Relating grass failure on the landside slope to wave overtopping induced excess normal stresses
Introduction
In line with the new risk based safety assessments performed on levees in The Netherlands and Belgium, the probability of levee failure with respect to applied loads needs to be assessed. An important failure mechanism is erosion of the landside slopes by overtopping waves, as indicated by the 1953 flood of The Netherlands or the effects of Hurricane Katrina in 2004. The most common cover layer of these landside slopes consists of grass on clay. To evaluate the erosion resistance of grass covers on the landside slope of levees, multiple large scale wave overtopping experiments have been performed (Van der Meer et al., 2012). Based on these tests empirical approaches have been developed that relate the damage to grass covers to the local flow velocity, shear stress, or stream power (Dean et al., 2010; Hughes, 2011; Van der Meer et al., 2012).
In this paper, first the main characteristics of the existing empirical approached for predicting grass failure on landside slopes are discussed. Next, the inferred damage mechanism and the approach for evaluating the impact of the momentum transfer by normal stresses is presented in Section 2. In Section 3, the approach is validated against two field scale wave overtopping experiments. The results are evaluated in Section 4, and conclusions and recommendations are presented in Section 5.
Up to a decade ago damage to grass slopes on the landside slopes of levees was mostly related to the mean overtopping discharge (Van der Meer, 2002). Lately, more local hydraulic loads are used to empirically quantify the erosion resistance of grass covers subject to overtopping waves. Dean et al. (2010) used the critical velocity concept for steady overflow from CIRIA 116 (Hewlett, 1985), (Whitehead et al., 1976) to arrive at a relationship for the failure of levees due to overtopping. Dean et al. (2010) thereby related the damage initiation of grass to a mean excess velocity, excess shear stress, or excess stream power. The excess stream power showed the smallest errors and was therefore the recommended method of damage description. Van der Meer et al. (2012) extended the approach by Dean et al. (2010). Instead of using mean values for the shear stress or stream power, Van der Meer et al. (2012) hypothesized that peak loads during wave overtopping are likely to contribute significantly more to the onset of damage than mean loads. This led to the cumulative overload method. For a certain location on the grass cover, the cumulative overload method predicts a damage factor D from (Van der Meer et al., 2012).where is the critical velocity [m/s] and is the peak velocity [m/s] that follows empirically from (Van der Meer et al., 2012):
With V the wave overtopping volume [m2] and is a flow acceleration factor which will be larger than 1, increasing down the slope. According to Van der Meer et al. (2012) initial damage is expected when = 500, severe damage should be observed when = 1000 and complete failure occurs when = 3500. These values are prone to large scatter.
Characteristic of these approaches (Dean et al., 2010; Hughes, 2011; Van der Meer et al., 2012) is that damage is assumed to initiate when a velocity, shear stress, or stream power exceeds a critical value. The summation of the excess load is an indicator of the extent of the damage induced by overtopping waves. The cumulative overload method by Van der Meer et al. (2012) is stress based and consequently related to , whereas the mean excess load approach (Dean et al., 2010; Hughes, 2011) is energy based and uses . As the flow velocity increases along the landside slope, due to acceleration of the flow by gravity, damage is consequently most likely to initiate at the toe of the landside slope.
A close evaluation of the excess velocity, stress, or stream power (Dean et al., 2010; Hughes, 2011) or cumulative overload (Van der Meer et al., 2012) have highlighted two problems. First, critical velocity values required for these methods are difficult to quantify. During steady overflow tests performed on grass (van Damme et al., 2016; Cantré et al., 2017) it was noted that the critical velocity needed to initiate damage to the grass far exceed predictions given by Hewlett (1985) and Whitehead et al. (1976). Second, according to the excess stress or excess volume approach grass covers should predominantly fail near the bottom of the landside slope as the energy of the flow is maximum there due to the acceleration of the flow along the landside slope. However grass has also been observed to fail near the top of the landside slope. Below the second knowledge gap is addressed, whether damage initiation should be correlated only with the slope parallel flow velocity, or (also) with the peak in momentum transfer perpendicular to the levee. This is done by relating damage to the normal stresses exerted on the grass by overtopping waves.
