Pathfinder Verification and Validation

2.1.1. Background

"Transitions in pedestrian fundamental diagrams of straight corridors and T-junctions" (Zhang et al. 2011), "Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram" (Zhang et al. 2011) and "Empirical Characteristics of Different Types of Pedestrian Streams" (Zhang and Seyfried 2013) describe a series of experiments in which they measured the fundamental diagram by controlling density in a corridor by varying the entrance and exit widths (Figure 2).

You can download the actual experimental videos and supporting documentation from the Pedestrian Dynamics Data Archive.

This validation case will focus on the unidirectional flow results.

A summary of the experimental results for unidirectional and bidirectional flows is shown in Figure 3. The corresponding SFPE specification curves are shown in Figure 4. Compared to the SFPE calculations, the Zhang and Seyfried experiments have a higher occupant speed (measured free velocity of 1.55 ± 0.18 m/s) and a significantly higher measured specific flow (although the paper notes large specific flow variations for small changes in the experimental setup for densities greater than 2 pers/m2).

2.1.2. Setup Notes

The Pathfinder model is shown in Figure 5. This model is a subset of the experiments reported in "Transitions in pedestrian fundamental diagrams of straight corridors and T-junctions" (Zhang et al. 2011). The Pathfinder model uses a 3 m corridor. For six cases the entrance width varied from 2 m to 3 m with the exit width held constant at 3 m (these are low density cases) followed by 10 cases where the entrance width was held constant at 3 m and the exit width varied from 3 m to 1 m (high density cases). The red rectangles indicate the regions used to measure the speed-density results. To ensure steady-state results, 1000 people were used for each case.

The sixteen cases were repeated for three walking speed assumptions:

2.1.3. Results

Speed-density and specific flow-density results are presented for each of the three cases. In these curves, the data is presented over time intervals when "steady-state" conditions have been reached. The gray points represent all the calculated speed-density pairs for all corridors.

2.1.4. Analysis

The Pathfinder calculations replicate the input speed-density curve. The calculated points are slightly below the input curves, making the results slightly conservative. The specific flow calculations also match the expected results. The comparisons show that Pathfinder correctly uses the input speed-density curve in the calculations.

2.2.1. Background

In addition to unidirectional flow, Zhang and Seyfried (Zhang and Seyfried 2013) and Zhang, Klingsch, Schadschneider, and Seyfried (Zhang et al. 2011) describe experimental results for bidirectional flow. The experimental bidirectional results are summarized and compared to unidirectional results in Figure 3.

The experimental setup is shown in Figure 10. For a Balanced Flow Ratio (BFR) the left and right entrance widths were identical. A limited number of tests used an Unbalanced Flow Ratio (UFR) with different entrance widths. The measured fundamental diagrams were the same for balanced and unbalanced flow.

In addition, participants were either allowed to select to exit to their left or right or were assigned a direction. When the participants selected the exit direction, Stable Separated Lanes (SSL) formed, but when required to exit a given direction, lanes were unstable and varied in time and space (Figure 11) resulting in Dynamical Multi-Lanes (DML) flow.

Figure 12 and Figure 13 show the parameters for the experiments.

You can download the actual experimental videos and supporting documentation at this link, Pedestrian Dynamics Data Archive.

This validation case will focus on bidirectional flow results.

2.2.2. Setup Notes

Pathfinder models were used to simulate the experimental cases with a 3.6 m wide corridor. The BFR-SSL model is shown in Figure 14. The widths of the two entry doors are always identical to each other, but the door widths change to control the density. The red rectangles indicate the regions used to measure the speed-density results. The measured experimental entry flow rates were used to specify the source time histories and the Enforce Flow Rate option was used.

For all cases, the measured walking speed of 1.55 ± 0.18 m/s was used with a speed profile that corresponds to the unidirectional speed-density data shown in Figure 6. We did not modify the speed-density profile for different problems, but use the unidirectional speed-density data for all cases. The intent is that the movement algorithm should adjust for different situations.

In Figure 14, the measured experimental entry flow rates are used to specify the input flows in the model. This model shows the BFR-SSL experiments, a similar model was used for the BFR-DML cases.

2.2.3. Results for Balanced Flow Ratio (BFR) and participant selected exits Stable Separated Lanes (SSL)

Speed-density and specific flow-density results are presented in Figure 15. In these curves, the data is presented over time intervals when "steady-state" conditions have been reached. The gray points represent all the calculated speed-density pairs for all corridors.

Figure 16 and Figure 17 provide a comparison of experimentally observed and calculated occupant paths at 50 seconds, 1.6 m entry width, free choice of destination. As shown in Figure 11 (a) and Figure 16, in the experiment occupants separated into separate lanes and maintained that separation throughout the experiment. Occupants exited through only the corridor door on the side of their lane. In Pathfinder, lanes form, but they are dynamic and occupants exit on both corridor doors.

2.2.4. Results for Balanced Flow Ratio (BFR) and assigned exits Dynamical Multi-Lane (DML)

Speed-density and specific flow-density results are presented for each of the three walking speed cases (Figure 18). In these curves, the data is presented over time intervals when "steady-state" conditions have been reached. The gray points represent all the calculated speed-density pairs for all corridors, while the black points are the averaged values for each corridor.

Figure 19 and Figure 20 provide a comparison of experimental and Pathfinder results at 30 seconds, 1.6 m entry width, assigned destination.

2.2.5. Analysis

Pathfinder includes only a simple lane-forming algorithm, so it does not replicate the ordered paths shown in Figure 11. Instead, the occupants tend to cross paths more frequently. As a result, for a given speed the calculated speed-density relationship and specific flow fall below the experimental data. At high densities, both can be reduced by factors of two or more.

We can explore this further by looking at the times for all occupants to pass through the corridor. Table 1 shows the corridor residence times calculated by subtracting the time the first occupant enters the corridor from the time the last occupant exits the corridor. As can be seen, at low densities the Pathfinder results are similar to experimental results. However, at high densities the Pathfinder residence times increase significantly.

This may be considered a conservative, non-optimal result.

2.3.1. Background

A series of experiments were performed to measure the fundamental diagram for turning and merging of pedestrian streams in T-junction (Zhang et al. 2011) (Figure 21). The corridor width was 2.4 m and density was controlled by using different widths of the entrance (from 0.5 m to 2.4 m), which is 4 m away from the corridor. A summary of the results for unidirectional and bidirectional flows is shown in Figure 23.

The Zhang et al. experiments have an occupant speed of 1.55 ± 0.18 m/s. As can be seen, the fundamental diagrams in front of the T-junction are different that the behind the junction. The authors state "However, we cannot conclude whether the merging behavior itself or the congestions caused by it lead to the difference at present."

