Residual strength of grass on clay in the wave impact zone. Basis for safety assessment method of WTI-2017, product 5.10

Transcription

1 Residual strength of grass on clay in the wave impact zone Basis for safety assessment method of WTI-2017, product 5.10

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3 Residual strength of grass on clay in the wave impact zone Basis for safety assessment method of WTI-2017, product 5.10 Mark Klein Breteler Product Deltares, 2015, B

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5 Title Residual strength of grass on clay in the wave impact zone Client Rijkswaterstaat WVL Project Reference HYE-0004 Pages 29 Keywords Dike, grass erosion, wave impact zone, safety assessment Summary This research has been carried out in the framework of WTI, Research and Development of Flood Defense Assessment Tools (Wettelijk Toetsinstrumentarium), which is called in Dutch: WTI-2017 Onderzoek en ontwikkeling landelijk toetsinstrumentarium. The objective of WTI programme is to provide a new set of safety assessment tools for water defences in 2017, while Cluster 5 of this program is focusing on dike revetments and residual strength. This is product 5.10 of The present study focuses on the erosion of grass in the wave impact zone on dikes. The wave impact zone is below the still water level. The residual strength of grass in the wave impact zone is primarily of interest for river dikes. On the other dikes the waves at design conditions are mostly so large that the dike is usually protected with a hard revetment in the impact zone. The research focuses on the grass layer and the upper 50 cm of the clay layer, in which roots more or less influence the erosion resistance of the clay. It deals with the erosion of the grass and clay after initial damage. A number of large-scale tests in the Delta Flume of Deltares and recent tests with the Wave Impact Generator have formed the basis for a new formula for the erosion of clay under grass due to wave attack, after initial damage to the grass. The resulting formula also includes the influence of transition structures and objects (like niet-waterkerende objecten, NWO's). With these formulae a procedure is given for the safety assessment of dikes with grass on clay in the wave impact zone. Samenvatting In het kader van het WTI-2017, Onderzoek en ontwikkeling landelijk toetsinstrumentarium, is onderzoek uitgevoerd naar de reststerkte van klei onder gras in de golfklapzone. Dit is vooral relevant voor rivierdijken, omdat die een grasbekleding hebben in de golfklapzone (onder de stilwaterstand). Op andere dijken is de golfbelasting zo zwaar dat er een harde bekleding in die zone wordt toegepast. Het onderzoek richt zich op de bovenste 50 cm van de kleilaag, direct onder het gras, waar wortels de erosiebestendigheid min of meer vergroten. Het gaat hierbij in dit rapport om de erosie van de klei en gras door golfaanval nadat initiële schade aan het gras is ontstaan. Er is in het verleden een aantal grootschalige proeven in de Deltagoot van Deltares uitgevoerd, aangevuld met proeven met de Golfklapgenerator. Op basis daarvan zijn nieuwe formules afgeleid voor de erosie door golfbelasting, waarin ook de invloed van enkele nietwaterkerende objecten is opgenomen. Met deze formules is een procedure gegeven voor de periodieke toetsing op veiligheid voor gras op klei in de golfklapzone. Residual strength of grass on clay in the wave impact zone

6 Title Residual strength of grass on clay in the wave impact zone Client Rijkswaterstaat WVL Project Reference HYE-0004 Pages 29 References Research and Development of Flood Defense Assessment Tools (WTI-2017, Onderzoek en ontwikkeling landelijk toetsinstrumentarium), Cluster 5, product 5.10 Version Date Author Initials Review Initials Approval Initials 1 Nov Mark Klein Breteler Jentsje vd Meer Marcel van Gent 3 June 2015 Mark Klein Breteler Jentsje vd Meer Marcel van Gent State Final Residual strength of grass on clay in the wave impact zone

7 Contents 1 Introduction 1 2 Results of large scale tests Large-scale flume tests Green Dike of Friesland with slope of 1: Grass dike with slope of 1: Grass slope of Oosterbierum and Harculo Tests with the wave impact generator 6 3 Erosion formula Plain grass slope without transitions or NWO's Influence of transitions and NWO's 15 4 Safety assessment method for wave impact zone 17 5 Conclusions 23 6 References 25 Residual strength of grass on clay in the wave impact zone i

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9 1 Introduction This research has been carried out in the framework of WTI, Research and Development of Flood Defense Assessment Tools (Wettelijk Toetsinstrumentarium), which is called in Dutch: WTI-2017 Onderzoek en ontwikkeling landelijk toetsinstrumentarium. The objective of WTI programme is to provide a new set of safety assessment tools for water defences in 2017, while Cluster 5 of this program is focusing on dike revetments and residual strength. This is product 5.10 of The present study is about the residual strength of the grass and clay layer in the wave impact zone on dikes, which is below the design water level (or determining water level in the safety assessment). The residual strength is the duration from initial damage (a 20 cm deep erosion of the grass cover) until dike failure (start of dike breach). The dike is considered to fail if the remaining crest height is lower than the water level, see Figure 1.1. At that moment a considerable amount of water is flowing into the hinterland. For practical reasons several components of the strength are considered. This is for example for river dikes with a sand core and clay layer with grass: strength of the grass against initial damage by wave attack residual strength of the grass and clay until the erosion has reached a depth of 50 cm (in the top 50 cm it is assume that the roots influence the erosion resistance) residual strength of the clay layer beneath the depth of 50 cm (zone with a negligable amount of roots) residual strength of the sand core All of these components together are the residual strength of the dike. The other components are quantified by Klein Breteler et al (2012) and Mourik (2015). grass on clay initial damage road sand grass on clay failure of clay terrace cliff road sand grass on clay failure of dike sand Figure 1.1 Cross-section of typical Dutch dike with a grass revetment and failure process due to wave attack Residual strength of grass on clay in the wave impact zone 1 of 29

