The mechanism of hindering occupants’ evacuation from seismic responses of building

Abstract

Pedestrian evacuation from buildings during an earthquake needs to consider human behavior and building shaking. This study sets up an indoor evacuation model based on the social force and dynamic mechanics. First, social forces were formulated in the Eulerian coordinate system, seismic force that excites on pedestrians in a multi-story building is derived from structural acceleration, and an evacuation criterion is given based on above forces. Second, a simulation was performed through VB programming, which accounts for the situation that people evacuate from a walkway. Parameters of the social force model are modified in order to estimate pedestrians’ acceleration in concerned situation. Third, structural dynamic responses under a series of ground motion excitations with varying peak values are acquired through finite element analysis to determine pedestrians’ seismic forces. Then, pedestrians’ ability to escape safely is evaluated according to evacuation criterion. Results show that seismic force would increase when pedestrian located on higher floor or ground excitation is of more dramatic level. Additionally, the possibility of survival is likely minimized as long as seismic force is larger than social force. This proposed model is capable of describing the effects of environment on human behavior during earthquake evacuation.

Appendix A: Notations

Symbol	Measure	Vector/scalar	Description
$A_{i}$	N	Scalar	The constant parameter of repulsive force
$\alpha_{j}$	rad	Scalar	The angle from the $x$-axis to the direction of force
$a_{ix}$	m/s2	Vector	The acceleration of pedestrian $i$ along the $x$-axis
$a_{iy}$	m/s2	Vector	The acceleration of pedestrian $i$ along the $y$-axis
$B_{i}$	m	Scalar	Fall-off length of the repulsive force between two pedestrians
$B_{w}$	m	Scalar	Fall-off length of the repulsive force between pedestrian $i$ and obstacle $w$
$\beta$	rad	Scalar	The angle from the $x$-axis to the direction of force
$d_{ij}$	m	Scalar	The actual distance between the two pedestrians $i$ and $j$
$d_{iw}$	m	Scalar	The actual distance between pedestrians $i$ and obstacle $w$.
$d_{x}$	m	Vector	The displacement of pedestrian along $x$-axis
$d_{y}$	m	Vector	The displacement of pedestrian along $y$-axis
$e_{i}^{0} (t)$	–	Vector	The expected speed direction
$F_{bNx}$	N	Vector	Seismic force of the Nth floor along $x$-axis
$F_{bNy}$	N	Vector	Seismic force of the Nth floor along $y$-axis
$F_{pNeqx}$	N	Vector	the relative seismic force of pedestrian in the Nth floor along the $x$-axis
$F_{pNeqy}$	N	Vector	The relative seismic force of pedestrian in the Nth floor along the $y$-axis
$F_{pNx}$	N	Vector	The absolute seismic force of pedestrian in the Nth floor along the $x$-axis
$F_{pNy}$	N	Vector	The absolute seismic force of pedestrian in the Nth floor along the $y$-axis
$F_{px}$	N	Vector	The social force of pedestrian along the $x$-axis
$F_{py}$	N	Vector	The social force of pedestrian along the $y$-axis
$f_{eqi}$	N	Vector	Inertia force of pedestrian i
$f_{i}$	N	Vector	Drive-to-target force of pedestrian i
$f_{i,jn}$	N	Vector	The attractive force between pedestrian $i$ and pedestrian $j_{n}$
$f_{ix}$	N	Vector	The drive-to-target force of pedestrian $i$ along the $x$-axis
$f_{iy}$	N	Vector	The drive-to-target force of pedestrian $i$ along the $y$-axis
$\sum\limits_{j} {f_{i,j} }$	N	Vector	The attractive force between pedestrians
$\sum\limits_{w} {f_{i,w} }$	N	Vector	The repulsive force between pedestrian $i$ and obstacles
$\sum\limits_{w} {f_{i,wx} }$	N	Vector	The repulsive force between pedestrian $i$ and obstacles along the $x$-axis
$\sum\limits_{w} {f_{i,wy} }$	N	Vector	The repulsive force between pedestrian $i$ and obstacles along the $y$-axis
$g(d_{ij} - r_{ij} )$	m	Scalar	Heaviside’s step function for pushing force
k	N/m	Scalar	Elasticity coefficient of pedestrian
$K$	N/m2 s	Scalar	Coefficient of sliding friction
$m_{bN}$	kg	Scalar	The mass of the Nth floor
$m_{i}$	kg	Scalar	The mass of pedestrian $i$
$r_{i}$	m	Scalar	The radii of pedestrians $i$
$r_{ij}$	m	Scalar	Sum of pedestrian $i$ and $j$’s radii
$r_{j}$	m	Scalar	The radii of pedestrians $j$
$v_{i}^{0} (t)$	m/s	Vector	The expected speed of pedestrian $i$
$v_{ix}^{0} (t)$	m/s	Vector	The expected speeds of pedestrian $i$ along the $x$-axis
$v_{iy}^{0} (t)$	m/s	Vector	The expected speeds of pedestrian $i$ along the $y$-axis
$v_{ix}^{{}} (t)$	m/s	Vector	The walking speeds of pedestrian $i$ along the $x$-axis
$v_{iy}^{{}} (t)$	m/s	Vector	The walking speeds of pedestrian $i$ along the $y$-axis
$\ddot{x}_{g} (t)$	m/s2	Vector	The ground acceleration along the $x$-axis
$\ddot{x}_{bN} (t)$	m/s2	Vector	Acceleration response of the Nth floor along the $x$-axis
$\ddot{y}_{g} (t)$	m/s2	Vector	Acceleration ground excitation along $y$-axis
$\ddot{y}_{bN} (t)$	m/s2	Vector	Acceleration response of the Nth floor along the $y$-axis
$\tau_{i}$	s	Scalar	The acceleration time