**1. Introduction**

Sand surfacing is seen on different sports such as, beach volleyball [1], equine racing [2,3] and greyhound racing [4–6]. The mechanical properties of the sand surface not only determines the performance of an athlete, be they human or a tetrapod, but also as an important injury contributing factor [7,8]. There is still a significant gap in understanding the behaviour of sand surface under impact load [9,10]. Accordingly, understanding the mechanical properties of sand surface, variables that alter the sand surface dynamic behavior, and methods to measure these variables, are of paramount importance.

The characteristics of the sand are identified through the shape, size and percentage of the sand particles. The shape of the sand particles can vary from a 'very angular' to a 'well rounded' shape [11] and is a key influence on the dynamic behaviour of the sand [12]. There are two key variables used to classify sand particles, namely 'roundedness' and 'sphericity' [13]. Figure 1 provides a pictorial representation of the various sand particle shapes. As much as roundedness is desirable in terms of the impact attenuation properties, angularity is not. When the particles are very angular, they tend to pack tightly as the sharp corners interlock and will resist the movement of the particles when subjected to an impact. In contrast, well-rounded particles tend to smoothly transit, or flow, to different locations upon impact [14].

The amount of water retained on the sand (the sand moisture contents) and the compaction rate (sand density), also determine the sand surface dynamic behavior [15,16]. Accordingly, in a sport arena, where it is assumed the characteristics of the sand is controlled, the sand moisture content and

density should be measured and compared against the safety benchmarks (The safety benchmark differs depending on the industry.) to avoid injuries. However, current safety benchmark, mainly those used in racing greyhound's arena, are not backed-up with science and research and are solely based on the experience of the track curators [2,17].

**Figure 1.** Sand particleshape in terms of sphericity, angularity and roundness [13].

An example of investigation on the effect on the sand moisture content and density on sports arena is a work conducted by Holt et al. [3], where the effect of sand moisture levels and rates of compaction of two different drainage systems (Limestone gravel and permavoid*TM* drainage), on the dynamic performance of synthetic equestrian surfaces (93.84% sand, 5.15% fibre and 1.01% binding polymer) was studied. They used the Orono Biomechanical Surface Tester (OBST) [18], a 2.25 kg Clegg hammer [19] and a 30 kg traction device equipped with a horseshoe. The OBST, which simulates the collision of horse forelegs and the ground, was dropped four times on each surface for each treatment. The Clegg hammer was dropped four times based on the protocol recommended by ASTM Standard [20]. A 30 kg traction device, which was also used to measure the traction of the surface, was dropped once in four different locations of the test chamber for each treatment from a height of 200 mm.

Thiel et al. [1] mainly focused on the dry sand and designed a penetrometer to measure the stiffness of beach dry sand in-situ. To validate their method, their results were compared with that of a in-laboratory study, where the penetrometer test were conducted on a sand box [21]. It is claimed that their results are similar to the in-lab study and their method can be used to measure the stiffness coefficient of the sand, prior to a sporting event on the dry sand.

Force transducer, mainly the wearable sensor, are extensively used for gait analysis as they are cheap, easy to use, and user friendly [22]. Therefore, inertial inertial measurement units (IMU) have been used in different applications, mainly in clinical setting for gait analysis [22].

IMU technology can be also used to study the limb-surface interaction. In a recent studies conducted by the same author of this work, a single IMU was used to study the impact of different sports surfacing (grass vs wet sand) on the locomotion dynamics of galloping greyhounds [4–6]. Details of the most recent work [4] are discussed in the following sections. Worsey et al. [16], also used IMU technology (9 degrees of freedom (DOF) inertial-magnetic sensors, incorporating an 16 G-accelerometer, gyroscope, and magnetometer) to compare athletes running over three different surfacing (running track, hard sand, and soft sand). The purpose of this work was to provide more insight on a previously observed fact that athletes alter their gait mechanics to accommodate different running surfaces [23].

