Crushed-rock Embankment Research Articles

Numerical study on cooling performance of the L-shaped crushed-rock embankment in permafrost regions

In permafrost regions, crushed-rock embankments are favored for their environmental compatibility and thermal efficiency. This study introduces the innovative L-shaped crushed-rock embankment (LCRE), which features a crushed-rock layer exclusively at the base and on the sunny slope, providing a cost-effective alternative to the conventional U-shaped design. Using numerical methods, we assessed the cooling performance of the LCRE compared to other crushed-rock embankments, focusing on the impact of its geometric parameters. The findings indicate that the overall cooling performance of the LCRE is situated between that of the crushed-rock interlayer embankment and the U-shaped crushed-rock embankment, and its ability to mitigate the shady and sunny slope effect is superior to that of the U-shaped crushed-rock embankment. Additionally, our analysis reveals that increasing the horizontal width of the revetment to enhance cooling is not a cost-effective approach. The LCREs is more suitable for higher embankments than U-shaped counterparts. Despite the LCRE's advantageous thermal performance and cost benefits, its asymmetric load distribution could lead to exacerbated differential settlement, highlighting the need for further research. This study offers pivotal insights into the design and development of innovative crushed-rock embankments in permafrost regions.

Performance and reinforcement of air-cooled embankments traversing degrading permafrost of the Qinghai-Tibet Plateau

The reliable operation of railway embankments traversing degrading permafrost regions is challenged by climate warming. This study examines performances of four main types of railway embankments on the Qinghai-Tibet Plateau in thermally stabilizing permafrost foundation over warm permafrost using numerical modelling and 10-year monitoring data. Then, a reinforcement measure that combines a thermal conductivity variable system (TCVS) was designed to improve the cooling capacity of the crushed-rock sloped embankment (CRSE) by countering the heat absorption of slopes during summers. A coupled thermal-fluid-solid model was built to simulate and assess the cooling performance and reinforcing capacity of the new design. Results show that the crushed-rock embankments can produce convection cooling on the permafrost subgrade but the performances vary with different structures. The CRSE has insufficient cooling capacity to withstand the underlying permafrost degradation in warm permafrost regions. The optimized CRSE that combines the TCVS can effectively cool the underlying warm permafrost and decrease the shady-sunny slope effect under a warming climate, and can be used as an effective reinforcement measure. This study confirms the application of air-cooled embankments in protecting permafrost subgrade and provides guidance for structural design of embankment traversing degrading permafrost.

Numerical simulation on the effects of deteriorating crushed-rock interlayers on thermal stability of embankments in permafrost regions

The crushed-rock layer (CRL) in permafrost regions frequently deteriorates due to aeolian sand, snow accumulation as well as vibrations induced by traffic loads. This degradation can adversely affect the thermal performance of crushed-rock embankments (CREs), potentially causing deviations from their designed specifications. Therefore, it is imperative to thoroughly investigate the thermal stability of CREs under conditions of CRL degradation. By utilizing the crushed-rock interlayer embankment (CRIE) as a representative case, this study employs numerical simulations to analyze six instances of crushed-rock interlayer (CRI) deterioration, employing a mathematical model incorporating adjusted thermal parameters specific to the CRIE. In addition, a novel methodology for quantitatively analyzing temperature distributions within permafrost embankments is employed to assess the results. The findings indicate that all embankment cases lose their cooling capacity on the underlying permafrost prior to the 35th service year. Therefore, mitigating the rate of CRI degradation is essential to preserving the integrity of its underlying permafrost throughout the entire lifespan of the CRIE. The results of this study contribute to the advancement of a theoretical framework for the construction of CRIEs with significant safety margins in permafrost regions.

Effects of porosity of crushed-rock layer on cooling performance of crushed-rock embankment in permafrost region of the Qinghai-Tibet Plateau

Effects of porosity of crushed-rock layer on cooling performance of crushed-rock embankment in permafrost region of the Qinghai-Tibet Plateau

Thermal stability of permafrost under U-shaped crushed rock embankment of the Qinghai‒Tibet Railway