2.3.2. Setup Notes

The corresponding Pathfinder model is shown in Figure 24. The paper does not provide the exact values of entrance widths to the 2.4 m corridor, so the Pathfinder calculation assumed five cases where the entrance widths were 0.5 m, 1.0 m, 1.5 m, 2.0 m, 2.4 m.

The five cases used the Zhang and Seyfried values of 1.55 ± 0.18 m/s with a speed profile that corresponds to the speed-density data shown in Figure 3. This input curve is shown in Figure 6. Thus, we used the same speed-density curve for our calculations as was determined based on the independent unidirectional flow experiments. We did not try to adjust the speed-density curve for the T-junction calculations. This curve results in a maximum specific flow of 1.45 pers/s-m at a density of 1.736 pers/m2 and speed of 0.835 m/s.

2.3.3. Results

Speed-density and specific flow-density results are presented in Figure 25. The data is presented over time intervals when "steady-state" conditions have been reached. The calculated points for the in front measurements tend to either lie at low densities (0.0 to 0.5 pers/m2) or at higher densities (2 to 3 pers/m2). The reason is that for the smaller entrance cases (0.5 m and 1`.0 m` width entry doors), no queues develop and so the densities stay low. However, when the entrances are larger (1.5 m to 2.4 m), then the supply flow is larger than can be supported by the exit width, so queues form. The queues cause the higher densities.

As previously mentioned, the specified speed-density profile was based on the unidirectional flow experiments. As can be seen, the behind data (and most of the in front data) lie on the specified curve.

2.3.4. Analysis

The Pathfinder calculations replicate the input speed-density curve. For the experiments, the measured "behind" data was similar to the unidirectional experimental data. However, the "in front" data had lower speeds for a given density. The Pathfinder results show the same effect. This is likely due to merging and turning behavior as the streams merge.

In general, the Pathfinder results match the experimental data satisfactorily. It is important to remember that we used a speed-density relationship based on unidirectional data. We did not modify the curve to better match the experimental results, so Pathfinder captures the measured differences between the "behind" data and the "in front" data.

2.4.1. Background

Pathfinder allows the user to define customized fundamental diagrams for movement up and down stairs and ramps. These are defined in the profiles, so now it is possible for each profile to have five fundamental diagrams (level, stairs up, stairs down, ramp up, ramp down) with different nominal speeds for each case (including the possibility of different distributions). While potentially complex, this give required flexibility to meet evacuation calculation standards required in some jurisdictions.

In this verification example, we will use one profile and define five different fundamental diagrams. The fundamental diagrams will correspond to the Russian evacuation code mobility profiles (M1-M4), shown in Figure 26.

In the Russian standards there are 4 types of person:

M1 - healthy person
M2 - older person or blind person or other disabled person
M3 - person with crutches
M4 - person in wheelchair

Speed depends of occupants' density:

\(D < D_{0}, V_{D} = V_{0}\)

\(D>D_{0}\), \(V_{D}=V_{0}\left(1-a\:\ln{\left(\frac{D}{D_{0}}\right)}\right)\)

Where:

\(V_{D}\) is person speed.
\(V_{0}\) is maximum velocity. People go with \(V_{0}\) if nobody has influence on them.
D is occupant density (m²/m²) or fraction of occupied area.

\(D = \frac{Nf}{S}\)

Where:

N is number of people in area
f is area occupied by a person, m²
S is the area, m²

For the healthy population (M1), the calculated fundamental diagrams are shown in Figure 27.

2.4.2. Setup Notes

Pathfinder models were used to simulate the Russian evacuation code for healthy people with a 0.1 m2 area for each person. Five models were used, corresponding to level walking, stairs up, stairs down, ramp up, ramp down. Because we are not replicating a specific set of experiments, we used room sources to supply the occupants.

The level model is shown in Figure 29, the sources are the rooms on the left and the occupants exit to the right. The sources introduce occupants to the model, the red squares indicate where speed-density is measured, and the occupants exit on the right. To control the densities, the source rate of the entry room and the flow rates of the exit doors were specified, as shown in Figure 28.

The values are different for different cases since the speed-density curves are different and different flow rates can be maintained. Similar models were used for stairs and ramps.

The input to Pathfinder consists of the speed (or speed ratio) for each case and the normalized speed-density curve, Figure 30.

In addition, it is necessary to set the occupant size to correspond to the person density defined by the standard.

Knowing the density, we can assume tight hexagonal packing as follows:

\(\rho_{\text{HEX}} = \frac{2}{\left( \left( \sqrt{3} \right) S^{2} \right)}\)

or:

\(S = \sqrt{\frac{2}{\left( \left( \sqrt{3} \right)\rho_{\text{HEX}} \right)}}\)

Where:

S is the spacing distance between centers of the hex-packed circles. For a density of 10 pers/m2 the spacing is 34 cm.

In addition, it is necessary to set the corresponding comfort distance to zero.

2.4.3. Results

Speed-density results are presented for each of the five path types (level, stairs up, stairs down, ramp up, ramp down). In these curves, the data is presented over time intervals when "steady-state" conditions have been reached. The gray points represent all the calculated speed-density pairs for all corridors, while the black points are the averaged values for each corridor.

2.4.4. Analysis

These results show that Pathfinder correctly uses the specified speed-density curves for the five different five path types (level, stairs up, stairs down, ramp up, ramp down). For the ramp down case which has specific flows much higher than possible on level space, the Pathfinder movement algorithm limited the maximum density to about 4 pers/m2.

3.1.1. Background

This test verifies the Pathfinder door flow rate calculation. In steering mode, the door flow rates are not specified, but are emergent behavior based on the occupant movement. SFPE calculates the door flow rates based on the maximum specific flow of 1.316 pers/s-m. For doors, the specified boundary layer is 0.15 m, so a 1 m wide door is calculated to flow at 0.92 pers/s.

3.1.2. Setup Notes

The corresponding Pathfinder model is shown in Figure 36. The door widths range from 0.7 m to 3.0 m, with the entry corridor width 5 m. Two Steering Mode cases were run, one with a constant velocity of 1.19 m/s and one with a uniform velocity distribution of 1.19 ± 0.25 m/s. In addition, SFPE mode and Steering+SFPE mode cases were run for a uniform velocity distribution of 1.19 ± 0.25 m/s

3.1.3. Results

The door flow rates are shown in Figure 37 through Figure 40. This data has been averaged over the time periods where the different doors have attained "steady state" flow. For comparison, the red lines show the SFPE flow rate for the door width and a 0.15 m boundary.

3.1.4. Analysis

The Pathfinder Steering mode calculations give slightly higher door flow rates than predicted using the SFPE calculations. The Pathfinder SFPE mode results are essentially identical to the SFPE predictions. The Steering+SFPE mode results are somewhat lower than the SFPE predictions.

The predictions are satisfactory.

