
          
        
        
          1
        
        
          and
        
        
          
            k
          
        
        
          2
        
        
          . Displacement
        
        
          
            u
          
        
        
          2
        
        
          was estimated by
        
        
          dividing the applied stress by
        
        
          
            k
          
        
        
          2
        
        
          . The parameter
        
        
          
            u
          
        
        
          2
        
        
          decreased
        
        
          and tended to show a constant value in each case with an
        
        
          increase in the number of cyclic loadings (Fig. 9). Therefore,
        
        
          these constant values will be used in the following discussion.
        
        
          Case2-2
        
        
          Case2-3
        
        
          Figure 8. Relationships between footing settlement and applied
        
        
          stress in Case 1-1 before tie-tamper implementation