The U-shaped crushed rock embankment (UCRE), of which widely utilized in the permafrost regions along the Qinghai‒Tibet Railway, has the capability to rapidly reduce the ground temperature of the underlying permafrost. However, there remains uncertainty regarding the adaptation of UCRE to climate change and its long-term cooling trend. This study focuses on nine UCRE monitoring sites along the Qinghai‒Tibet Railway to analyze the dynamic variations of the ground temperature underlying permafrost from 2006 to 2020. The efficiency of UCRE in stabilizing permafrost temperature in different permafrost zones is evaluated by considering the permafrost table, ground temperature, and MAGT, as well as the temperature difference between the top and bottom of the crushed rock layer and the ground temperature variation index (GTVI). The results show that UCRE is suitable for application in extremely unstable warm permafrost regions where the MAGT is higher than −0.5 °C. Moreover, UCRE effectively diminishes the disparity in permafrost thermal stability between the sunny and shaded shoulders of the embankment. The short-term and long-term effect of cooling permafrost is experiencing a change related with permafrost stability. Notably, in stable cold permafrost regions with MAGT lower than −1.5 °C, the long-term cooling effect of UCRE on permafrost seems to gradually diminishes, but UCRE continues to fulfill the role of stabilizing the underlying permafrost thermal state over the long-term. These results show that UCRE can quickly restore and stabilize the thermal state of permafrost in the early stages of construction, and adapt to the influence of future climate change. The findings provide important guidance for understanding the variations of permafrost thermal stability beneath the embankment in permafrost regions, as well as for improving the embankment stability and operational safety of the Qinghai‒Tibet Railway.

Study on the lateral thermal disturbances of three parallel embankments on permafrost along the Gonghe-Yushu Engineering Corridor in China

The mutual thermal disturbance of built structures along narrow permafrost engineering corridors has become an evident influencing factor on the thermal stability of frozen soil engineering. To analyse the mutual thermal disturbance of the built structures along a permafrost engineering corridor in the Qinghai-Tibet Plateau, three parallel permafrost embankments (along the G214 Highway and the first- and second-stage projects of the Gonghe-Yushu Highway in the Gonghe-Yushu Engineering Corridor) were chosen as the research sites. These three highways were built at different times following different standards; thus, complicated lateral thermal disturbances occurred among the three parallel embankments. The embankment distress investigations, typical section drilling, and ground temperature observations were used for analysis. Then, the thermal distress and service status were analyzed under the mutual thermal disturbances of the three embankments. The continuous wave settlements and inclination deformations were relatively developed due to the remarkable mutual thermal disturbances from the shorter distances among the three embankments. Moreover, missing or poor drainage systems further aggravated the mutual thermal disturbances. The monitored data revealed that the transverse thermal disturbances weakened the cooling effects of several special structures to a certain degree; these structures included the ventiduct embankments and crushed-rock embankments. A thermal disturbance simulation model for the three parallel permafrost embankments was proposed and included the assignment of the general influence, core influence, and severe influence zones of the thermal disturbance. The computed results showed that the general influence zones and core influence zones under the three embankments were linked together after 3 and 10 years of construction, respectively, on the Gonghe-Yushu Highway. After 50 years, a vast thermal influence area almost 100 m wide and 20 m deep would form under the three embankments. The thermal disturbances at different distances between embankments were also analyzed using this model; the distances between G214 and the first-phase project of the Gonghe-Yushu Highway were inferred to be more than 15 m and 20 m between the first- and second-phase projects of the Gonghe-Yushu Highway, respectively.

Experimental study of natural convection and cooling capacity of closed crushed-rock layers affected by summer rainfall in cold regions

Climate-induced rises in air temperature and humidity on the Qinghai-Tibet Plateau modify the hydrothermal conditions of closed crushed-rock embankments (CRE). This alternation arises from the infiltration of summer rainfall, which is closely correlated with the cooling performance of the crushed-rock layers (CRL). Nevertheless, the cooling performance of the closed CRL during the summer rainfall season remains unexplored. In these present, physical models were employed to examine the convective properties and hydrothermal response processes. The results reveal that summer rainfall greatly diminishes the natural convection intensity within the closed CRL. Conversely, cycle-average temperatures showed an upward trend under these conditions. Moreover, based on fluctuations in the thawing/freezing index, the cooling capacity of the CRL weakens post-summer rainfall, with a maximum decline of 27.3% compared with the initial cycle. Additionally, the humidity in the subsoil layer experiences a stepwise growth followed by a gradual decrease owing to concentrated rainwater percolation. After enduring four rainfall events, the volumetric water content in the subsoil layer presents an upward trajectory. Overall, infiltrated water introduces additional heat, modifying the hydrothermal and convective properties of closed CRE, consequently impairing the cooling efficacy of the CRL.

