NR
Niels Ruiter
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Master thesis
(2026)
-
L. Belkacem, Bas Hofland, Marcel van gent van Gent, Niels Ruiter, T.M. Ruwiel
Rubble-mound breakwaters armoured with single-layer interlocking concrete units, such as the Xbloc, get their stability from the way the units interlock across the whole armour layer. The standard design rules for these units come from model tests on uniform slopes. But designers increasingly need to add a horizontal berm on the seaward side with a sharp transition between lower slope and the berm. The berm dissipates more wave energy, which allows a lower crest without too much overtopping, and this is useful where the crest must be kept low for visual or functional reasons. A berm breaks up the interlocking network: it adds slope transitions that concentrate the wave load, and the units on the flat part lose the downward pressure that normally comes from the units higher up the slope. The uniform-slope formulae can therefore not be used directly for a bermed cross-section. Yet it is not known how the berm geometry affects the Xbloc stability, or where the damage starts. This thesis fills that gap. The aim was to find how berm width and height affect Xbloc stability, and where the damage begins.
The stability of Xbloc armour on a bermed breakwater was studied through two-dimensional physical model tests in a wave flume. Five cross-sections were examined: four with a berm, combining two widths ($6D_n$ and $9D_n$) and two elevations (at the still-water level and emerged above it), and one no-berm reference cross-section. Each section was loaded with irregular waves whose height was increased in steps, at two wave steepnesses. The armour response was quantified through three indicators, rocking, settlement and extraction, recorded by visual observation and by image correlation of the cross section before and after each loading step to obtain the displacement fields.
The results show that rocking, settlement and extraction are different aspects of the same armour response. Rocking and settlement develop together as the load increases, and extraction is the most severe response, occurring only at very high wave loads.
Rocking was quantified using the cumulative rocking number $N_{or,\mathrm{cum}}$, which counts every unit that rocked at any prior loading step. On every bermed cross-section the critical rocking limit ($N_{or,\mathrm{cum}} = 0.20$) was reached at only $70$--$90\%$ of the standard uniform-slope design wave height ($N_s = 1.96$--$2.53$), well below the standard uniform-slope value ($N_s \approx 2.77$). The reference cross-section reached the same limit much later, between $N_s = 2.84$ and $3.07$. The berm therefore lowers the stability number by $\Delta N_s \approx 0.5$ to $1.1$. Rocking concentrated at the seaward berm edge and the top row of the lower slope, and migrated landward across the berm, while the upper slope and crest stayed largely stable. On the reference cross section, by contrast, rocking spread along the seaward side around water level and reached the crest, without forming a single weak point. The berm therefore both lowers the stability and concentrates the damage at the transition.
Settlement developed in two different forms. On the lower slope the units settled coherently downslope and compacted tighter. On the berm the units moved apart and some toward each other and opened gaps, the divergent movement that caused the loss of interlocking. The maximum row-averaged settlement reached about $0.35\,D$ on two sections, above the $0.3\,D$ settlement limit, while the global average stayed below this limit on every section. The upper slope settled less on the bermed sections than on the reference cross section. This shows that the berm dissipates the incoming wave energy, which reduces the wave load on the upper armour.
Extraction occurred only at high loads ($N_s \gtrsim 3.4$) and only on the emerged berms\textbf{;} no units were extracted on the still-water-level berms or the reference cross section within the tested range. On the still-water-level berms the water running over the units held the loosened units in place.
Berm elevation was the main influential geometric parameter, while berm width had no clear effect. The emerged berms rocked more than the still-water-level berms and were the only sections where units were extracted. Widening the berm from $6D_n$ to $9D_n$ did not change the damage location and quantity. The wave conditions acted in the same direction on all three indicators: all forms of damage increased with wave height, and the longer, less steep waves ($s_{0p}=0.02$) were the more damaging condition, producing more cumulative rocking and most of the extraction events.