3.2.1. Background

This test verifies the Pathfinder stair flow rate calculation. In steering mode, the stair flow rates are not specified, but are emergent behavior based on the occupant movement, including maximum speed as a function of stair riser/tread dimensions and occupant density. SFPE calculates the stair flow rates based on the maximum specific flow that is a function of riser/tread dimensions, see Figure 41. For stairs, the specified boundary layer is 0.15 m, so a 1 m wide stair with rise/run of 178/279 is calculated to flow at 0.71 pers/s.

3.2.2. Setup Notes

The corresponding Pathfinder model is shown in Figure 42. The door widths range from 0.7 m to 3.0 m. Entry corridor width is 5 m. Stairs have a total rise of 7 m and a run of 11 m.

Two Steering Mode cases were run, one with a constant velocity of 1.19 m/s and one with a uniform velocity distribution of 1.19 ± 0.25 m/s. In addition, SFPE mode and Steering+SFPE mode cases were run for a uniform velocity distribution of 1.19 ± 0.25 m/s

3.2.3. Results

The stair flow rates are shown in Figure 43 through Figure 46. This data has been averaged over the time periods where the different stairs have attained "steady state" flow. For comparison, the red lines show the SFPE flow rate for the stair width and a 0.15 m boundary.

3.2.4. Analysis

The Pathfinder Steering mode calculations lie close to the SFPE calculations. The Pathfinder SFPE mode results are essentially identical to the SFPE predictions. The Steering+SFPE mode results are somewhat lower than the SFPE predictions.

The predictions are satisfactory.

3.3.1. Background

This test is similar to the door flow rate verification but examines flow rates through corridors for which SFPE species a 0.2 m boundary layer (a 1 m corridor has a 0.79 pers/s flow rate). It also tests the sensitivity of Pathfinder to the width of the entry shoulder on each side of the corridor.

3.3.2. Setup Notes

The Pathfinder models are shown in Figure 47 and Figure 48. The corridor widths are 1 m and 3 m and the shoulder widths range from 0 to 2 m. Steering Mode cases were run, one with a constant velocity of 1.19 m/s and one with a uniform velocity distribution of 1.19 ± 0.25 m/s. In addition, SFPE mode and Steering+SFPE mode cases were run for a uniform velocity distribution of 1.19 ± 0.25 m/s

3.3.3. Results

The corridor flow rates are shown in Figure 49 through Figure 56. This data has been averaged over the time periods where the different doors have attained "steady state" flow. For comparison, the blue lines show the SFPE corridor flow rate.

3.3.4. Analysis

For the 1 m wide corridor, the Pathfinder calculations give slightly higher flow rates than predicted using the SFPE calculations. For the 3 m door, the flow rates are nearly identical to the SFPE calculations. The results are not sensitive to the width of the entry shoulder.

For SFPE mode, the corridor width does not affect the calculation, so the flow rates are controlled primarily by the exit door flow rate. Also for SFPE mode, when the corridor is the same width as the entry room, the density in the corridor/entry room slows the walking speed so the zero shoulder width corridor cases show slightly lower flow rates.

The correlation between the Pathfinder calculations and the expected flow rates is satisfactory.

4.1.1. Background

This tests simple behaviors, including exits and a refuge room. 150 occupants were evenly divided with three different behaviors: go to one of two exits or go to the refuge room (a final destination).

4.1.2. Setup Notes

The occupants were initially located in one room and then proceed to their exits as shown in Figure 57.

4.1.3. Results

Figure 58 shows a plot of the refuge room usage. The 50 occupants assigned to use the refuge did so. The same results were obtained for SFPE and Steering+SFPE modes.

4.1.4. Analysis

The occupants proceeded to use the exits and refuge associated with their behaviors.

The Pathfinder calculations performed as expected.

4.2.1. Background

This case tests the effect of grouping on door flow rates. We use the same model as used for the door flow rate tests, but the occupants are grouped into groups of 3 and 5 people.

4.2.2. Setup Notes

The model is shown in Figure 59. It is the same as the previous door flow rate model (steering mode with a uniform velocity distribution of 1.19 ± 0.25 m/s), except the space downstream of the doors is extended to allow group leaders to pause and wait for the rest of their group to catch up.

Dynamic grouping was used with the Number of Members in the group defined as 3 and 5 and the group minimum size of 1. Two group formations were used: a tight group formation with a Maximum Distance of 1.0 m and a Slowdown Time of 3 s, and the default group with properties with a Maximum Distance of 2.0 m and a Slowdown Time of 3 s. The maximum speed was defined as a uniform distribution of 1.19 ± 0.25 m/s. As a result, members of a group will have different speeds, so the faster members slow down to keep the group together.

4.2.3. Results

Figure 60 through Figure 64 show plots of door flow rates in steering mode. Without grouping (Figure 60) the door flow rate for the 3 m door is slightly less than the previous model. This is due to the downstream effect of movement in the corridor that slightly slows movement through the door.

When grouped, the steering mode door flow rates do not change significantly for the default grouping parameters, but do decrease for the tight grouping parameters. This is because the tight grouping means increased delays as the group waits to reform.

Grouping in SFPE mode does not change the door flow rates, Figure 65.

Figure 66 shows the results for Steering+SFPE mode for the tight grouping with a group size of 5. These results show that the door flow rate constraint slows the door flow rate further.

4.2.4. Analysis

Tight groups show slower movement through doors. For the default group parameters, which allows the members of the group to become more separated, the effect on door flow rates is small.

The Pathfinder calculations performed as expected.

4.3.1. Background

This test expands a corridor merging problem discussed by Galea et al. (Galea, Sharp, and Lawrence 2008). The problem consists of two flow streams meeting at a junction and continuing to the exit. We add a variation in corridor width to the original Galea problem. We also add a T-junction geometry as described by Zhang et al. (Zhang et al. 2011).

4.3.2. Setup Notes

Figure 67 shows the Galea ("adjacent") geometry and typical merging behavior for a 3 m wide corridor. Figure 68 shows the T-junction ("opposite") geometry model with typical merging behavior. For both geometries we also solve for 1 m wide corridors.

4.3.3. Results

The merging ratios and exit flow rates for the adjacent geometry are shown in Figure 69. These were calculated after the door flow rates had reached "steady state" values. Figure 70 shows the same results for the "opposite" geometry.

4.3.4. Analysis

In all cases for the "opposite" geometry, the merging flows are balanced with 50:50 ratios. This matches the Zhang et al. (Zhang et al. 2011) experimental results.

The "adjacent" geometry case is more interesting. For a 1 m corridor, the merging ratios favor the south (straight) corridor flow (approximately 60:40). However, for the wider 3 m corridor, the south (straight) corridor flow strongly dominates the merging behavior (approximately 75:25). The Galea et al. (Galea, Sharp, and Lawrence 2008) paper examines the effects of different occupant "drives" on merging, but does not examine the effect of different corridor geometry.