10 The present report focuses only on the residual strength of the top 50 cm of the clay layer with grass, because in this layer the grass roots more or less influence the erosion resistance of the clay. Deeper into the clay (at a larger distance from the grass surface) it is assumed that the influence of the roots is negligible. Although the erosion process by waves proceeds into the dike primarily in a horizontal direction (see Figure 1.1), the erosion depth is taken as the most important parameter for the safety assessment. This erosion depth is measured perpendicular to the slope surface and can be compared directly with the layer thickness of the clay. The residual strength of grass in the wave impact zone is primarily of interest for river dikes. On the other dikes the waves at design conditions are mostly so large that the dike is protected with a hard revetment in the impact zone. The clay is assumed to be structured. The structuring of clay is caused by the influence of the weather, such as dry/wet and cold/warm seasons and related physical, biological and chemical processes in the clay layer. It leads to a so-called macro soil structure, here referred to as structured clay. The processes result in cracks and fissures in the clay, disintegrating the layer into large and small lumps of clay (several mm up to a few decimeter) in a specific vertical profile with decreasing intensity with depth, near vanishing below about m in The Netherlands. This kind of structured clay is typical for Dutch dikes. The objective of the study is to analyse the available large-scale tests in order to derive an erosion formula which can be used in the safety assessment method. The safety assessment method for grass on dikes will contain the first 3 components of the above list. The present report focuses only on the second component: the residual strength of the grass and top 50 cm of the clay. It is developed for river dikes, which usually have a slope of 1:3.5 to 1:3, design wave attack with a wave height H s < 1.0 m and rather large wave steepness (H s /L op = 0.04 to 0.06). In rare cases the significant wave height can be slightly higher than 1.0 m. Very small waves (H s < 0.5 m) are less relevant in this study, because these will not lead to initial damage of the grass cover. The initial damage of the grass is assumed in this study to be a small hole with a diameter of 30 cm and depth of 20 cm. If the hole in the grass is smaller, than it is not considered as damage. From this initial situation the damage usually grows quite easily to a hole with a larger surface, but with a depth in the same order of magnitude. In the present study attention is focused on the growth of the depth, which is a much slower process (see also Van Steeg, 2014). All mentioned depths and layer thicknesses in this report are measured perpendicular to the slope surface. The formulae developed here give the mean value, while the uncertainty is described as a standard deviation, assuming a normal distribution. In the future safety factors should be introduced in the formulae to account for the uncertainties, based on the given quantification of the uncertainties. The latter will be derived later with the help of Cluster C (Uncertainties) of the WTI-2017 programme. That will eventually lead to a semi-probabilistic safety assessment method, with formulae containing safety factors which match the acceptable probability of failure. 2 of 29 Residual strength of grass on clay in the wave impact zone

11 2 Results of large scale tests 2.1 Large-scale flume tests The erosion resistance of grass and clay can only be measured in a large scale facility, because neither the grass nor the clay can be reproduced on small scale. The erosion resistance of grass and residual strength of the clay layer with grass under wave attack has been investigated several times in the Delta Flume of Deltares and once in the Groe Wellen Kanal in Hannover. The results of the large scale tests carried out before 2010 were summarised by Verheij et al (2011). All tests were carried out with blocks of clay excavated from real dikes, although those used in the Groe Wellen Kanal were rather thin (only 30 cm). The tests in the Groe Wellen Kanal (see Verheij et al 2011) didn't provide any useful information about the residual strength Green Dike of Friesland with slope of 1:8 The first research with grass and clay in the Delta Flume was carried out for the Green Dike of Friesland (Burger, 1984). The model setup had a grass slope of 1:8, constructed from blocks of clay with grass from Friesland. It was sandy clay with the sand content ranging from 45% to 60%, with a rather large content of small stones and shells (a few percent of the volume). The latter is not reported, but is clearly visible in the pictures. The report unfortunately gives hardly any information on the clay. The slope of the dike was unusual gentle compared to river dikes. The consequence was that wave impacts are less violent then on dikes with a normal steepness. The residual strength was measured by creating initial damage of 7 cm deep under the water line (2 spots of 20x50 cm 2 ) and performing a test with waves of H s = 1.57 m (T p = 5.26 s). The size of this initial damage is different than used in more recent research, where an artificial damage of 30 cm diameter and depth of 20 cm is applied. After 6 hours of continuous wave action the maximum erosion depth increased approximately 37 cm. The surface area of the erosion had grown to 2.6 m Grass dike with slope of 1:4 Smith (1994) has carried out tests in the Delta Flume on a dike protected with a clay layer with grass on a slope of 1:4. Unfortunately, the clay characteristics were not measured. It is assumed that the clay was rather sandy, considering the location in Friesland where the clay was obtained. At the end of the test series the residual strength was measured. The tests started with initial damage of 10 to 15 cm deep, with a local pit of 20 cm deep near the side wall, which was formed in a natural way by the previous tests. The length of the erosion perpendicular to the waterline was approximately 6 m in a region where the erosion depth was 5 to 10 cm. The length with erosion of at least 15 cm was only 0.4 m (close to the side wall). Residual strength of grass on clay in the wave impact zone 3 of 29

