3. Procesos de gramaticalización en las construcciones del tipo Si…es porque
3.1. La gramaticalización Concepto
Bottleneck conditions are common when evacuees have to exit from confined spaces. In a ship environment this could happen, for instance, in case of exiting of passengers from public spaces. As a result, investigating the capability of the mathematical model to properly reproduce crowd behaviour in such conditions is of practical importance if the evacuation simulation is to be used within a risk assessment framework. The IMO test case 4, discussed before, addresses a bottleneck condition, but it only provides an indication of a maximum expected flow (1.33 p/s with a 1 m wide exit, corresponding to a specific flow of 1.33 p/s/m). To further address this situation, reference is made in this section to the experimental data presented by Liao et al. [124], who report results from controlled laboratory experiments which was carried out in Düsseldorf in 2009 to investigate pedestrian behaviour through wide bottlenecks.
The geometry of the experiment from Liao et al. [124] is reported in Figure 4.34 taking also into account additional specifications reported by Liao et al. [124].. For consistency with the data analysis by Liao et al. [124], in this section the flow is defined as the number of agents initially the room (N ), divided by the total exit time (A T ), i.e. the E
total time to empty the room.
A first series of simulations have therefore been carried out with the developed tool to compare results with available experimental data. According to information from
Liao et al. [124], the agents’ unimpeded speed has been considered to be uniformly
distributed in the interval 1.55 0.± 18 m/s. For each condition, a total of 50 Monte Carlo realizations have been run. Results from these simulations are shown in Figure 4.35, both in terms of percentiles (5%, 25%, 50%, 75% and 95%) and also as scatter data. From the reported data, it is evident that the flow increases as the width of the exit increases, and it can be seen that the flow predicted by the UNITS software tends to be smaller than the experimentally measured one.
Figure 4.35: Bottle neck experiment by Liao et al. [124]. Flow (NA/TE) as a function of the width of
the bottle neck br, as obtained from 50 realizations for each test case using UNITS code with default parameters. The flow obtained by Liao et al. [124] is also reported for comparison.
An underestimation of the experimental flow was also found by Liao et al. [124] when trying to validate FDS+Evac on the same experimental data from Liao et al. [124]. More specifically, Liao et al. [124] observed that the experimental evacuees speed was overestimated by the simulations and, conversely, the density in the experiments was underestimated by the simulations.
Figure 4.36 shows the density inside the region reported in Figure 4.34 for all test cases, as obtained from UNITS code. Results from Liao et al. [124] are reported for comparison. The model seems incapable of reproducing the high density peaks reported
experiments could also be a consequence of the fact that participants to the experiments were mostly young students, and it is therefore possible to imagine that, during the tests, there could have been a reduced tendency of maintaining sufficient distance between people and avoiding contacts.
Figure 4.36: Bottle neck experiment by Liao et al. [124]. Instantaneous density as function of time, from 50 realizations using UNITS code with default parameters. Experimental data from
Liao et al. [124] are reported for comparison.
In order to try to get a better matching with experimental flow, Liao et al. [124]
modified the anisotropy parameter of the social force model λa. The resulting flow
actually increased and better matched experimental results. However, it was observed that decreasing the anisotropy of the social-force model has the effect of increasing the force that an agent behind exerts on agent in front, and this leads to a tendency towards a sharp increase of the speed inside the bottleneck which was already overestimated by the default choice of parameter of the model. This effect could be reproduced also by the model developed herein. Figure 4.37, in particular, reports the average speed in area 2 considering the condition with bottleneck with of 3.6 m. The speed is reported for three cases with different parameter choices: the default choice of parameters (λa =0.3,
a w 2000 N
A = A = ), the case with modified anisotropy (λa =0.5and default values for all the other parameters), and the case with modified repulsive force intensity parameter (Aa =Aw =1000 Nand default values for all the other parameters). It is observed that while the modification of the anisotropy parameter causes an evident increase of the
average speed inside the area, the modification of the parameter Aa =Aw allows
maintaining the speed almost equal with respect to the situation of default parameter choice (see Figure 4.37).
Figure 4.37: Bottle neck experiment by Liao et al. [124]. Effect of modification of the anisotropy parameter λ and of the parameters a A A of the UNITS model on the average speed inside a, w
Average speed inside area 2 for br =3.6m.
Driven by these indications and considerations, it has therefore been decided to run another set of simulations with the intention of promoting an increase of density in the crowd without increasing the speed. To this end, agent-agent and wall-agent interaction forces parameters A and a A have been halved compared to default values (w
a w 1000 N
A =A = ).
Simulation results obtained with such modified parameters are reported in Figure 4.38, which are to be compared with those based on default parameters and reported in Figure 4.35.
It can be noticed from Figure 4.38 that the modification (reduction) of the interaction forces, which allows achieving higher densities, significantly improves the matching between simulations and experiments. It is also worth noticing that a reduction in the agent-agent interaction force was also used by Heliövaara et al. [76], combined with a decrease in the relaxation factor f
i
τ of the motive force and an increase in the fluctuation of the random forces, in order to model agents which are considered to be
Figure 4.38: Bottle neck experiment by Liao et al. [124]. Flow (NA/TE) as a function of the width of the bottle neck br, as obtained from 50 realizations for each test case using UNITS code with
modified parameters. The flow obtained by Liao et al. [124] is also reported for comparison.
A recent study by Liao et al. [125] suggests a similar modification of the parameters related to the repulsive forces. However, in results reported by Liao et al. [125] the spatiotemporal profile of density shows that the density in area 1 is quite low whereas a strange high density value is found in correspondence of the edges of the bottleneck. This unrealistic behaviour was observed by the authors and justified by an inappropriate agent routing algorithm used in the work. The agent routing algorithm, which, in the present model, is governed by the waypoint logic, is however fundamental in a bottleneck condition and the erroneous increase of density in correspondence to the edges of the bottleneck show that the model presented by Liao et al. [125], although allowing a reasonable flow rate, does not assure, globally, a realistic behaviour.
Driven by those observation an analysis related to the density in area 1 was carried out also in the condition of modified parameters A and a A , and it is reported in Figure w
4.39 (to be compared with Figure 4.36). The density obtained following the modification of parameters is closer to the experimental density, although the median is still below the measured experimental data.
Figure 4.39: Bottle neck experiment by Liao et al. [124]. Instantaneous density as function of time, from 50 realizations using UNITS code with default parameters. Experimental data from
Liao et al. [124] are reported for comparison.
According to the obtained results, the developed model looks like being capable of correctly simulating the exit from a bottleneck. However, the parameters of the model may need to be calibrated / modified in relation to the analysed population and to the test condition.
It is also interesting to observe that the specific flow resulting from the experiments from Liao et al. [124] is significantly higher than the reference value in the IMO test case 4. For example, the measured flow for =2.4 mbr (the smallest width) is about
5.8 p/s corresponding to a specific flow of 2.4 p/s/m, which is 80% larger than the value 1.33 p/s/m which would correspond to the upper acceptable limit of flow indicated in the IMO test case 4. Reference parameters of UNITS model have been based taking into significant account requirements set by IMO Test cases. However, results of the comparison shown in this section, combined with the observed discrepancy between the IMO limit flow rate and the trend obtained by Liao et al. [124], indicate that further modelling improvements and, possibly, further experimental efforts would be worth being pursued.