The Pathfinder results are satisfactory.

4.4.1. Background

This test expands the stair merging problem discussed by Galea et al. (Galea, Sharp, and Lawrence 2008). The paper categorizes two stair merging geometries: "adjacent" (Figure 71) and "opposite" (Figure 71) defined by how the floor occupants merge at the landing relative to the occupants descending the stairs. We have added a third "open" geometry in which the floor has direct access to the exit stair (Figure 73).

The following images show the categorization of stair merging geometries. The arrows indicate the "up" direction on the stairs, not the flow direction.

4.4.2. Setup Notes

The width of the stairs was 1.5 m and solutions were made for corridor widths of 1.0 m and 1.45 m (Figure 74). The first floor is at Z = 1.6 m and the second at Z = 3.2 m. The rise/run of the stairs is approximately 7/11 with a total stair length of 2.97 m. For this stair, the SFPE guidelines give a speed that is 77% of the free walking speed.

4.4.3. Results

Typical results for the merging behavior for the adjacent geometry with corridor widths of 1.0 m (Figure 75) and 1.45 m (Figure 76) are shown below. For the default occupant dimensions, the 1.0 m narrow corridor requires a "staggered" walking pattern while the wider corridor enables "side by side" walking. As a result, the floor flow is more dominant for the wider entry corridor.

The merging ratios and exit flow rates for all cases are shown in Figure 79 and Figure 80. In the "open" geometry, the floor flow dominates the merging behavior.

Typical merging behavior for the "opposite" configuration with 1.19 m/s occupant speed and different corridor entry widths are shown below.

4.4.4. Analysis

The calculated merging ratios fall within the range of experimental data summarized by Galea et al. (Galea, Sharp, and Lawrence 2008). The results match a general trend discussed by Galea et al. for the "opposite" geometry to favor floor merging over the "adjacent" geometry. This would appear to be related to congestion that forms at the landing. For the "adjacent" geometry both streams must merge and then proceed to the landing leading to the exit. For the "opposite" case the two streams approach the exit stair in an approximately symmetric pattern, similar to the T-junction case for corridor merging discussed above.

However, it should be noted that Boyce et al. states, "The results indicate that, despite differences in the geometrical location of the door in relation to the stair and the relative stair/door width, the merging was approximately 50:50 across the duration of the merge period in each of the buildings studied." (Boyce, Purser, and Shields 2012) Their experiments noted how individual behavior could change the merge ratios.

The exit flow rates are controlled by the stair flow rate, not the exit door capacity.

The Pathfinder results are satisfactory.

4.5.1. Background

This test evaluates the Pathfinder capability to simulate passing behavior around slow occupants on stairs. For this behavior, it is expected that when the stair width is sufficient, faster occupants will pass slower occupants on stairs.

However, the actual effect of disabled or wounded occupants on stairs can be complex. Averill et al. in their report on occupant behavior and egress in the World Trade Center disaster (Averill et al. 2005) noted the following different situations:

In modeling, the user must be aware of these situations and model accordingly.

4.5.2. Setup Notes

The same model used for the stair width study was used for this study. The door widths range from 0.7 m to 3.0 m, with the entry corridor width 5 m. Stairs have a total rise of 7 m and a run of 11 m.

Two occupant profiles were defined: a default profile with a uniform velocity distribution of 1.19 ± 0.25 m/s, and a slow profile with a constant velocity of 0.5 m/s. The 0.5 m/s velocity as a low end of the walking speeds for impaired individuals described in Figure 41 of the SFPE Handbook (SFPE 2016).

10 percent of the occupants were given the slow profile (red occupants in Figure 81). Steering mode was used, since this is the mode in which passing behavior is used.

4.5.3. Results

The stair flow rates with mobility-impaired occupants are shown in Figure 82. This data has been averaged over the time periods where the different stairs have attained "steady state" flow. For comparison, the red lines show the SFPE flow rate for the stair width and a 0.15 m boundary.

4.5.4. Analysis

The presence of mobility-impaired occupants reduces the stair flow rates (compare with Figure 44). No experimental data is available for comparison, but the trend is reasonable.

4.6.1. Background

100 occupants are located in a 10x10 m room at an elevation of 10 m. The occupants exit using an elevator with dimensions 2 m wide and 1.7 m deep, for a typical elevator loading of about 16 people (Klote and Alvord 1992) and the elevator door width is 1.2 m. The elevators have an Open+Close Time of 7.0 s, Pickup and Discharge times of 10.0 s, and Open and Close delays of 5.0 s (see the Pathfinder User Manual for more information). There are four elevators, with specified Nominal Loads of 5, 10, 20, and 50 persons (Figure 83).

4.6.2. Setup Notes

The four problems are independent, so allow a quick verification.

4.6.3. Results

The resulting elevator loads for the steering simulation are shown in Figure 84 and match the expected results. The results for Steering+SFPE and SFPE modes also matched the expected results.

4.6.4. Analysis

The elevator loadings matched the expected values.

4.7.1. Background

The example was originally presented in the FDS+Evac Technical Reference and User’s Guide (Korhonen 2018). The problem describes an assembly space filled with 1000 occupants. The initial room measures 50 m x 60 m. At the right, there is a 7.2 m doorway leading to a 7.2 m corridor. The corridor contains a sharp turn to the left before continuing to the exit.

The feature of interest in this problem is the corner in the corridor. Based on how different simulators handle the flow of large groups around a corner, different simulators can produce substantially different answers. Notably, the current body of movement research presents us with little guidance toward a "correct" solution to this problem.

4.7.2. Setup Notes

In addition to the two-corner problem, we simulated a single corner and a straight corridor without a corner. Only steering mode results are presented, since that is the case for which the corner slows movement.

4.7.3. Results

The primary interest is in how effectively the simulator uses the full width of the corridor and corner, Figure 86. In the Pathfinder simulation, there is some grouping that occurs in the vertical section of the corridor. This is a result of increased density which leads to slower movement.

The time for all occupants to exit was 164 seconds for the straight corridor, 163 seconds for one corner, and 185 seconds with two corners.

The model with a straight corridor has a 7.2 m wide corridor and a path length from the room to the exit of 41.5 m. An SFPE calculation using the flow rate and walking speeds at a density of 1.88 pers/m2 and gives a total time of 171 seconds.

4.7.4. Analysis

The Pathfinder results are reasonable.

5.1.1. Movement Speed on Level Surface

This test verifies that during assisted evacuation, the speed of the person being assisted controls the movement speed.

5.1.1.2. Setup Notes

Figure 87 shows the test geometry. The default speed of the assistants is 1.19 m/s and the speed of the bed is 1 m/s.

