  Fast interplanetary coronal mass ejections (interplanetary CMEs, or ICMEs)
are the drivers of strongest space weather storms such as solar energetic
particle events and geomagnetic storms. The connection between space weather
impacting solar wind disturbances associated with fast ICMEs at Earth and the
characteristics of causative energetic CMEs observed near the Sun is a key
question in the study of space weather storms as well as in the development of
practical space weather prediction. Such shock-driving fast ICMEs usually
expand at supersonic speed during the propagation, resulting in the continuous
accumulation of shocked sheath plasma ahead. In this paper, we propose the
"sheath-accumulating propagation" (SAP) model that describe the coevolution of
the interplanetary sheath and decelerating ICME ejecta by taking into account
the process of upstream solar wind plasma accumulation within the sheath
region. Based on the SAP model, we discussed (1) ICME deceleration
characteristics, (2) the fundamental condition for fast ICME at Earth, (3)
thickness of interplanetary sheath, (4) arrival time prediction and (5) the
super-intense geomagnetic storms associated with huge solar flares. We
quantitatively show that not only speed but also mass of the CME are crucial in
discussing the above five points. The similarities and differences among the
SAP model, the drag-based model and the`snow-plough' model proposed by
\citet{tappin2006} are also discussed.
