Slips and falls on sloped roof surfaces remain an important safety issue among construction workers. The slip potential has been conventionally analyzed and assessed primarily based on ground reaction forces, which cannot differentiate the specific roles of each of the force factors (e.g., workers’ motions-induced dynamic forces and slope-induced static forces) contributing to the slip potential. Their differentiation may enhance the understanding of the slip mechanisms on the sloped roof surfaces and help develop effective walking and working strategies/tactics to minimize the dangerous slips on the elevated roofs. Hence, the objective of this study is to develop a biodynamic method as an additional tool for analyzing the slip potential of a worker walking or working on sloped roof surfaces. A whole-body biodynamic model is proposed and used to develop the alternative method, in which the slip potential is expressed as an analytical function of its major controlling factors including coefficient of friction, slope angle, and biodynamic forces. Some experimental data available in the literature are used to demonstrate the application of the proposed method. The results suggest that the slope may not change the basic trends of the biodynamic forces, but the slope may affect their magnitudes, which can be explained using the system’s energy equation also derived from the whole-body biodynamic model. The analytical results suggest that reducing the body acceleration in uphill direction or the deceleration in downhill direction can reduce the slip potential. ‘Zigging’ and ‘zagging’ walking on a sloped surface may also reduce the slip potential, as it reduces the effective slope angle. The proposed biodynamic theory can be used to enhance the safety guidelines not only for roofers but also for people walking on ramps, inclined walkways, and mountain terrains.

Slips and falls remain very important safety issues among roof construction workers (

A large number of investigations on the slips and falls have been conducted, especially on level surfaces, and their basic mechanisms and characteristics have been understood (

On a level floor or surface, the shear force results fully from the human motions. Theoretically, it can be quantified from the distributed mass and acceleration of the human body according to Newton’s second law; hence, it is termed as biodynamic force in this study. On a sloped surface, the shear force includes not only the biodynamic force but also a portion of the gravitational force. The addition must increase the slip potential. The slope also increases the slip potential through reducing the ground reaction force in the normal direction, as the gravitational portion of the normal force reduces with the increase in the slope angle. In addition to these physical effects, the slope may also change the characteristics of the gait and ground reaction forces (

The same as the assessment of the slip and fall potentials on a level surface, the risk assessment on a sloped surface has been conventionally performed primarily through measuring the ground reaction forces in the shear and normal directions, calculating their ratio, and comparing the ratio with the dynamic coefficient of friction (CF) between the foot and the contact surface (

Some of these issues and scientific gaps can be addressed through developing biodynamic force-focused theory and method for the analysis and assessment of the slip potential. Because the slope-induced changes actually reduce the available friction force for supporting the human motions on a sloped surface, the slip potential on the sloped surface can be studied by examining the biodynamic shear force required for supporting the human dynamic motions, and comparing it with the maximum friction force available for the human dynamic motions. The objective of this study is to implement this concept to establish the basic biodynamic theory and to develop an alternative method for helping analyze and assess the slip potential on a sloped surface. Some experimental data available in the literature were used to demonstrate the application of the developed method. A general mechanical energy equation is also proposed to help analyze and understand the biodynamic forces on the sloped surfaces. Based on the proposed theory, method, and results, some hypotheses for further studies are also proposed and discussed.

Using the symbols shown and defined in

As mentioned earlier, these ground reaction forces generally include the human biodynamic forces and a portion of the static gravitational force acting on the human body. Their specific formulas can be derived from the equations of motions written based on Newton’s second law and the model shown in

where _{DX}, _{DY}, and _{DZ} are the biodynamic forces in the three orthogonal directions. The vector sum of the biodynamic forces distributed in the _{β}). Its magnitude and direction can be determined using the following formulas:

It should be noted that although the walking direction (

As above-mentioned, the human biodynamic forces in the three directions can also be calculated using the mass and acceleration distributed in the body (including carried tools and materials) in the three directions from the following formulas:

where _{X}, _{Y}, and _{Z} are the distributed accelerations in the three axial directions, _{X}, _{Y}, and _{Z} are the overall equivalent accelerations in the three directions.

The total ground shear force (_{S}) required for standing or walking on a sloped surface is the vector sum of the ground reaction forces measured in the

For the purpose of this study, the dynamic coefficient of friction (

In principle, the entire body mass of a person will not be at risk of slipping if _{S} < _{MAX}. Using

This equation can be alternatively written as follows:

If the total ground reaction forces in this equation are replaced with those distributed on each foot, it becomes the equation conventionally used in the assessment of the slip and fall potentials, i.e.

where RCF denotes required coefficient of friction and ACF denotes available coefficient of friction.