5.1.2. Stairway Speed Up

This test verifies that during assisted evacuation, the speed of the person being assisted controls the movement speed up stairs.

5.1.2.2. Setup Notes

The width of the stairs was 1.1 m. The total horizontal distance of the stairs is 40 m and the vertical distance is 24 m, so the diagonal distance on the stairs is 46.64 m. The patient speed up the stairs was specified as 0.3 m/s.

5.1.3. Stairway Speed Down

This test verifies that during assisted evacuation, the speed of the person being assisted controls the movement speed down stairs.

5.1.3.2. Setup Notes

The width of the stairs was 1.1 m. The total horizontal distance of the stairs is 40 m and the vertical distance is 24 m, so the diagonal distance on the stairs is 46.64 m. The speed down the stairs was specified as 0.5 m/s.

5.1.4. Team Assignment

This test verifies the capability to assign assistants to teams and then assign occupants that need evacuation assistance to be assisted by specific teams.

5.1.4.2. Setup Notes

Figure 90 shows the model used to test the assignment of assist teams. The smaller occupants needing assistance are wheelchairs and the larger are beds. Each team is assigned to evacuate the wheelchairs first, then the beds.

5.1.4.3. Results

Figure 91 shows the result early in the evacuation, the wheelchairs are being assisted first. Three members of the red team are assisting wheelchairs, so the other two red team members are assisting the bed. The two blue team members are assisting wheelchairs. For assisted occupants, if a path is blocked, the assisted beds (or other vehicle) are briefly represented as cylinders to allow some overlap with the blocking wheelchairs (vehicles).

Figure 92 shows the movement near the end of the simulation. Notice that the red occupants needing assistance have been nearly all helped. It takes longer to assist the blue occupants, since there are only two members in the blue team.

5.1.5. Ghent Hospital Simulation

This test replicates a simulation of evacuation from the 11th floor of a hospital, as described in a paper by Hunt, et al. (Hunt, Galea, and Lawrence 2013).

5.1.5.2. Setup Notes

Figure 93 shows the basic geometry of the hospital floor to be evacuated. In this figure, some of the dimensions such as corridor door widths have been estimated by scaling the drawing.

Figure 94 shows the geometry of the stairs. Key dimensions of the stairs are that each step has a rise of 17.5 cm and a run of 29 cm, there are 12 rises in each flight of stairs (this model neglected the detail that flights between floors 2 and 3 have only 10 risers), and the width of the stairs are 1.4 m between the handrails.

The geometry of the evacuation chair (Figure 95), evacuation stretcher (Figure 96), and assistant positions are shown below.

Table 5 gives the speeds for the patients and assistants.

Role	Horizontal (m/s)	Stair Down (m/s)	Stair Up (m/s)	Initial Delay (s)
Stretcher (male team)	1.09 ±0.08	0.63	N/A	67.6
Evacuation Chair (female team)	1.39 ±0.03	0.82	N/A	35.9
Female and Male Assistants	1.385±0.055	0.885±0.125	0.655±0.015	0.0

5.2.1. Background

Sources can be assigned to: a rectangular area, rooms, and doors (both internal and exit).

Source parameters include: flow rate (constant or periodic), the profile distribution, the behavior of occupants, and an option to either delay introducing occupants into a crowded room or to enforce the flow rate (even if that will result in overlapping occupants).

5.2.2. Setup Notes

The model is shown in Figure 98. Four source types were tested: rectangle, door, exit door, and room. The occupants were distributed uniformly between two profiles (red and blue). The source flowrate is constant at 2.5 pers/s. The Enforce Flowrate option was selected.

5.2.3. Results

Figure 99 shows the exit door flow rates for the four cases. In all cases, the flow reaches a steady-state value of 2.5 pers/s. Results for steering behavior (shown), SFPE and Steering+SFPE are similar.

5.2.4. Analysis

The Pathfinder calculations performed as expected.

5.3.1. Background

The implementation is the same as used in FDS+EVAC (Korhonen 2018), using only the concentrations of the asphyxiant gases \(CO\), \(CO_{2}\), and \(O_{2}\) to calculate the FED value.

\(\text{FED}_{\text{tot}} = \text{FED}_{\text{CO}} \times \text{VCO}_{2} + \text{FED}_{O_{2}}\)

This calculation does not include the effect of hydrogen cyanide (HCN) and the effect of \(CO_{2}\) is only due to hyperventilation.

See the Pathfinder User Manual and Technical Reference Manual for more details.

5.3.2. Stationary Occupant

5.3.2.1. Setup Notes

This validation problem tests the calculation of FED for a stationary occupant. The PyroSim model is shown in Figure 100. The model includes a fire and devices that measure the volume fractions of \(CO\), \(CO_{2}\), and \(O_{2}\) at the location of the height of the occupant. The model also uses FDS to calculate FED which is compared to the Pathfinder calculation.

The Pathfinder model is shown in Figure 101. Pathfinder samples FED quantities at 90% of occupant height. The default height is 1.8288 m, so devices are located at a height of 1.6459 m in the PyroSim model.

5.3.2.2. Results

Comparisons of the FDS device outputs and the Pathfinder inputs and calculated FED are shown in Figure 102. Pathfinder reads 3D Plot data and then interpolates, so there is some difference between the device and interpolated values for \(CO_{2}\), \(CO\), and \(O_{2}\).

5.3.3. Moving Occupant

5.3.3.1. Setup Notes

This validation problem tests the calculation of FED for a moving occupant. The PyroSim model is shown in Figure 103. The model is divided into three initial (INIT) regions separated by thin wall obstructions.

The init regions used a mix of air and combustion products. The mass fractions of species in the two mixtures are shown in Table 9. Init Region 1 has 100% mass fraction combustion products, Init Region 2 has 75% combustion products and 25% air, and Init Region 3 has 50% combustion products and 50% air.

Species	Combustion Products	AIR
Carbon Dioxide	0.010000	0.000592
Carbon Monoxide	0.001000	0.000000
Nitrogen	0.839000	0.763018
Oxygen	0.150000	0.231164
Water Vapor	0.000000	0.005226

The Pathfinder model is shown in Figure 104. The occupant starts on the left and has a velocity of 0.25 m/s. The distance to the exit is 30 m, so the time to exit is approximately 120 seconds (there is some acceleration time at the start). As the occupant moves through the model, they are exposed to the different gas mixtures.

5.3.3.2. Results

Comparisons of the FDS device outputs and the Pathfinder inputs and calculated FED are shown in Figure 105. The data shows how the occupant is exposed to different concentrations as they move through the model.

6.1.1. Setup Notes

Since Pathfinder tracks occupant location by the center point, the navigation mesh was extended 0.5 meters behind the occupant to allow space for the back half of the occupant when standing exactly 40 meters from the exit.

6.1.2. Expected Results

SFPE mode should give an exit time of 40.0 seconds.