When the three forms of damage are examined together, cumulative rocking and lower-slope settlement rise together on every section. As the seaward edge rocks and its units diverge, the gaps at the lower-slope-to-berm transition widen with settlement. As settlement increases, the gaps widen, varying from $\approx 0.4\,D$ to roughly $0.9\,D$. Furthermore, the gaps only reach a full unit diameter ($\approx 1\,D$) on the emerged berms, which are the exact configurations where unit extraction occurred. Tracking individual units revealed that those losing their interlock at the transition were the exact units later extracted. The lower-slope settlement at first extraction ranged from about $0.22\,D$ to $0.41\,D$, around the $0.3\,D$ limit. This gap widens about $2.5$ times faster than the settlement, and reaches a full diameter only on the sections that lost units. It therefore reflects the loss of interlocking more directly than the maximum row averaged settlement. A transition-gap limit of about $0.5\,D$ is recommended as the design damage criterion for bermed breakwaters.
These findings show that a horizontal seaward berm lowers the stability of an Xbloc layer by breaking up its interlocking network, with the extent of this stability loss determined primarily by the berm elevation relative to the water level rather than by its width. This is because the seaward transition row loses the support of the units that would otherwise sit above it on a continuous slope. The standard uniform-slope stability number ($N_s \approx 2.77$) is therefore not a safe value for a bermed cross-section, and rocking, rather than extraction, is the more reliable design indicator. If a horizontal berm is retained, the seaward units must be enlarged to recover the lost stability, requiring an increase of roughly $50$--$56\%$ in nominal diameter and about $3.5$--$3.8$ times the unit mass. To address this critical vulnerability at the transition zone and restore the necessary interlocking support, the study recommends reshaping the cross-section to work with the interlocking mechanism by rounding the slope--berm transition and giving the berm a gentle seaward slope. This modified cross-section should be tested in future physical-model studies.
...
The stability of Xbloc armour on a bermed breakwater was studied through two-dimensional physical model tests in a wave flume. Five cross-sections were examined: four with a berm, combining two widths ($6D_n$ and $9D_n$) and two elevations (at the still-water level and emerged above it), and one no-berm reference cross-section. Each section was loaded with irregular waves whose height was increased in steps, at two wave steepnesses. The armour response was quantified through three indicators, rocking, settlement and extraction, recorded by visual observation and by image correlation of the cross section before and after each loading step to obtain the displacement fields.
The results show that rocking, settlement and extraction are different aspects of the same armour response. Rocking and settlement develop together as the load increases, and extraction is the most severe response, occurring only at very high wave loads.
Rocking was quantified using the cumulative rocking number $N_{or,\mathrm{cum}}$, which counts every unit that rocked at any prior loading step. On every bermed cross-section the critical rocking limit ($N_{or,\mathrm{cum}} = 0.20$) was reached at only $70$--$90\%$ of the standard uniform-slope design wave height ($N_s = 1.96$--$2.53$), well below the standard uniform-slope value ($N_s \approx 2.77$). The reference cross-section reached the same limit much later, between $N_s = 2.84$ and $3.07$. The berm therefore lowers the stability number by $\Delta N_s \approx 0.5$ to $1.1$. Rocking concentrated at the seaward berm edge and the top row of the lower slope, and migrated landward across the berm, while the upper slope and crest stayed largely stable. On the reference cross section, by contrast, rocking spread along the seaward side around water level and reached the crest, without forming a single weak point. The berm therefore both lowers the stability and concentrates the damage at the transition.
Settlement developed in two different forms. On the lower slope the units settled coherently downslope and compacted tighter. On the berm the units moved apart and some toward each other and opened gaps, the divergent movement that caused the loss of interlocking. The maximum row-averaged settlement reached about $0.35\,D$ on two sections, above the $0.3\,D$ settlement limit, while the global average stayed below this limit on every section. The upper slope settled less on the bermed sections than on the reference cross section. This shows that the berm dissipates the incoming wave energy, which reduces the wave load on the upper armour.
Extraction occurred only at high loads ($N_s \gtrsim 3.4$) and only on the emerged berms\textbf{;} no units were extracted on the still-water-level berms or the reference cross section within the tested range. On the still-water-level berms the water running over the units held the loosened units in place.