For the whole-body method considered in the current study, the _{β}, _{DZ}), slope angle (

In this equation, the human biodynamic forces and slope geometric factors are coupled together. It is very difficult to analyze and understand the specific role of each factor in determining the slip potential from this equation. This is a limitation of the conventional approach.

This difficulty can be alleviated by using the biodynamic approach proposed in this study. The required formulas for the proposed method can be derived from

Dividing this equation by the gravity force (

In this equation, _{β}/

This equation can be interpreted as follows: a slip will not occur if the normalized biodynamic shear force (on left side of the equation) is less than the normalized maximum friction force (on the right side of the equation) available for supporting the human motions on the surface. With

If RBCF ≥ ABCF, the slip will occur in the direction (

For each stance, the height change (_{T}), kinetic energy change (_{k}), and potential energy change (_{p}) can be expressed as follows:

where _{i} is initial step speed, and _{e} is end step speed.

In each stance, the mechanical energy (_{Traction}) gained from the traction force (_{β-T}: along walking direction) and the mechanical energy (_{Resistance}) consumed by the friction resistant force (_{β-R}: opposite to walking direction) are expressed as follows:

where

The biodynamic forces result from the human motions, but the resulted mechanical energy cannot be converted back to the biological energy stored in the human body. Then, the four types of mechanical energy expressed in

or

Dividing

Because the step length or distance (_{e} + _{i})}

in which

While the CF values for the roofers’ footwear on the roof surfaces were not found in the current literature, a preliminary experiment was conducted to explore the possible range of the CF values for parametric study of the slope effects on the slip potential on the roof surface. For this purpose, a simple tilt testing method (Angle of Repose Method) shown in

As an example, a set of experimental data reported by

As shown in _{DZ}), it has no interaction term with the slope factors in the equation; therefore, it can be ignored (or _{DZ} = 0) in the initial parametric study for identifying and understanding the basic roles of the CF, slope angle, and biodynamic force direction in determining the slip potential. Then, the ABCF formula expressed in

For demonstration purposes,

When _{β}) is in the straight uphill direction, as defined in

The corresponding ABCF_{β=90°} is the lowest among all the possible directions of the biodynamic shear force for each given slope angle, as shown in

When _{β=−90°} is the largest one at each slope angle, as also shown in

When

As also shown in _{β=0°} is substantially larger than that for

When 0° <

To demonstrate the effect of the normalized biodynamic normal force (_{DZ}/_{DZ}/_{DZ}/

The two forces for each slope angle can be input to the formulas in _{DZ}

As shown in

As also shown in

Before this study, it has been generally understood that the slip potential on a sloped surface depends on the dynamic CF, slope angle, ground reaction shear force, and ground reaction normal force (

This study confirmed that the dynamic CF is certainly the most important factor determining the slip potential, as reflected in

As shown

The worst case, however, usually occurs only when walking along a straight line in the uphill or downhill direction, when the shear force in the X direction is negligible. In such a scenario, the direction of the major traction or resistant force required for walking is aligned with the direction of the slope-induced additional biodynamic force in the Y direction. In any other walking direction, their directions must be different, as the required walking traction or resistant force should be approximately aligned with the working direction. This indicates that the

The magnitudes of the RBCF shown in

In the experiment reported by _{R}) must be greater than the average traction force (_{T}) if the slope angle is not equal to zero in downhill walking. Also, their difference must increase with the increase in the slope angle. This is consistent with the effect of the slope on the RBCF’s peak-to-peak values listed in

As shown

According to the energy equation (

The energy equation (

As dictated by

While the ground reaction forces simultaneously measured on both feet were not available for this study, the total ground forces assembled in this study may not accurately represent any real situation. While this should not affect the purpose of the application example, the values listed in

It should also be emphasized that the purpose of the proposed biodynamic method is not to replace the conventional method but to provide an additional tool to help analyze and understand the overall slip potential. In fact, these two methods can be complementary to each other. For example, while the conventional method is effective for detecting the potential instantaneous slip event on each foot that may occur during the heel striking phase during a normal walking, the proposed biodynamic method may provide a reasonable evaluation of the overall slip potential by considering the walking or working conditions (CF, slope angle, and possible range of biodynamic forces) without conducting any experiment. While the knowledge on the heel striking slip can help design a better heel of the footwear, the knowledge on the overall slip potential can provide a guidance to improve workers’ safe practices at workplaces. The conventional method may overestimate the risk of slip, as the single-foot slip probability is usually much larger than the fall probability (

The current study proposed a novel biodynamic method for analyzing and assessing slip potential on a slope surface. It enhanced the understanding of the biomechanics of slips in the following aspects: (1) it formulated a basic biodynamic theory for studying and understanding the slips on a sloped surface; (2) it developed an alternative method for analyzing the slip potential in any walking direction on the sloped surface; (3) it clearly identified mechanical effects of the slope angle and biodynamic force direction on the slip potential; and (4) it proposed to analyze and understand the biodynamical forces and their related slip potential from a view of mechanical energy. The proposed biodynamic method can be complementary to the conventional method for the analysis and assessment of slip potential.