Steering mode uses inertia and we need to account for the time it takes to accelerate to 1.0 m/s. Occupants in Pathfinder can accelerate to maximum speed in 1.1 s. From \(d_{1} = 0.5 * (v_{1} - v_{0}) * t_{1}\) we know that with \(v_{0} = 0.0 text_{m/s}\) , \(v_{1} = 1.0\ m/s\), at t=1.1 s the occupant will have travelled 0.55 m. The remaining 39.45 meters will be covered at 1.0 m/s. Thus, steering mode should give an exit time of 40.55 seconds.

6.1.3. Results

Table 10 shows the time to exit in each tested mode.

6.1.4. Analysis

All test cases were successful.

6.2.1. Setup Notes

The occupant was positioned on a lower landing at a distance 1.0 m from the staircase. For the steering mode this allows the occupant enough distance to accelerate to full speed before reaching the stairway. Pathfinder summary file reports the time of the first person entering a stairway and the time the last person leaves, so this provides an accurate measure of time on the stairs for a single occupant.

6.2.2. Expected Results

The occupant is given a base maximum speed of 1.0 m/s. The default Pathfinder assumption is to use the SFPE stair speed factors. This speed reduction will be used in all modes with the scaling factor based on the slope of the stairway. Using the velocity equations presented in the Pathfinder Technical Reference, this scale factor will be (0.918 m/s) / (1.19 m/s) = 0.77. This makes the effective stairway speed of the occupant (1.0 m/s)*0.77 = 0.77 m/s. Based on this speed, the results for all modes should be the same at 12.99 s.

6.2.3. Results

Table 11 shows the time to ascend the staircase in each mode (i.e. the stair exit time minus the stair entry time).

6.2.4. Analysis

All test results are within an acceptable margin of error.

6.3.1. Setup Notes

The occupant was positioned on the upper landing at a distance 1.0 m from the staircase. For the steering mode this allows the occupant enough distance to accelerate to full speed before reaching the stairway. The length between the occupant’s center starting position and the bottom of the staircase is slightly less than 10.0 m, since at the top of the stairs an occupant must allow for the door tolerance.

6.3.2. Expected Results

The occupant is given a base maximum speed of 1.0 m/s. The default Pathfinder assumption is to use the SFPE stair speed factors. This speed reduction will be used in all modes with the scaling factor based on the slope of the stairway. Using the velocity equations presented in the Pathfinder Technical Reference, this scale factor will be (0.918 m/s) / (1.19 m/s) = 0.77. This makes the effective stairway speed of the occupant (1.0 m/s) * 0.77 = 0.77 m/s. Based on this speed, the results for all modes should be the same at 12.99 s.

6.3.3. Results

Table 12 shows the time to descend the staircase in each tested mode (i.e. the stair exit time minus the stair entry time).

6.3.4. Analysis

All test results are within an acceptable margin of error.

6.4.1. Setup Notes

Flow rate is measured using the simulation summary data. This average flow rate is defined as the number of occupants to pass through a door divided by the amount of time the door was "active." A door is considered to be active after the first occupant has reached the door and is no longer active when the last occupant has cleared the door.

Following SFPE guidelines, the boundary layer for all modes was 15 cm. With this boundary layer, the expected door flow rate for SFPE mode is 0.92 pers/s.

6.4.2. Expected Results

The maximum observed flow rate should be less than 1.33 persons per second.

6.4.3. Results

Table 13 shows the average exit door flow rates observed in each tested mode.

6.4.4. Analysis

The Steering+SFPE mode shows a slower exit door flow rate, due to the combination of steering movement and door flow rate limits. All test results are within an acceptable margin of error.

6.5.1. Setup Notes

Occupants were assigned initial delays between a min = 10.0s and max = 100.0s.

Occupant parameters were not randomized between simulations. This should lead to similar occupant count graphs.

6.5.2. Expected Results

Initial movement times should vary between occupants. This was verified by viewing the results animation. Pathfinder also has the option to output detailed comma-separated files for each occupant.

6.5.3. Results

Results for this problem were first verified using the animation. Results were also verified by examining the output in the detailed output data for each occupant.

6.5.4. Analysis

All simulator modes passed the test.

6.6.1. Setup Notes

20 persons are uniformly distributed in the first 4 meters of the corridor.

6.6.2. Expected Results

Each occupant should navigate the model while staying inside the model boundaries. For the steering modes the occupants will retain a separation distance, but the SFPE mode allows multiple occupants to be located at the same space.

6.6.3. Results

Figure 112, Figure 113, and Figure 114 show the occupant trails for all 3 simulator modes. These movement trails can be used to verify that all occupants successfully navigated the corner.

6.6.4. Analysis

Occupant trails indicate that no occupants passed outside the simulation boundary in any of the three simulation modes. All simulation modes successfully pass the verification test. The SFPE mode is basically a flow calculation, so occupants may be superimposed in the same space. The steering mode provides the most realistic movement.

All simulator modes passed the test.

6.7.1. Setup Notes

A walking speed profile representing males 30-50 years old is distributed across 50 occupants. The walking speeds are a uniform random distribution with a minimum of 0.97 m/s and a maximum of 1.62 m/s. The information for this profile comes from Table 3.4 in the appendix to the Interim Guidelines for the advanced evacuation analysis of new and existing ships.

The occupants were positioned in a line 0.5 m from the left side of a 40.5 x 51.0 m room. The exit door is on the opposite side of the room. Each occupant moves with their assigned speed in a straight line to the right.

6.7.2. Expected Results

The occupants should display a range of walking speeds within the specified limits, so that the arrival times at the right edge of the room should be between 24.7 s and 41.2 s (neglecting the inertia in the steering mode).

6.7.3. Results

The occupants' speeds observed in the simulation were within the specified limits. The first arrival and last arrival times at the exit are given in the table below. Figure 117 shows the occupant paths at 20 s for steering mode (other cases are similar).

6.7.4. Analysis

All simulator modes passed.

6.8.1. Setup Notes

The problem geometry is set up as described above, with exits at the far walls. The occupants in each room are assigned the exit in the opposite room.

To simplify collection of results, all four simulation scenarios are created in the same model. This can be accomplished by duplicating the initial geometry 3 times, then using different numbers of occupants in the room at the right.

A walking speed profile representing males 30-50 years old is distributed across all occupants. The walking speeds are a uniform random distribution with a minimum of 0.97 m/s and a maximum of 1.62 m/s. The information for this profile comes from Table 3.4 in the appendix to the Interim Guidelines for the advanced evacuation analysis of new and existing ships.

6.8.2. Expected Results

As the number of occupants in counterflow increases, the occupants should slow down and increase the evacuation time.

Since in the SFPE mode, there is no restriction on occupants being superimposed in the same space, counterflow does not slow the movement (room density does reduce walking speed for this case).