12 After 4 hours of wave attack with waves of H s = 1.38 m (T p = 4.69 s) the maximum depth of the erosion had increased approximately 67 cm near the side wall (local pit) and approximately 33 cm elsewhere with a length perpendicular to the waterline of approximately 4 m. The width of the erosion along the side wall was less than 1 m. The erosion along the flume wall was probably affected by the presence of the side wall and the initial opening of a few millimetres between the side wall and the clay. From the above numbers we see an erosion rate of approximately 17 cm/hour. Further away from the side wall, at a location which was not affected by the side wall, the erosion rate was about half of the erosion rate at the side wall: 8 cm/hour Grass slope of Oosterbierum and Harculo In framework of the present research programme (WTI-2017) two tests were carried out in the Delta Flume, reported by Van Steeg (2014). The tests were carried out with a slope of 1:3, with grass and clay from Oosterbierum on a 2 m wide slope on one side of the flume and with grass and clay from Harculo on the 2 m wide slope on the other side. In this way the two types of grass and clay could be tested simultaneously. The clay from Oosterbierum had a sand content of 49% and that from Harculo 68%. The grass and clay from Oosterbierum were from the inner side of a sea dike, which is a freshwater region and is therefore not different from grass and clay on a river dike. The dike was built with a long slope with 8 clay blocks of 2x2x0.8 m 3 on either side. The erosion in each test was usually concentrated in a 2 to 3 m long zone, which offered the possibility of conducting 3 test series at different water levels. The tests with the smallest wave height gave so little erosion, that the test with the largest wave height was conducted at the same zone. All tests were carried out with a wave steepness of s op = H s /((g/2)t p 2 ) 0,05, since this is a typical wave steepness at river dikes. The main test results are given in Figure 2.1 and Figure 2.2. The graphs show the maximum erosion depth on the vertical axis and the duration of the test on the horizontal axis. The erosion starts at a depth of 20 cm, which was the artificially made initial damage. The diameter of the artificial damage was 30 cm. Also results of the wave impact generator (wave height of H s 0.65 m) are given in the graph, which will be explained in more detail in section 2.2. The erosion rate of Oosterbierum was larger for H s = 0.7 m than for H s = 0.9. This is probably because of variations of the clay quality. This will be included in the analysis by introducing a standard deviation of the results. From these test results the average erosion rate is derived (erosion velocity). The erosion rate is the increase of the erosion depth per hour. The result is given in Figure 2.3 and Figure 2.4 as a function of the significant wave height H s. In these figures also the maximum measured erosion rate is given, which provides insight in the variability of the erosion rate. Notice that the erosion rate for waves with H s < 0.5 m is zero. Apparently there is a threshold above which the erosion starts. The relation between the wave height and the erosion rate is assumed to be linear, as is concluded from the tests in the Delta Flume of Van Steeg (2014) and the analysis of Mourik (2015), see also section of 29 Residual strength of grass on clay in the wave impact zone

13 0.80 maximum depth d_max (m) duration t (hours) Figure 2.1 Maximum erosion depth as function of time (Oosterbierum) Delta Flume Hs = 0.5 m Delta Flume Hs = 0.7 m Delta Flume Hs = 0.9 m Delta Flume Hs = 1.1 m Wave impact generator 0.80 maximum depth d_max (m) duration t (hours) Figure 2.2 Maximum erosion depth as function of time (Harculo) Delta Flume Hs = 0.5 m Delta Flume Hs = 0.7 m Delta Flume Hs = 0.9 m Delta Flume Hs = 1.1 m Wave impact generator The relation between the erosion depth and the load duration turns out to be approximately linear as well: d e t. This is surprising, because Klein Breteler et al (2012) found a linear relation between the erosion volume and the load duration: V e t. Since d e V e we expected to find d e t. During the Delta flume tests it was noticed that the erosion quite quickly leads to a very large damaged area (large width and length), while the erosion depth remains quite limited. The width of the erosion hole (perpendicular to the waterline) was usually 4 to 5 times larger than the depth. The erosion terrace was rather short in these tests (see Figure 1.1 for the definition of the terrace and cliff). These aspects can explain the very limited influence of the erosion depth on the erosion rate, leading to a linear relation between the depth and the load duration. The same linear trend was also found in the test results from the wave impact generator (see Figure 2.6). This linear relation might only be the case for a limited erosion depth (of up to approximately 0.5 m). It could well be that for a larger erosion depth the relation becomes d e t. Residual strength of grass on clay in the wave impact zone 5 of 29

14 Figure 2.3 Erosion rate (erosion depth increase per hour) during tests on Oosterbierum clay and grass Figure 2.4 Erosion rate (erosion depth increase per hour) during tests on Harculo clay and grass 2.2 Tests with the wave impact generator To measure the erosion by wave impacts a Wave Impact Generator has been developed, see Figure 2.5 (Van Steeg 2013). It consists of a water tank with two valves in the bottom that can be opened very quickly to release the water from the tank. The falling water with a width of 0.4 m hits the grass surface and generates a wave impact and some wave run-up. Different fill levels give different impacts and these were validated against impacts measured in the Delta Flume. By repeating the generation of impacts for thousands of times the erosion of the grass can be measured as a function of the number of impacts. Since it is known how many 6 of 29 Residual strength of grass on clay in the wave impact zone