Berm elevation was the main influential geometric parameter, while berm width had no clear effect. The emerged berms rocked more than the still-water-level berms and were the only sections where units were extracted. Widening the berm from $6D_n$ to $9D_n$ did not change the damage location and quantity. The wave conditions acted in the same direction on all three indicators: all forms of damage increased with wave height, and the longer, less steep waves ($s_{0p}=0.02$) were the more damaging condition, producing more cumulative rocking and most of the extraction events.
When the three forms of damage are examined together, cumulative rocking and lower-slope settlement rise together on every section. As the seaward edge rocks and its units diverge, the gaps at the lower-slope-to-berm transition widen with settlement. As settlement increases, the gaps widen, varying from $\approx 0.4\,D$ to roughly $0.9\,D$. Furthermore, the gaps only reach a full unit diameter ($\approx 1\,D$) on the emerged berms, which are the exact configurations where unit extraction occurred. Tracking individual units revealed that those losing their interlock at the transition were the exact units later extracted. The lower-slope settlement at first extraction ranged from about $0.22\,D$ to $0.41\,D$, around the $0.3\,D$ limit. This gap widens about $2.5$ times faster than the settlement, and reaches a full diameter only on the sections that lost units. It therefore reflects the loss of interlocking more directly than the maximum row averaged settlement. A transition-gap limit of about $0.5\,D$ is recommended as the design damage criterion for bermed breakwaters.
These findings show that a horizontal seaward berm lowers the stability of an Xbloc layer by breaking up its interlocking network, with the extent of this stability loss determined primarily by the berm elevation relative to the water level rather than by its width. This is because the seaward transition row loses the support of the units that would otherwise sit above it on a continuous slope. The standard uniform-slope stability number ($N_s \approx 2.77$) is therefore not a safe value for a bermed cross-section, and rocking, rather than extraction, is the more reliable design indicator. If a horizontal berm is retained, the seaward units must be enlarged to recover the lost stability, requiring an increase of roughly $50$--$56\%$ in nominal diameter and about $3.5$--$3.8$ times the unit mass. To address this critical vulnerability at the transition zone and restore the necessary interlocking support, the study recommends reshaping the cross-section to work with the interlocking mechanism by rounding the slope--berm transition and giving the berm a gentle seaward slope. This modified cross-section should be tested in future physical-model studies.
...
Rubble-mound breakwaters armoured with single-layer interlocking concrete units, such as the Xbloc, get their stability from the way the units interlock across the whole armour layer. The standard design rules for these units come from model tests on uniform slopes. But designers increasingly need to add a horizontal berm on the seaward side with a sharp transition between lower slope and the berm. The berm dissipates more wave energy, which allows a lower crest without too much overtopping, and this is useful where the crest must be kept low for visual or functional reasons. A berm breaks up the interlocking network: it adds slope transitions that concentrate the wave load, and the units on the flat part lose the downward pressure that normally comes from the units higher up the slope. The uniform-slope formulae can therefore not be used directly for a bermed cross-section. Yet it is not known how the berm geometry affects the Xbloc stability, or where the damage starts. This thesis fills that gap. The aim was to find how berm width and height affect Xbloc stability, and where the damage begins.
The stability of Xbloc armour on a bermed breakwater was studied through two-dimensional physical model tests in a wave flume. Five cross-sections were examined: four with a berm, combining two widths ($6D_n$ and $9D_n$) and two elevations (at the still-water level and emerged above it), and one no-berm reference cross-section. Each section was loaded with irregular waves whose height was increased in steps, at two wave steepnesses. The armour response was quantified through three indicators, rocking, settlement and extraction, recorded by visual observation and by image correlation of the cross section before and after each loading step to obtain the displacement fields.
The results show that rocking, settlement and extraction are different aspects of the same armour response. Rocking and settlement develop together as the load increases, and extraction is the most severe response, occurring only at very high wave loads.