6.8.3. Results

Figure 119 shows the occupant positions for the steering mode, 100 person counterflow case at 75 s.

Table 15 shows the time it takes occupants that start on the left to exit the simulation on the right. The times are given as a function of the number of occupants in counterflow.

6.8.4. Analysis

In each mode, more counterflow increases evacuation time. The SFPE mode does not account for counterflow interference, the increased times are due to increased room density slowing the speed.

See Section 2.2 for a comparison with experimental data for bidirectional flow.

All modes passed test criteria.

6.9.1. Setup Notes

Occupants are given a profile corresponding to males 30-50 years old from Table 3.4 in the appendix to IMO 1238 (IMO 2016). The walking speeds are a uniform random distribution with a minimum of 0.97 m/s and a maximum of 1.62 m/s.

To simplify data collection, both model configurations are added to a single simulation model.

6.9.2. Expected Results

Simulation time should approximately double when using half as many doors.

For the SFPE mode, the expected single door flow rate is 0.924 pers/s (15 cm boundary included), giving an evacuation time of 541 s for two doors and 271 s for four doors.

6.9.3. Results

Table 16 shows the time it takes to exit the simulation for both cases. Since the initial locations of the occupants were randomly assigned, the number of persons that exit each door are not exactly equal.

6.9.4. Analysis

For all modes, the simulation times, while not exactly double, are well within the acceptable margin for validity.

All modes passed test criteria.

6.10.1. Setup Notes

The occupants in the left 8 rooms are assigned to the main (top) exit. The occupants in the remaining 4 rooms are assigned to the secondary (right) exit. Occupants are given a profile corresponding to males 30-50 years old from Table 3.4 in the appendix to IMO 1238 (IMO 2016). The walking speeds are a uniform random distribution with a minimum of 0.97 m/s and a maximum of 1.62 m/s.

6.10.2. Expected Results

Each occupant should leave the model using the specified exit.

6.10.3. Results

Figure 122 shows the paths taken by occupants in steering mode (other modes were similar). The trails of the four occupants intended to use the secondary exit are shown in red, all other occupant trails are shown in blue.

6.10.4. Analysis

The results for all simulator modes indicate that the four occupants directed to exit via the secondary exit, did so.

All modes passed test criteria.

6.11.1. Setup Notes

The 150 occupants are added to the initial room using a uniform distribution.

All occupants were assigned a profile corresponding to 30-50 year old males (as specified in Table 3.4, International Maritime Organization, 2016). On level terrain (corridor), this gives a uniform speed distribution ranging from 0.97 m/s to 1.62 m/s (mean 1.3 m/s). Table 1.1 of the IMO report gives the speed-density curve to be used in calculations. For a corridor, at a density of 0.5 pers/m2 the speed is 1.2 m/s and at a density of 3.5 pers/m2 the speed is 0.1 m/s. The corresponding normalized speed-density profile is shown in Figure 124.

When walking up on stairs, the speed is a uniform speed distribution ranging from 0.47 m/s to 0.79 m/s (mean 0.63). Table 1.3 of the IMO report gives specific flow and speed curves to be used on stairs up. At a density of 0.5375 pers/m2 the speed is 0.8 m/s and at a density of 2 pers/m2 the speed is 0.44 m/s. The corresponding normalized speed-density profile on stairs up is shown in normalized-speed-density.

6.11.2. Expected Results

Congestion should form in the corridor leading to the stairs. This will be measured by the mean density and mean velocity of the occupants in a 2x2 m rectangle at the base of the stairs. The results with and without stairs will be compared.

We can estimate the fastest exit time for the SFPE case. For a walking speed of 1.62 m/s, the time to cross the 12 m corridor is 7.4 s (neglecting inertia). The length of the stairs is 5.7 m, so for a 50% speed decrease on stairs, the time required is 7.0 s. Crossing the landing requires another 1.2 s, for a total of time of 15.6 s.

6.11.3. Results

The total evacuation times for the three cases are given in Table 17.

Figure 126 visually shows congestion forming at the base of the stairs. The density contour shows densities of about 2.75 pers/m2 at the base of the stairs.

Time history data describing the mean density and walking speeds for the occupants at the base of stairs with and without stairs are shown in Figure 127. Without stairs, the occupants continue moving to the exit with a speed of about 1 m/s and the maximum density is about 1.25 pers/m2. With stairs, congestion forms leading to a maximum density of about 3.0 pers/m2 and the speed drops to about 0.25 m/s.

6.11.4. Analysis

Congestion forms at the base of the stairs as shown by comparing the mean density and speeds at the base of the stairs for cases with and without stairs. Because of the assumed fundamental diagram, the maximum density reaches approximately 3.0 pers/m2, not the 3.5 pers/m2 assumed in HMO for congestion.

However, the Pathfinder results show congestion that is consistent with the specified walking speeds and speed-density curves.

7.7.1. Setup Notes

The Pathfinder calculation of Fractional Effective Dose (FED) uses the equations described in the SFPE Handbook of Fire Protection Engineering (5th Edition, Vol 3, Chapter 63, pages 2308-2428). The implementation uses only the concentrations of the asphyxiant gases \(CO\), \(CO_{2}\), and \(O_{2}\) to calculate the FED value.

This calculation does not include the effect of hydrogen cyanide (HCN) and the effect of \(CO_{2}\) is only due to hyperventilation.

See the Pathfinder User Guide and Pathfinder Technical Reference for more details.

Table 18 gives the mass and volume fractions of air and the gas mixture used for the incapacitation calculation. The FED was calculated for air and for the incapacitation case.

7.7.2. Expected Results

The FED calculation for air should be approximately zero for all time. The FED calculation using the incapacitation gas mixture should increase linearly with time. The time at which FED is equal to one should match the hand calculation and the fire simulator calculation.

7.7.3. Results

At 300 seconds, the FED calculation for pure air was 0.001567. The small non-zero value is due to the slight difference in default \(O_{2}\) volume fraction assumed in FDS as compared to the value of 20.9 in the SFPE equations.

For the incapacitation calculation, FED = 1 was calculated to occur at 247.5 seconds. The hand calculation gives 247.4. The calculated result matches the expected result.

7.8.1. Setup Notes

Room 1 is located at Z=0.0 and Room 2 at Z=3.5 m. An elevator connects the two rooms in accordance with Figure 130. The Floor 1 exit door is 1 m wide. The elevator is called from Room 1, reaches Room 2 and carries the occupant and back to Room 1.

The occupant has an unimpeded walking speed of 1 m/s in Room 2 with an instant response time. To minimize inertia effects, the Acceleration Time was set to zero. To simplify distance calculations, the occupant size was set to 50 cm. The initial distance between the center of the occupant and the elevator door is 17.5 m. However, since the occupant radius is 0.25 m and the distance from the elevator to activate a call is 0.5 m, the occupant walks 16.75 m to activate the call.