15 wave impacts per hour occur during wave attack, this number can be translated to a duration of the hydraulic load. The horizontal cross section of the wave impact generator is 2.0 x 0.4 m 2. It releases the water in an angle of approximately 45 which matches roughly the normal angle of a wave tongue when hitting the grass surface. The test setup is such that the erosion rate of various locations (with different clay quality and grass quality) can be compared. It is not a full simulation of all impacts in a sea state since all small impacts and the very large ones are missing, but this is regarded as sufficient for the purpose of comparison. Figure 2.5 Wave impact generator During the design and construction phase of the wave impact generator many tests have been carried out with pressure cells in the wave impact zone (Van Steeg 2012). These tests were compared with the pressure measurements on slopes in the Delta flume with real waves. This analysis has led to the conclusion that the wave impact generator generates wave impacts of waves with a significant wave height of approximately 0.7 m. With tests in the Delta Flume (Van Steeg 2014) on grass and clay from Oosterbierum and Harculo this conclusion was further evaluated, based on the measured erosion. It was concluded that the wave impact generator generates wave impacts of waves with a significant wave height of approximately H s 0.65 m. The erosion with real waves in the Delta flume with a wave height of H s 0.65 m gave a similar erosion rate as the tests with the wave impact generator. The wave impact generator has been used to measure the erosion rate at four locations in the Netherlands (Van Steeg 2013). The main characteristics of these sites are given in Table 2.1. At Oosterbierum it was the inner slope of the dike along the Waddensea, at Harculo the outer slope of the dike along the River IJssel, at Berkum it was the outer slope of the River Vecht and at Olst it was the bank of a canal (Soestwetering). Grass coverage Root quantity Soil quality Sand content Oosterbierum 99% good poor clay 49% Harculo 86% poor poor clay 68% Olst 78% poor Very poor clay 89% Berkum 98% moderate sand 97% Table 2.1 Main characteristics of grass and clay at the test sites These locations were selected because the grass or clay quality was rather poor and in one case even sand. It means that the majority of dikes will have a lower erosion rate than Residual strength of grass on clay in the wave impact zone 7 of 29

16 measured on these dikes (larger residual strength). Based on experience these locations were put in a specific class of river dikes by Gerard Kruse (clay expert at Deltares): Oosterbierum: 40 à 50% of the Dutch dikes have a lower clay quality. Harculo: 10 à 30% of the Dutch dikes have a lower clay quality. Olst: 10 à 20% of the Dutch dikes have a lower clay quality. Berkum: 0 à 10% of the Dutch dikes have a similar or lower soil quality. Prior to the tests an artificial erosion with a cylindrical shape was made (initial damage). This artificial erosion had a diameter of 30 cm and a depth of 20 cm. During the tests it was noticed that at first the erosion primarily grew in the top grass layer (of a few cm thickness), enlarging the eroded surface. The erosion hole hardly deepened. This could be seen as the residual strength of the grass cover, which turned out to be rather small. From this it was concluded that the grass in the upper 20 cm hardly contributes to the residual strength and is therefore not considered separately. Once initial damage occurs (as was done artificially in these tests) the erosion grows rather quickly in this zone. However, the erosion depth increases only slowly under the wave impacts, unless the soil quality is very poor, such as sand. From this observation it was concluded that the grass quality hardly influences the residual strength, as long as some minimum grass quality is present (still to be defined). It is assumed that this influence can be neglected. The test results on plain grass are as follows (definition 2 of Van Steeg (2013)): erosion from an initial depth of 20 cm up to an erosion depth of 50 cm): Oosterbierum: residual strength 18 hour Harculo: residual strength 17 hour Olst: residual strength 5 hour Berkum: residual strength 4 hour depth d (m) Oosterbierum Harculo Olst Berkum 50 cm depth duration of wave attack (hours) Figure 2.6 Measured erosion depth for the test sites with wave impact generator From these results we see that the residual strength is substantial, unless the clay quality is very poor. At these locations additional tests have been carried out on objects and transition structures: Oosterbierum at stairs on sand: residual strength 1 hour Harculo at an asfalt road: residual strength 17 hour Harculo at a pole: residual strength 16 hour Olst at transition to concrete slope: residual strength 1 hour Berkum at transition with concrete grass tiles: residual strength 9 hour 8 of 29 Residual strength of grass on clay in the wave impact zone

17 These tests have been carried out in the same way as the other tests, starting with an initial damage with diameter of 30 cm and depths of 20 cm. The stairs at Oosterbierum were placed on a layer of sand, which eroded very quickly. The presence of the sand is the reason why the residual strength is so low at this location. The road and the pole at Harculo had no influence, although the grass quality at the pole was much worse than elsewhere at this location. Along the concrete slope at Olst the soil was not very well compacted and very sandy, leading to an even smaller residual strength. During the test at the transition structure at Berkum it was noticed that the erosion hole could not grow in upward direction, as it usually does, because of the concrete grass tiles. This has led to a larger residual strength than on plain grass. Residual strength of grass on clay in the wave impact zone 9 of 29