Rocking was quantified using the cumulative rocking number $N_{or,\mathrm{cum}}$, which counts every unit that rocked at any prior loading step. On every bermed cross-section the critical rocking limit ($N_{or,\mathrm{cum}} = 0.20$) was reached at only $70$--$90\%$ of the standard uniform-slope design wave height ($N_s = 1.96$--$2.53$), well below the standard uniform-slope value ($N_s \approx 2.77$). The reference cross-section reached the same limit much later, between $N_s = 2.84$ and $3.07$. The berm therefore lowers the stability number by $\Delta N_s \approx 0.5$ to $1.1$. Rocking concentrated at the seaward berm edge and the top row of the lower slope, and migrated landward across the berm, while the upper slope and crest stayed largely stable. On the reference cross section, by contrast, rocking spread along the seaward side around water level and reached the crest, without forming a single weak point. The berm therefore both lowers the stability and concentrates the damage at the transition.
Settlement developed in two different forms. On the lower slope the units settled coherently downslope and compacted tighter. On the berm the units moved apart and some toward each other and opened gaps, the divergent movement that caused the loss of interlocking. The maximum row-averaged settlement reached about $0.35\,D$ on two sections, above the $0.3\,D$ settlement limit, while the global average stayed below this limit on every section. The upper slope settled less on the bermed sections than on the reference cross section. This shows that the berm dissipates the incoming wave energy, which reduces the wave load on the upper armour.
Extraction occurred only at high loads ($N_s \gtrsim 3.4$) and only on the emerged berms\textbf{;} no units were extracted on the still-water-level berms or the reference cross section within the tested range. On the still-water-level berms the water running over the units held the loosened units in place.
Berm elevation was the main influential geometric parameter, while berm width had no clear effect. The emerged berms rocked more than the still-water-level berms and were the only sections where units were extracted. Widening the berm from $6D_n$ to $9D_n$ did not change the damage location and quantity. The wave conditions acted in the same direction on all three indicators: all forms of damage increased with wave height, and the longer, less steep waves ($s_{0p}=0.02$) were the more damaging condition, producing more cumulative rocking and most of the extraction events.
When the three forms of damage are examined together, cumulative rocking and lower-slope settlement rise together on every section. As the seaward edge rocks and its units diverge, the gaps at the lower-slope-to-berm transition widen with settlement. As settlement increases, the gaps widen, varying from $\approx 0.4\,D$ to roughly $0.9\,D$. Furthermore, the gaps only reach a full unit diameter ($\approx 1\,D$) on the emerged berms, which are the exact configurations where unit extraction occurred. Tracking individual units revealed that those losing their interlock at the transition were the exact units later extracted. The lower-slope settlement at first extraction ranged from about $0.22\,D$ to $0.41\,D$, around the $0.3\,D$ limit. This gap widens about $2.5$ times faster than the settlement, and reaches a full diameter only on the sections that lost units. It therefore reflects the loss of interlocking more directly than the maximum row averaged settlement. A transition-gap limit of about $0.5\,D$ is recommended as the design damage criterion for bermed breakwaters.
These findings show that a horizontal seaward berm lowers the stability of an Xbloc layer by breaking up its interlocking network, with the extent of this stability loss determined primarily by the berm elevation relative to the water level rather than by its width. This is because the seaward transition row loses the support of the units that would otherwise sit above it on a continuous slope. The standard uniform-slope stability number ($N_s \approx 2.77$) is therefore not a safe value for a bermed cross-section, and rocking, rather than extraction, is the more reliable design indicator. If a horizontal berm is retained, the seaward units must be enlarged to recover the lost stability, requiring an increase of roughly $50$--$56\%$ in nominal diameter and about $3.5$--$3.8$ times the unit mass. To address this critical vulnerability at the transition zone and restore the necessary interlocking support, the study recommends reshaping the cross-section to work with the interlocking mechanism by rounding the slope--berm transition and giving the berm a gentle seaward slope. This modified cross-section should be tested in future physical-model studies.
The stability of Xbloc armour on a bermed breakwater was studied through two-dimensional physical model tests in a wave flume. Five cross-sections were examined: four with a berm, combining two widths ($6D_n$ and $9D_n$) and two elevations (at the still-water level and emerged above it), and one no-berm reference cross-section. Each section was loaded with irregular waves whose height was increased in steps, at two wave steepnesses. The armour response was quantified through three indicators, rocking, settlement and extraction, recorded by visual observation and by image correlation of the cross section before and after each loading step to obtain the displacement fields.