This study confirmed that the most important physical factor that determines the slip potential on a sloped surface is the CF. This suggests that the selection of appropriate footwear with a high CF value should be considered as the first intervention method for workers working on sloped surfaces, as it is probably the least expensive, easily applicable, and most effective method to reduce slipping risk. As the CFs of footwear on various roof surfaces have been far from sufficiently studied, it is recommended to consider their measurements in further studies. The results of the study suggest that the slope angle as the second most important factor in determining the slip potential. A zigging and zagging walking strategy is likely to reduce the slip potential, as it reduces the effective slope angle. This walking strategy, however, may need further studies to help optimize its application, as the cross-slope walking may increase the injury potential of some substructures of the human body. Furthermore, this walking strategy becomes ineffective when the slope angle reaches a certain level. It is essential to use some fall protection devices when walking on a high pitch roof. The biodynamic shear force is generally ranked as the third important factor in determining the slip potential on sloped surfaces, but it may become a critical factor on a high pitch roof. The results of this study revealed some interactions between the slope angle and the biodynamic forces. While the slope may not change the basic trends of the human biodynamic forces, the slope may influence their peak magnitudes. Theoretically, the biodynamic forces are directly related to the accelerations of the human body. Any measure that can reduce the biodynamic forces or body accelerations can reduce the slip potential. The footwear may play an important role in determining the biodynamic forces and the body stability on the sloped surfaces, which should also be further studied to optimize the selection of the footwear.

The findings and conclusions in this manuscript are those of the authors and do not necessarily represent the views of the National Institute for Occupational Safety and Health, Centers for Disease Control and Prevention.

A whole-body biodynamic model of a person walking in a direction on a sloped surface: its global coordinate system has its _{X}, _{Y}_{Z} are the overall accelerations of the person in the three coordinate directions; _{X}, _{Y}_{Z} represent the total ground forces in the three directions; _{β}); ^{2}) is gravity acceleration.

The measurement of the coefficients of friction of six shoes on simulated roof surfaces: (A) Measurement principle; (B) Footwear tested for CF: 1–3 are roofer footwear and 4–6 are not considered roofer footwear; (C) Non-roofer footwear on oriented strand board (OSB); and (D) Roofer footwear on a standard asphalt shingle.

The method for calculating the total ground reaction force in each direction: the measured left foot ground force reported by

The ABCF as a function of the slope angle for several special cases (_{DZ} = 0; CF = 0.6, 0.7, 0.8; and

The effect of the biodynamic normal force (_{DZ}) on the ABCF as a function of the slope angle for several special cases (CF = 0.7; and

The total ground forces for different slope angles (0°, 5°, 10°, 15°, and 20°), which were derived using the method illustrated in

The required biodynamic coefficient of friction (RBCF) and its corresponding available biodynamic coefficient of friction (ABCF) with

The coefficients of friction of six models of shoes measured in the preliminary experiment.

Shoe ID | Description | Wood board | Shingle |
---|---|---|---|

1 | Models 1, 2, & 3 are advertised as roofers’ | 1.03 | 0.95 |

2 | shoes. | 0.87 | 0.95 |

3 | 0.74 | 0.97 | |

4 | Models 4, 5, & 6 are ordinary walking shoes. | 0.80 | 0.87 |

5 | 0.65 | 0.95 | |

6 | 0.63 | 0.78 |

The normalized biodynamic forces in shear direction (RBCF: peak-to-peak value) and normal direction (_{DZ}

Slope angle (deg.) | RBCF (Peak-to-peak) | _{DZ}/ | Min(ABCF-RBCF) | |||||||
---|---|---|---|---|---|---|---|---|---|---|

0 | 0.32 | 0.29 | 0.42 | 0.44 | 0.51 | 0.54 | 0.61 | 0.64 | 0.70 | 0.74 |

5 | 0.39 | 0.44 | 0.38 | 0.48 | 0.46 | 0.58 | 0.54 | 0.68 | 0.62 | 0.78 |

10 | 0.45 | 0.51 | 0.30 | 0.52 | 0.38 | 0.62 | 0.46 | 0.71 | 0.53 | 0.78 |

15 | 0.44 | 0.54 | 0.25 | 0.58 | 0.32 | 0.68 | 0.40 | 0.76 | 0.48 | 0.83 |

20 | 0.47 | 0.53 | 0.16 | 0.60 | 0.25 | 0.69 | 0.32 | 0.77 | 0.39 | 0.84 |