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19 3 Erosion formula 3.1 Plain grass slope without transitions or NWO's The basis for a safety assessment method is a formula to predict the erosion of the clay under the grass after initial damage. In this chapter a formula is derived from the results of Delta Flume tests and Wave Impact Generator tests described in the previous chapter. It is first focused on a plain grass slope without the influence of objects in the grass, transitions to hard revetments/roads or not-water-retaining objects (niet-waterkerende objecten, NWO's). The validity of the results is restricted to the tested circumstances. This means that it is only meant for grass with closed or open sods (not for fragmental grass; fragmentarische zode) (see definition in RWS 2012) with clay or sand subsoil. It is assumed that waves attack perpendicular, which probably gives more erosion then oblique wave attack, leading to safe results. Furthermore, it is assumed that in the initial erosion is a small hole of 30 cm diameter and 20 cm depth. The relatively small size of the area of the initial erosion is expected to have only a minor influence on the results, because the growth of the area is quite quick compared to the growth of the erosion depth. For residual strength we focus primarily on the erosion depth. At first the erosion process is such that the damaged surface quickly grows, but hardly deepens. This phase hardly contributes to the residual strength and is further neglected. This is independent on the grass quality. It is therefore assumed that the grass quality also has a negligible influence on the rate in which the erosion hole deepens. Influence of wave height on the erosion rate The tests in the Delta Flume of Van Steeg (2014) are first used to find the relation between the erosion rate (increase of the erosion depth per hour) and the significant wave height. From the tests it was concluded that there is a threshold at approximately H 0.5 m, beyond which the erosion starts. The following formula was suggested by Van Steeg ( means proportional to ): R e H 0.5 s With: R e = erosion rate (increase of erosion depth per hour) (m/h) H s = significant wave height at the toe of the dike (m) Influence of the slope steepness on the erosion rate The available Delta flume test have been carried out with slopes in a range of 1:3 to 1:8. This range is so wide, that we have to include the influence of the slope steepness in the analysis. This influence of the slope will be neglected in the final erosion formula, which is used in the safety assessment procedure, because the slope of Dutch river dikes vary only in a small range. We need to include this influence of the slope angle only because of the large range of slope angles in the available Delta Flume tests (see chapter 2). The influence of the slope angle on the erosion rate has been studied by (Mourik 2015). In appendix A his formulae have been used to extend formula (1) with the influence of the slope angle. The result is: R H 0.5 (tan ) e s 1.5 (1) (2) Residual strength of grass on clay in the wave impact zone 11 of 29

20 This formula is used to analyse the available test results. Analysis of available test results The next step is to find the proportionality constant in above formula, which might be dependent on the type of clay. The tests with the wave impact generator have shown that the influence of the grass is negligible as long as the grass is similar to the tested grass: with open or closed sods (not fragmental grass; fragmentarische zode). The proportionality constant c d = R e /((H s 0.5)tan 1.5 ) can easily be derived from the test results. Figure 3.1 shows the results given in the previous chapter as a function of the sand content F sand Oosterbierum, average Harculo, average c d (-) Green Dike slope 1:8 Slope 1:4 Smith (1994) Wave impact generator average trend upper border 90% confidence interval Sand content (-) Figure 3.1 Measurements of c d = R e/((h s 0.5)tan 1.5 ) For the wave impact generator tests the slope angle is less relevant, because a specific wave impact is created, irrespective of the slope angle. For the figure it is assumed that all tests have been carried out on a slope of 1:3. The sand content of the tests on the green dike with slope of 1:8 (Burger 1984) is not exactly known. It is between 45 and 60%. The measurement point in the figure has been put at the average (52.5%). The erosion rate turns out to be remarkably high compared to the other tests. The reason for this is still unknown. The size of this initial damage (50x20x7 cm 3 ) is different than used in more recent research, where an artificial damage of 30 cm diameter 12 of 29 Residual strength of grass on clay in the wave impact zone

21 and depth of 20 cm was applied, but it is not expected that this is the reason for the large erosion rate. In most tests we noticed that the erosion surface quite quickly grows, but the erosion depth increases much slower. The much smaller depth of the initial damage would rather lead to a smaller erosion rate in the first part of the test of Burger, but this is not reported. The sand content of the tests of Smith (1994) is unknown. Since it is assumed to be sandy clay, the measurement point has been put at 50%. The process of finding the best fit line and 5% exceedance level was started by analysing the data points at approximately 50% sand content and at approximately 70% sand content. To calculate the average and standard deviation the average erosion rate over several hours of wave attack are used as they are plotted in Figure 3.1, see also Table 3.1. The average values per test are used, because the total erosion after several hours of wave attack is most relevant for the residual strength. Delta Flume, Van Steeg (2014) H s (m) R e /(H s 0.5)/tan 1.5 Sand content Sand content F sand 50% F sand 70% Sand content F sand 90% Burger (1984) Smith (1994) Wave impact generator, Van Steeg (2013) Average Standard deviation % exceedance level Table 3.1 Measurements of c d = R e/((h s 0.5)tan 1.5 ) This procedure has led to the surprising result that the 5% exceedance level is higher at a sand content of 50% then at the sand content of 70%. This is primarily due to the limited amount of tests with a sand content of 70%. It was expected that the erosion rate would not decrease with increasing sand content. Therefore, we fall back to the assumption made by Klein Breteler et al (2012) and Klein Breteler (2013) that the clay quality and sand content has little influence on the erosion rate as long as the sand content and amount of sand inclusions are lower than a certain limit. Following this assumption we have calculated the average, standard deviation and 5% exceedance level for all tests in the range of F sand = 50 70%. The result is: Average: (c d ) = 0.59 standard deviation: (c d ) = % exceedance level: = 1.12 These results are assumed to be valid for clay with F sand < 70%. For a higher sand content it is assumed that the c d -value increases linearly, matching the two results from the wave impact generator with F sand 90%. Unfortunately, there is no proper information on the 5% exceedance level at F sand 90%. It is assume that the width of the 5% confidence interval is equal for all values of the sand content. Residual strength of grass on clay in the wave impact zone 13 of 29