During wave overtopping experiments performed at Wijmeers (van Damme et al., 2016) it was noted that overtopping waves separated at the end of the crest before reattaching with the landside slope, as can be seen in Fig. 1. The impact of an overtopping wave was more powerful and the impact zone was further down the landside slope than the impact of overtopping flow due to a higher flow velocity at the crest. It was inferred that at the point of reattachment both shear stresses and normal stresses are transferred to the levee surface. The significant normal stress component at the point of reattachment of overtopping waves causes for a peak in momentum transfer higher up the landside slope. Differences in normal stresses exerted on the landside slope of the levee between overflow and overtopping would explain why grass covers fail during overtopping but not during overflow. Here the hypothesis is tested whether the location of damage on the landside slope due to wave overtopping could be caused by peaks in momentum transfer due to the normal impact by overtopping waves.
Grass failure is expected to start with existing small cracks in the grass/clay cover (See Fig. 2a). These cracks are often present due to natural expansion and shrinkage of the clay cover. Normal forces exerted on the landside slope by overtopping waves (Fig. 2b) cause these cracks to widen. In accordance with Führböter (1966), the increase in water pressure in the crack during wave impact is expected to push the walls of the crack aside and cause for the crack to deepen. When the crack extends over the depth of the turf layer, grass can reasonably be expected to become subject to deformation due to lower cohesion of the clay under the turf layer compared to that of the root/clay mixture (Fig. 2c). The hole that originates under the grass cover will then cause for the grass aggregate to be pushed up (Fig. 2d), allowing for further expansion of the hole under the grass by flow induced scour. The continuous increase of space beneath the grass, causes grass aggregates to be pushed out of the soil. The flow over the grass cover and the overpressure under the grass cover separates the grass sod from the clay layer, making it roll up like a carpet in downstream direction, which is in accordance with observations made by Hai and Verhagen (2014). At a certain moment the induced pressure under the grass cover becomes too high leading to a piece of grass sod to be ripped from the grass cover and washed away by the flow.
Depending on the curvature of the levee at the intersection of the crest and landside slope overtopping waves separate from the landside slope at the downstream end of the crest before reattaching with the landside slope further down the landside slope (see Fig. 1). The point of reattachment of large volume waves is thereby located further downstream than for small volume waves. This is due to the higher horizontal flow velocity component at the downstream end of the crest. This process was observed during the Wijmeers overtopping experiments (van Damme et al., 2016) whereby immediate failure of the grass cover initiated after one 3000 l per m wave. The hypothesis that the location of grass failure is related to the summation of normal stresses exerted by overtopping waves to the slope at the location of reattachment is furthermore supported by reports on the overtopping experiments in Zeeland (Bakker et al., 2008). Here damage to the grass cover first initiated at the end of the landside slope where the flow was redirected and hence a significant momentum was exchanged with the grass cover. Based on this hypothesis a new approach was developed which relates the initiation of damage to the normal stresses at the point of reattachment. Hereonwards this approach is referred to as the wave impact approach.
Section snippets
Normal stresses acting on the grass cover
To evaluate the normal stresses exerted on the levee the location of wave impact is determined and compared to the location of the (initial) damage. In a Cartesian reference framework, the horizontal distance travelled by a wave is given by , where is the horizontal, time dependent, coordinate of reattachment relative to the intersection of the crest and landside slope, is the horizontal velocity component, t [s] is the separation time. During the separation time, the
Testing of the wave impact approach
The assumption that the failure of grass is related to the sum of normal stresses exerted on a slope during wave overtopping has been tested against the results of two wave overtopping experiments. The first experiment was the experiment performed at Wijmeers (van Damme et al., 2016) and the second was the overtopping experiments performed in Zeeland (Bakker et al., 2008). For those overtopping tests where damage on the landside slope occurred a value for the critical stress was determined
Discussion
Evaluating the predictions of the wave impact approach has highlighted some interesting aspects. First the locations where the grass failures initiated were all subject to normal stresses indicating that a peak in momentum transfer may better describe the initiation of grass failure than a peak in stream power of the flow. At the test site at Wijmeers a clay layer was present at the landside slope which was protected by a poor quality grass cover. The grass cover failed during the first test at
Conclusions and recommendations
This paper presents a new method for predicting the onset of failure of grass covered inner slopes of levees. The normal stresses exerted during wave overtopping events have been shown to exceed the resistance. The cumulative effect of normal stresses exerted by overtopping waves at the point of reattachment on the landside slope has been shown to be indicative of the onset of failure of grass covers. Besides the critical load at which damage to the grass cover commences, the method also
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