The results show that rocking, settlement and extraction are different aspects of the same armour response. Rocking and settlement develop together as the load increases, and extraction is the most severe response, occurring only at very high wave loads.
Rocking was quantified using the cumulative rocking number $N_{or,\mathrm{cum}}$, which counts every unit that rocked at any prior loading step. On every bermed cross-section the critical rocking limit ($N_{or,\mathrm{cum}} = 0.20$) was reached at only $70$--$90\%$ of the standard uniform-slope design wave height ($N_s = 1.96$--$2.53$), well below the standard uniform-slope value ($N_s \approx 2.77$). The reference cross-section reached the same limit much later, between $N_s = 2.84$ and $3.07$. The berm therefore lowers the stability number by $\Delta N_s \approx 0.5$ to $1.1$. Rocking concentrated at the seaward berm edge and the top row of the lower slope, and migrated landward across the berm, while the upper slope and crest stayed largely stable. On the reference cross section, by contrast, rocking spread along the seaward side around water level and reached the crest, without forming a single weak point. The berm therefore both lowers the stability and concentrates the damage at the transition.
Settlement developed in two different forms. On the lower slope the units settled coherently downslope and compacted tighter. On the berm the units moved apart and some toward each other and opened gaps, the divergent movement that caused the loss of interlocking. The maximum row-averaged settlement reached about $0.35\,D$ on two sections, above the $0.3\,D$ settlement limit, while the global average stayed below this limit on every section. The upper slope settled less on the bermed sections than on the reference cross section. This shows that the berm dissipates the incoming wave energy, which reduces the wave load on the upper armour.
Extraction occurred only at high loads ($N_s \gtrsim 3.4$) and only on the emerged berms\textbf{;} no units were extracted on the still-water-level berms or the reference cross section within the tested range. On the still-water-level berms the water running over the units held the loosened units in place.
Berm elevation was the main influential geometric parameter, while berm width had no clear effect. The emerged berms rocked more than the still-water-level berms and were the only sections where units were extracted. Widening the berm from $6D_n$ to $9D_n$ did not change the damage location and quantity. The wave conditions acted in the same direction on all three indicators: all forms of damage increased with wave height, and the longer, less steep waves ($s_{0p}=0.02$) were the more damaging condition, producing more cumulative rocking and most of the extraction events.
When the three forms of damage are examined together, cumulative rocking and lower-slope settlement rise together on every section. As the seaward edge rocks and its units diverge, the gaps at the lower-slope-to-berm transition widen with settlement. As settlement increases, the gaps widen, varying from $\approx 0.4\,D$ to roughly $0.9\,D$. Furthermore, the gaps only reach a full unit diameter ($\approx 1\,D$) on the emerged berms, which are the exact configurations where unit extraction occurred. Tracking individual units revealed that those losing their interlock at the transition were the exact units later extracted. The lower-slope settlement at first extraction ranged from about $0.22\,D$ to $0.41\,D$, around the $0.3\,D$ limit. This gap widens about $2.5$ times faster than the settlement, and reaches a full diameter only on the sections that lost units. It therefore reflects the loss of interlocking more directly than the maximum row averaged settlement. A transition-gap limit of about $0.5\,D$ is recommended as the design damage criterion for bermed breakwaters.
These findings show that a horizontal seaward berm lowers the stability of an Xbloc layer by breaking up its interlocking network, with the extent of this stability loss determined primarily by the berm elevation relative to the water level rather than by its width. This is because the seaward transition row loses the support of the units that would otherwise sit above it on a continuous slope. The standard uniform-slope stability number ($N_s \approx 2.77$) is therefore not a safe value for a bermed cross-section, and rocking, rather than extraction, is the more reliable design indicator. If a horizontal berm is retained, the seaward units must be enlarged to recover the lost stability, requiring an increase of roughly $50$--$56\%$ in nominal diameter and about $3.5$--$3.8$ times the unit mass. To address this critical vulnerability at the transition zone and restore the necessary interlocking support, the study recommends reshaping the cross-section to work with the interlocking mechanism by rounding the slope--berm transition and giving the berm a gentle seaward slope. This modified cross-section should be tested in future physical-model studies.