22 Note that the standard deviation is so large that a negative erosion rate seems possible. Therefore these values are only used to estimate a 5% exceedance level. This leads to the following formula for the erosion of the clay under grass, after initial damage to the grass: e d s 0.5tan 1.5 R c H With: Average: cd 0.6 max 0 ; 8Fsand 0.7 5% exceedance level: c 1.1 max 0 ; 8F 0.7 (4) d (5) This formula can be simplified for practical applications for Dutch river dikes with slope steepness of approximately 1:3 and wave attack with < s op < 0.060: R c H e c s With: 0.5 Average: cc 0.1 max 0 ; 1.5Fsand 0.7 5% exceedance level: c 0.2 max 0 ; 1.5 F 0.7 sand (7) c (8) These results can be used for grass (with open sods or closed sods; not fragmental grass; geen fragmentarische zode ) on naturally formed clay with a limited quantity of organic material. The maximum amount of organic material is limited to 5%, just as required by TAW (1996). The top 20 cm with grass roots may contain more than 5% organic material. Artificial clay, thermally cleaned soil and peat are excluded. The formula predicts the average erosion rate during the erosion of the clay layer up to a depth of 50 cm after initial damage to the grass and gives for this average the expected value (with the average c d ) and a value of the 5% exceedance level. The residual strength, defined as the duration of erosion from an erosion depth of 20 cm (initial damage) to 50 cm, is: dc 0.2 trs, grass (9) R e With: d c = clay layer thickness (with maximum of 50 cm because of the definition of this component of the residual strength) (m) t RS,grass = residual strength of grass and clay up to a erosion depth of 50 cm (hour) The 20 cm is subtracted in this formula because the initial damage to the grass has already led to an erosion of 20 cm. Example: Situation: The example dike has a slope of 1:3.5 and can have wave attack with waves of H s = 0.8 m. The sand content of the clay is 55%. Question: what is the residual strength of the grass and clay up to a depth of 50 cm after initial damage with a depths of 20 cm? sand R c H 0.5 tan = c d ( )*(1/3.5) 1.5 = 0.046c d. The average Answer: 1.5 e d s value of c d is c 0.6 max 0 ; 8F 0.7 d = 0.6, which leads to an expected sand (3) (6) 14 of 29 Residual strength of grass on clay in the wave impact zone

23 erosion rate of R e = = m/h. The 5% exceedance level of the erosion rate is R e = = m/h. This leads to an expected residual strength of ( )/0.027 = 11 hours and a lower limit of the 5% confidence interval of the residual strength of 6 hours. The final value for c c for the periodic safety assessment of Dutch dikes is going to be determined by Cluster C (dealing with uncertainties), based on the information given in this report. 3.2 Influence of transitions and NWO's The influence of transitions (where the grass ends against a hard pavement, block revetment or asphalt) or objects (niet waterkerende objecten, NWO's) has been investigated with the wave impact generator (Van Steeg 2013). Klein Breteler et al (2014) has analysed the results and concluded that an influence factor f NWO should be added to the formula for the erosion rate: R e c c H f s 0.5 NWO (10) with: f NWO = influence of transition structures and NWO's (-) This influence factor includes the influence of transitions and NWO s. The value of f NWO according to the test results is: grass along stairs on sand: f NWO = 0.06 grass along an asphalt road on a berm with clay under and along the asphalt: f NWO = 1.0 grass around a pole with 15 cm diameter: f NWO = 0.94 grass along a concrete revetment on a slope with poor clay and poor compaction: f NWO = 0.2 grass along a transition with concrete grass tiles on clay: f NWO = 2.3 (1.0) In these values it is assumed that the results of the tests are representative for other similar cases. Note that a value larger than 1 will lead to the conclusion that plain grass without the transition structure or NWO will determine the safety assessment outcome. This means that in practical cases it is useless to calculate with f NWO > 1. Therefore the value of f NWO is changed to 1.0 for grass along a transition with concrete grass tiles on clay. The number of tests is rather small, which means that the results should be used cautiously. Fortunately, the test results were very clear: some NWO's showed hardly any influence, while others had a very strong influence, without results in between. Therefore, it is assumed to be useful, although the number of tests is only small. During the tests of Smith (1994) a large and deep hole developed along the side wall of the flume. It is very likely that the erosion was influenced by this wall and also by the probably poor contact between the wall and the clay block. Also the research of Van Steeg (2014) suffered problems with an open joint between the clay and side wall, although the clay was pushed with hydraulic jacks firmly against the side wall. Residual strength of grass on clay in the wave impact zone 15 of 29

24 This is probably the worst case situation for grass along a vertical wall (building, sluice, etc) on a real dike. The test results showed an erosion rate which was twice as high compared to the tests on the plain grass slope. Since this only occurred on one side of the flume, it is assume that this higher erosion rate is primarily caused by the open joint between the clay and the side wall. This is confirmed with recent tests by Van Steeg (2015), who did tests with the wave impact generator along a wall perpendicular to the waterline. He found no difference in the erosion rate compared to the situation with plain grass. In practical cases various angles of wave attack occur (see Figure 3.2). A dike with a wall with oblique wave attack will have an increased water motion along the wall, probably leading to a larger erosion rate than without the wall. Oblique wave attack, however, will probably give less violent wave impacts than perpendicular wave attack. Combining these influences leads to the estimation of a slightly higher erosion rate along the wall for small angles of wave attack (smaller f NWO ), but slightly smaller erosion rate for large angles (larger f NWO ). This has not been tested and can therefore not be included in the safety assessment method. These cases should be assessed with an advanced safety assessment method (toets op maat). Vertical wall Vertical wall crest slope toe Wave direction Equal erosion along the wall as on plain grass Larger erosion along the wall than on plain grass Figure 3.2 Top view of dike with vertical wall on the slope (provided there is an excellent contact between the clay and the wall) 16 of 29 Residual strength of grass on clay in the wave impact zone