Mathematical modelling, mainly Spring-Loaded-Inverted-Pendulum (SLIP) models, firstly introduce by Blickhan et al. [24] are extensively used for gait analysis in different fields of science and engineering. SLIP models are simple and easy to interpret, yet provide substantial information about the under-studied subjects [24]. There are numerous off-the-shelf SLIP models, which one can modify based on their application. For instance, a SLIP model of a greyhound galloping

on sport sand surfacing was modelled to study the effect of the sand surface with different moisture content levels and rate of compaction on the canine locomotion dynamics [25]. The results showed that small changes in sand surface mechanical properties can significantly affect the amount of force acting on the greyhound hind-leg which well correlates with the high rate of hind-leg severe injuries in this industry.

It was discussed previously that the ideal track surface should have enough impact attenuation properties to damp the initial impact shock, as well as providing enough traction for a stable gallop [26–28]. The surface with ideal mechanical properties has a low amount of energy loss and low impact acceleration (G*max*) when the foot comes into contact with the surface. The low energy loss, would also increase the performance of the animal in the race [29].

The surface with high performance was associated with a higher risk of injuries. By contrast, the surface with impact attenuation properties tended to increase the muscular effort of the runner which affected their running performance [2].

The low density of the sand or the rates of compaction are also associated with the low rates of injury [30]. In practice, For sand sport surfacing, 'harrowing' is suggested, which can reduce the density or the rates of surface compaction [31]. However, a very low density surface may have a detrimental effect on locomotion efficiency as it affects the support needed for grip and propelling the body forward [2].

Surface traction is another variable identifying a safe surface composition. High traction will increase the bending moment applied to the bones, mainly the tarsal bones, and increase the risk of injuries [7]. However, not enough traction, usually seen in drier sands, will cause the surface not to sufficiently support the limb during the stance. Accordingly, as suggested by Holt et al. [3], increasing the moisture content of the sand while keeping its density low would result in a surface ideal in both race performance and injury reduction [3]. Overall, apart from acting as a supporting surface, the sand layer also acts as an energy absorbing layer to mitigate the impact shock. The optimal condition of the sand layer should have enough energy absorbing capacity (reflected as energy loss and contact time) while providing acceptable surface traction [32,33].

Contact time is another critical variable that affects the safety performance of the surface. The shorter the contact time, the higher the risk of injuries, because of an increased load rate to the musculoskeletal system [34,35]. Accordingly, this variable is considered as one of the primary safety thresholds in different applications such as playground surfacing tests [36,37].

The purpose of this work is to introduce methods to study the dynamic behaviour of athletic sand surfaces, with the aim of improving athletes performance while minimising the risk of injuries. The methods introduced here were originally designed for greyhound racing arenas but are adaptable to other sports such as horse racing [3], beach relay and sand volleyball [1].

## **2. Materials and Methods**

#### *2.1. A Drop Test to Study the Dynamic Behaviour of the Sport Sand Surfaces*

It is discussed above that the sand characteristics contribute to the dynamic behaviour of the sand, mainly under impact loads. Below the sand particle sizes and percentages recommended for greyhound racing arena are given in Table 1.

The sample was taken from a typical greyhound racing arena. The sample was then oven dried for 24 h based on the AS 1289 Part 2.1.1 Standard [38]. As per the Standard, the sand sample should be heated up in an oven, between 105 to 110◦ for 16 to 24 h.

The sample was then loaded on the sieve shaker. The procedure adopted for this test was following the AS 1289 Part 3.6.1 2009 Standard [38]. To do so a sieve shaker, model EFL 2000, was used. As per the Standard, the size of the sieve tray was selected from 4.75 mm to 75 μm. The procedure was done as such the EFL 2000 were not overloaded. In the case of any sieve being overloaded, the overloaded sieve sample was further sieved into two or more portions. The sieve shaker was set to

shake for a time duration in between 5–10 min so that the sand was completely separated according to their sizes. The same procedure was repeated for 6 samples of soil.