The elevator parameters include: door open and close times of 3.5 s, pickup and discharge travel times of 2.5 s between the two floors, and door open and close delays of 5.0 s. The open delay is the minimum time an elevator’s door will stay open on a floor (does not impact this test case) and the close delay is the time the elevator door will remain open after the last person enters.

7.8.2. Expected Results

The occupant starts walking at time zero and the elevator is called from the discharge floor after the occupant has walked 16.75 m. Once called, the door must close on the discharge floor and then the elevator must move to the second floor. The door then opens, the occupant enters the elevator by moving the distance of the occupant radius away from the door (the occupant moves at about a 45° angle), there is a door close delay, and finally the door closes. The elevator then moves to the discharge floor, the door opens, and the occupant leaves the building. The total expected evacuation time is 60.60 s, Table 19.

7.8.3. Results

The observed exit time is 60.5 s for steering mode. Identical results (within tolerance) were obtained for the Steering+SFPE and SFPE modes.

All modes passed test criteria.

7.10.1. Setup Notes

Two parameters in Pathfinder control group behavior: Maximum Distance and Slowdown Time. Members of the group try to maintain a distance between themselves less than the maximum distance. If any member is separated by more than the maximum distance, the leading members slow down for an interval equal to the Slowdown Time. If the group has still not reformed after that time, then the leading members will stop and wait for the group to reform.

Results will be presented using the default Pathfinder parameters that define a relatively loose group, Maximum Distance = 2 m and Slowdown Time = 3 s.

Only results for steering mode are presented because steering+SFPE gives similar results. In SFPE mode occupants can overlap so, as expected, the group just proceeds through the slow occupants without interaction.

7.10.2. Expected Results

The group of five occupants should remain together and exit the door within a time frame of 10 seconds.

7.10.3. Results

Figure 134, Figure 135, and Figure 136 show a sequence of images for default grouping showing movement at 20 s, at 36.5 seconds when the first group member exits, and at 45 seconds when the last group member exits. The time interval for the group to exit is 8.5 seconds.

7.11.1. Setup Notes

The room geometry is setup as defined. The shoulder width of the 24 occupants is 45.58 cm and of the disabled person 75 cm. The walking speed of the 24 occupants is Room 1 is 1.25 m/s and the walking speed of the disabled person was defined as 0.8 m/s. The disabled occupant was given a ramp speed was 0.4 m/s with other occupants walking the same speed on the ramp and level.

The SFPE and Steering+SFPE calculations included a 15 cm boundary layer.

7.11.2. Expected Results

All occupants will reach the exit. Scenario 1 will have a longer evacuation time than scenario 2.

7.11.3. Results

Table 20 shows the time to evacuate all occupants. The disabled occupant did slow the evacuation slightly by blocking flow on the ramp, but after leaving the ramp the faster occupants moved around the disabled occupant, so the slowing effect was reduced, Figure 139 and Figure 140.

7.15.1. Setup Notes

The room geometry is setup as defined. Pathfinder uses a "locally quickest" algorithm to select the exit door from a room. To ensure that the occupant selects Exit 1, the occupant was located at X=4.5 m or X=0.5 m closer in the X direction to Exit 1.

7.15.2. Expected Results

The occupant will initially select Exit 1, then at 1.0 s will change to Exit 2.

7.15.3. Results

Figure 142 shows path used by the occupant. At 1.0 s, the occupant changes from Exit 1 to Exit 2. The same result was obtained for Steering+SFPE and SFPE modes.

8.1.1. Setup Notes

The door boundary layer is specified as 6 in.

8.1.2. Expected Results

In this example, the door entering each stairway is the controlling component. The problem is symmetrical so, for the hand calculation, the divided flow can be modeled as a single wide door and stairway. To calculate the total movement time, we must calculate \(T_{TOTAL} = T_{1} + T_{2} + T_{3}\) where: (T_{1}) is the time it takes the first occupant to reach the controlling component, (\(T_{2}\)) the time it takes 300 occupants to flow through two 32-inch doors, and (\(T_{3}\)) the time it takes the last occupant to move from the controlling component to the exit.

The value of T_{1} depends on the location of the occupants. For this model, the value is approximately \(T_{1} = \mathbf{1.0\ s}\).

The time needed for 300 occupants to pass through the two 32 inch doors, \(T_{2}\) is:

The time needed for the last occupant to move down the stairs and out the landing, \(T_{3}\) is:

The total evacuation time, \(T_{total}\) is:

8.1.3. Results

For each simulation mode, Table 21 lists the number of people that used each stair and the total evacuation time. Because the number of people that use the left and right exits are not equal, we present the times for each side.

8.1.4. Analysis

All cases show satisfactory comparison with the expected result.

8.2.1. Setup Notes

Detailed setup notes are presented in the Pathfinder example guide.

Following the intention of the problem, all occupants of the ground floor exit from four large side doors and all occupants on higher floors exits from doors at the base of the stairs.

A second steering mode case was run where occupants had an increased preference to remain in their current door queue (Current Door Preference parameter of the Profile). This parameter was changed from the default 35% to 80%.

8.2.2. Expected Results

In this example, the controlling component is the exit door at the base of the stairway. We will assume the occupants use the stairways evenly, in which case we only need to model the time it takes for half the occupants on the second through fifth floors to pass through the controlling 32 inch door.

To calculate the total movement time, we must calculate \(T_{TOTAL} = T_{1} + T_{2} + T_{3}\) where:

The calculation for T1 has four parts:

We assume a low-density velocity calculation for the first occupant to reach the stairs and the landing. For \(T_{A}\) we assume the person must walk 6 ft to reach the center of the stairs. For \(T_{B}\) we will assume the occupant must walk 8 ft, an average length of travel, to traverse the platform. This leads to the following calculations:

The time for 400 people to move through a 32 inch door, \(T_{2}\) is:

The time for the last person to move from the stairs to the exit is:

The total evacuation time, \(T_{total}\) is:

8.2.3. Results

For each simulation mode, Table 22 lists the results for both exits, including the number of people that used each exit. When queues form on the upper floors, people waiting in the queues can decide to leave their current queue when another door begins to flow, even if the flow is intermittent. The resulting back and forth behavior, while it does not significantly affect the total exit time, can appear somewhat unexpected. Pathfinder allows the user to increase the commitment of occupants to remain in the queues they are currently in. These are the results reported for the Steering (queue) case.

8.2.4. Analysis

The average exit time for the SFPE case matches the expected value within tolerance. The Steering+SFPE case is slower. The Steering mode is faster, since door flow rates are not explicitly specified. Adding the increased commitment to remain in the current queue had the effect of stopping the back and forth movement to alternate queues.