25 4 Safety assessment method for wave impact zone Initial damage of grass The safety assessment of the grass and clay in the wave impact zone on a river dike starts with evaluating whether the grass will fail or not: is it likely that initial damage will occur. This part of the safety assessment method falls outside the scope of this study. The safety assessment procedure regarding initial damage is given by Rijkswaterstaat (2012). This procedure distiguises open sods on poor clay (open zode, schrale grond), open sods on good clay (open zode, stevige grond) and closed sods on poor or good clay (dichte zode, schrale grond / stevige grond). The maximum acceptable wave load duration is given in Figure 4.1. Figure 4.1 Load duration until initial damage occurs in the wave impact zone (Rijkswaterstaat 2012) If the grass doesn't pass the safety assessment procedure regarding initial damage (load duration is longer than the duration until damage), the residual strength of the grass and top 50 cm of the clay should be evaluated. This is done with the formulae derived in the previous chapter, and is further explained in this chapter. Although the wave conditions and water level will vary during the storm, the detailed safety assessment is carried out with the highest wave conditions and most unfavourable water level during the entire duration of the wave load. This will lead to a safe result. In an advanced safety assessment the calculation can be carried out more accurately by including the influence of the variation of wave conditions and water level. This method is explained at the end of this chapter. The wave height should be adjusted if it is expected that waves will break on the foreshore. The maximum wave conditions in a limited water depth can be calculated with (Caires 2012): Hs dl/2 max 0.5 (11) Residual strength of grass on clay in the wave impact zone 17 of 29

26 With: H s = significant wave height at the toe of the dike (m) [H s ] max = maximum value of H s due to wave breaking on the foreshore (m) d L/2 = water depth at a distance of L op /2 from the dike, in the direction from where the waves approach (m) L op = gt 2 p /(2) 1.2gT 2 m-1,0 /(2) = equivalent wave length on deepwater (m) T p = wave period at the peak of the spectrum (s) T m-1,0 = spectral wave period (s) g = acceleration of gravity (m/s 2 ) Residual strength of grass The residual strength of the grass and top 50 cm of the clay is calculated with the following formula for open grass and closed grass sods (not fragmental grass; geen fragmentarische zode ) for a slope steepness of approximately 1:3 and H s > 0.5 m: cc Hs 0.5 Re (12) fnwo min( dc; 0,5) 0.2 trs, grass (13) R e With: R e = erosion rate (increase of erosion depth per hour) (m/h) f NWO = influence of transition structures and NWO's (-) c c = constant, dependent on the sand content (hour 1 ) = slope angle ( o ) t RS,grass = residual strength of the grass and top 50 cm of the clay (hour) The value of c c has to be determined by Cluster C of the WTI-2017 research programme, based on the information given in this report. Preliminary values are: Average: cc 0.1 max 0 ; 1,5 Fsand 0.7 5% exceedance level: c 0,2 max 0 ; 1,5 F 0.7 (14) With: F sand = sand content of the clay (-) c (15) These formulae can be used for grass (with open sods or closed sods; not fragmental grass, geen fragmentarische zode ) on naturally formed clay with less than 5% organic material (TAW 1996). Artificial clay, thermally cleaned soil and peat are excluded. The influence of transitions and NWO s is included in the parameter f NWO. The value has been derived from the results of the wave impact generator tests: grass along stairs on sand: f NWO = 0.06 grass along an asphalt road on a berm with clay under and along the asphalt: f NWO = 1.0 grass around a pole with 15 cm diameter: f NWO = 0.94 grass along a concrete revetment on a slope with poor clay and poor compaction: f NWO = 0.2 grass along a transition with concrete grass tiles on clay: f NWO = 1.0 sand 18 of 29 Residual strength of grass on clay in the wave impact zone

27 If the clay is also present under the stairs, in stead of sand as in the tested case, the residual strength is probably much larger. In that case the residual strength can be estimated with the formulae of Mourik (2015), derived for clay under a hard revetment. The most relevant value for the sand content is the average in a few cubic metres of clay. For the residual strength of clay, where a few cubic metres of erosion per metre of dike is important, the average erodibility is more important than the erodibility measured for samples with a volume of about a litre at a specific point in the dike (Koelewijn et al 2014). The average sand content can easily be measured by creating a mixed sample, with some clay taken from a number of points in the dike at a specific cross-section. 1. Calculate the wave load duration until failure of the grass cover layer (Rijkswaterstaat, 2012) 2. Is this duration longer than the storm? yes no 3. Calculate duration of the residual strength of the grass and top 50 cm of the clay (in hours) with the formulae given in this chapter. 4. Is the duration until failure of the grass cover layer (step 1) plus the duration of the residual strength of the grass and top 50 cm of the clay (step 3) larger than the storm duration? yes no Is the clay layer thicker than 50 cm? yes no Calculate the residual strength of the clay below 50 cm under the grass surface (see e.g. Klein Breteler 2013). Is the the duration until failure of the grass cover layer (step 1) plus the residual strength of the grass and top 50 cm of the clay (step 3) plus the residual strength of the clay below 50 cm under the grass surface (step 5) larger than the storm duration? yes no Grass and clay are sufficiently safe Grass and clay are insufficient Figure 4.2 Flow chart of the safety assessment process regarding the residual strength of clay under grass. Residual strength of grass on clay in the wave impact zone 19 of 29