**Table 1.** Recommended sand particle sizes and percentage for greyhound racing surfaces.

The calculations for generating the grading curve plots, which is based on AS 1289 Part 3.6.1 2009 Standard [38] is given below Equations (1) and (2):

$$\text{Percent retained } (\%) = \frac{\text{Mass of the particles retained on selected sieve}}{\Sigma \text{Total retained mass}} \times 100 \text{ \%} \tag{1}$$

*Mass o f soil retained* = *mass o f the selected sieve with soil* − *mass o f empty sieve* (2)

Once the percent retained is calculated. The cumulative percent retained for each sieve tray is calculated by adding the percent retained from the largest size sieve to the current size sieve, and then the percentage of the sand passing through the current sieve size can be obtained through Equation (3):

$$Percent\,\,\text{passing}\,\,(\%) = 100 - \text{cumulative\,\,percent\,\,retained.}\,\text{total}.\tag{3}$$

The sand grading curve is plotted and given in Figure 2. The cumulative percent passing is plotted against the sieve size (in logarithmic scale).

**Figure 2.** Typical soil grading curves for a greyhound racing surface.

The soil grading curve given above proved the fact that the soil used in the greyhound racing track is loamy sand, combination of sand with traces of clay [39]. The slight difference in each test can

be attributed to the loss of soil during the test and therefore caution should be taken while conducting the test.

The sand moisture content and compaction rate are two important parameters that alter the mechanical behaviour of the sand. To study the effect of these two parameters on the dynamic behavior of the sand, collected from a typical sport arena (in our case, it was collected from a typical greyhound racing arena), an impact test which complies with AS 1289 Part 2.1.1 Standard [38], can be applied.

To perform the impact test, a conventional Clegg hammer was modified, by mounting two calibrated laboratory-grade Endevco high-G accelerometers. Adding the high-G precision accelerometers allowed a higher degree of experimental accuracy than that offered by the standard Clegg hammer. The reliability of the system was tested in previous studies on children's playgrounds for impact attenuation of surfacing [36,37].

The dynamic behaviour of the sand sample was studied by analysing the impact data, namely the maximum acceleration (G*max*), the maximum rate of change of acceleration (Jerk) (J*max*), the impact duration (contact time), and the energy loss. Before treating the sand sample, it should be again air or oven dried. The AS 1289 Part 2.1.1 Standard [38] is used to dry the sand sample. Based on the Standard, the sand sample was heated up in an oven, between 105 to 110◦ for 16 to 24 h.

The effect of three moisture levels—dry (12%), medium to ideal (17%), and ideal (20%); and three rates of compaction: low traffic (1.35 g/cm3), medium traffic (1.45 g/cm3), and high traffic (1.55 g/cm3), on the dynamic behaviour of the sand sample, were studied. The density of the sand to replicate the traffic condition of the surface was previously used by Holt et al. [3].

For all three conditions, we used a cylindrical container with an inner diameter of 15.6 cm. The sand was filled at 3.0 cm increments until reaching the depth of 12.0 cm. The applied tampering here was manual. Preferably, the tamper should be equipped with an accelerometer which can provide a measure of the applied force. However, achieving a certain depth was the only possible control we could apply. The average of sand density (the mass of the sand sample divided by its volume) for the simulated traffic conditions was also calculated and given as follows:


**Figure 3.** (**A**) Low traffic condition with the density of 1.35 g/cm3. (**B**) Medium traffic condition with the density of 1.45 g/cm3. (**C**) High traffic condition with the density of 1.55 g/cm3.

After preparing the sand sample, an impact attenuation test, which complied with the ASTM-F3146 Standard [20], was conducted from three different heights, namely: 400 mm, 500 mm and 600 mm. Based on the Standard, the test was repeated four times from each height, and the maximum value was reported that is, the maximum value for G*max*, J*max* and contact time. After the fourth drop at each height in the same location, the sand sample was reconstructed to avoid the effect of over compacting of the lower layers on the results. The impact attenuation data were then post-processed using LabVIEW software and plotted in MATLAB R18. An ANOVA test (two-factor with replication) was conducted. Values of *p* ≤ 0.05 were considered statistically significant. The experimental setup is illustrated below in Figure 4.

**Figure 4.** The process of drying the sand sample, altering the moisture content and impact testing using a modified Clegg hammer.