28 The evaluation in the safety assessment will be as follows with this formula (detailed safety assessment), see also Figure 4.2: 1 Calculate the wave load duration until failure of the grass cover layer (Rijkswaterstaat, 2012) 2 If this duration is longer than the storm, the grass is sufficient. If not, then proceed with the next step. 3 Calculate the duration of the residual strength of the grass and top 50 cm of the clay (duration in hours) with the formulae given in this chapter. 4 If the duration until failure of the grass cover layer (step 1) plus the duration of the residual strength of the grass and top 50 cm of the clay (step 3) is longer than the storm duration, then the grass is sufficient. If not, proceed with the next step. 5 If the clay layer is thicker than 50 cm, then calculate the residual strength of the clay below 50 cm under the grass surface (see e.g. Klein Breteler 2013). If not, then the grass and clay or insufficient. 6 If the duration until failure of the grass cover layer (step 1) plus the duration of the residual strength of the grass and top 50 cm of the clay (step 3) plus the duration of the residual strength of the clay below 50 cm under the grass surface (step 5) is longer than the storm duration, then the grass is sufficient. If not, the grass and clay are insufficient. Advanced safety assessment In an advanced safety assessment there are a number of ways of improvement compared to the detailed safety assessment. Two of these are: Divide the storm in small periods if there are varying wave conditions or water level during the storm Divide the slope in segments A more accurate way of dealing with varying hydraulic boundary conditions (water level and wave conditions), then just taking the highest water level and wave conditions, is to divide the storm into smaller parts. In each small part the water level, wave height, wave period and wave direction are assumed to be constant. With these boundary conditions the erosion in each part can be calculated. By simply adding up the erosion during all parts, the total erosion is obtained. Note that this method assumes that the erosion hole is shifting along the slope, following the water level. This will overestimate the total erosion and is therefore a safe approximation. In HR 2006 (Min. V&W 2007, fig. 2-2 up to 2-11) a prescribed water level as function of time was given for the 3 rd round of the periodic safety assessment. It is assumed that these will be updated in the WTI These form the basis for the calculation of the hydraulic load duration of each grass section (see Figure 4.3). A more refined procedure for the safety assessment can be achieved by dividing the slope into a number of small sections and carry out the above procedure for each of these sections. This can be done by taking into account that the section is only subjected to a hydraulic load by wave impacts as long as the water level is within a certain range. The upper limit of this range is H s /2 above the upper limit of the section and the lower limit is at the same height as the lower limit of the section, see Figure 4.3. This range is similar as given in the VTV2006 at page 338. Because the water level is only during a limited time in the specified range, the load duration of the section is smaller than if the grass slope is considered as a whole. 20 of 29 Residual strength of grass on clay in the wave impact zone

29 Water level range with impacts on section i Section 2 Section 1 H s/2 Section i Figure 4.3 Division of grass slope in sections and water level range relevant for section i. These two improvements of the safety assessment procedure are not a part of the detailed safety assessment, but can be carried out in the advanced safety assessment. In the advanced safety assessment there is also a possibility to include the influence of the width of the dike. Especially if it is calculated that the grass will fail at a section which is much lower than the crest, the dike width will be quite large at this level. At such a level the residual strength of the entire dike is larger than for sections closer to the crest. It is advised to carry out a probabilistic calculation of the probability of failure of the dike in the advanced safety assessment. Residual strength of grass on clay in the wave impact zone 21 of 29

30

31 5 Conclusions The present study focuses on the erosion of grass in the wave impact zone on river dikes. The wave impact zone is below the still water level. A number of large-scale tests in the Delta Flume of Deltares and recent tests with the Wave Impact Generator has formed the basis for a new formula for the erosion of clay under grass due to wave attack, after initial damage to the grass. The resulting formula also includes the influence of transition structures and objects (like niet-waterkerende objecten, NWO's). The derived formulae for the erosion of grass in the wave impact zone is: cc Hs 0.5 Re f NWO Provided grass with open sods or closed sods (not fragmental grass; geen fragmentarische zode ), naturally formed clay (no artificial clay or thermally cleaned soil or peat) with less than 5% organic material below 20 cm under the clay surface and 0.5 < H s < 1.5 m and slope of approximately 1:3. With: R e = erosion rate (increase of erosion depth per hour) (m/h) f NWO = influence of transition structures and NWO's (-) c c = constant, dependent on the sand content (hour 1 ) = slope angle ( o ) H s = significant wave height at the toe of the dike (m) The value of c c is dependent on the sand fraction F sand : Average: cc 0.1 max 0 ; 1,5 Fsand 0.7 5% exceedance level: c 0,2 max 0 ; 1,5 F 0.7 (16) (17) c (18) If the wave conditions are only mild (H s < 0.5 m) the erosion velocity is negligible (R e 0). In such cases the grass passes the safety assessment, irrespective of the storm duration. sand The duration of the residual strength can be calculated with: min( dc; 0,5) 0.2 trs, grass R e t RS,grass = residual strength of the grass and top 50 cm of the clay (hour) d c = clay layer thickness (m) (19) The influence of transitions and NWO s is included in the parameter f NWO. The value has been derived from the Wave Impact Generator tests: grass along stairs on sand: f NWO = 0.06 grass along an asphalt road on a berm with clay under and along the asphalt: f NWO = 1.0 grass around a pole with 15 cm diameter: f NWO = 0.94 grass along a concrete revetment on a slope with poor clay and poor compaction: f NWO = 0.2 grass along a transition with concrete grass tiles on clay: f NWO = 1.0 Residual strength of grass on clay in the wave impact zone 23 of 29