Field forensic and numerical investigation of thermal stability of a permafrost-protecting granular embankment structure of asphalt-pavement expressways in cold regions

The traditional crushed-rock embankment (CRE) has proven to be one of the most successful cooling embankment structures during the operation of Qinghai-Tibet Railway. However, it remains untested whether or not traditional CRE can maintain stability of permafrost foundation under expressways under strong heat absorption of asphalt-pavement and climate warming. For the study, field tests were performed to evaluate cooling performance of traditional CRE in wider-width expressways. Then, A heat transfer model of the CRE was established, and a novel inverted “M”-shaped crushed-rock embankment (MCRE) was proposed. Finally, large numbers of numerical simulations were further performed to comparatively evaluate thermal behavior and cooling performances for both traditional CRE and novel MCRE in wider-width expressway construction. The study shows that (1) the expressway accelerates degradation rate of permafrost foundation under traditional CRE; (2) traditional CRE shows obvious sunny-shady slope effect, which cannot guarantee thermal stability of expressway; (3) the novel MCRE for the expressway increases the entry of cooling energy and therefore accelerates heat dissipation from the permafrost foundation; and (4) the novel MCRE improves long-term thermal stability of the expressway. The research could provide important technical reference for the construction of wider-width expressways in permafrost areas in the future.

Effects of complex environment on soil thermal regime alteration under crushed-rock embankment structures in the permafrost region on the Roof of the World

The thermal stability of permafrost under complex environment (climate scenarios, permafrost types and regional air temperatures) directly affects the long-term service performance of highway or railway. This study uses a large amount of valuable soil temperature monitoring and simulation data to examine the stability of typical crushed-rock embankments (CREs) along Qinghai-Tibet Railway, which is located in the permafrost region on the Roof of the World. Firstly, a novel numerical model for CREs considering a complex heat transfer environment is established and verified. Then, alteration characteristics of recent-term thermal regime of permafrost across time and space under three CREs are revealed based on a decade of field monitoring data. Finally, long-term thermal regime of permafrost under three CREs under complex environment is analyzed by numerical simulation. Results include: 1) Soil temperature near the ground surface under the three CREs shows a decreasing trend, whereas the overall temperature around the deep permafrost increases over time under a recent climate warming. 2) The warming rate of permafrost under CREs rises with the acceleration of climate scenarios and regional air temperature and the decrease of regional ground temperatures. 3) U-shaped crushed-rock embankment is the most suitable CRE for managing complex environment, especially when the mean annual ground temperature is 0 ∼ − 1 °C or climate scenarios are RCP 2.6 and RCP 4.5. 4) Transition from low-temperature permafrost to warm permafrost is a warning signal of permafrost degradation under climate warming. 5) With an increase of permafrost degradation rate (the thawing and warming rates of permafrost), embankment stability becomes worse. These findings will not only serve as a scientific basis for the embankment damage prevention of the Qinghai-Tibet Railway, but also provide important technical supports for the successful building of infrastructure in permafrost regions under complex environment.

Thermal-deformation behavior of a crushed-rock embankment along a high-grade highway in permafrost regions

Numerous studies have been conducted to investigate the thermal stability of crushed rock embankments (CREs). In this study, we developed an automatic field monitoring system for a CRE during the construction of the Gonghe–Yushu High-grade Highway (GYHH) to explore both the convective cooling and the deformation controlling effect of the crushed rock layer (CRL). We evaluated the thermal-deformation performance of a the CRL based on the long-term field monitoring data. The results reveal that the upper peat layer could slow down the degradation of shallow permafrost. However, the heat absorbed by the black asphalt pavement significantly contributed to the degradation of the permafrost beneath the contrast embankment without the CRL. The CRL had an obvious cooling effect range for the shallow stratum, where an effective cooling zone formed (about 4 m deep in the 4th year after the construction of embankment). Nevertheless, deep permafrost beyond this effective cooling range continued to warm owing to the downward heat flux. Consequently, the total settlement of the CRE decreased by 23% compared with the contrast embankment in the 5th year. This work is expected to provide a reference for the design of the CREs in permafrost regions.

Numerical evaluation of thermal stability of a W-shaped crushed-rock embankment with shady and sunny slopes in warm permafrost regions

The crushed-rock interlayer structure, crushed-rock revetment, and insulation board have been successfully applied in low-grade highways in low-temperature permafrost regions. However, it is doubtful whether the composite structure of the W-shaped crushed-rock embankment (W-CRE) composed of the three measures can be applied to high-grade highways in warm permafrost regions. For this reason, a model coupled with water, heat, and deformation in unsaturated soil was established for the high-grade highway with the W-CRE in warm permafrost regions. The cooling effect of the composite structure on the embankment with shady and sunny slopes in 20 service years was evaluated by numerical calculation, and the unfrozen water distributions and deformation characteristics were analyzed. The results show that (1) the W-CRE can cool the embankment of the high-grade highway in warm permafrost regions and improve the asymmetric ground temperature distributions caused by the shady and sunny slopes. (2) the W-CRE can improve the asymmetry of unfrozen water distributions, reduce the uneven settlement, and thus improve the mechanical stability of the embankment. (3) Although the cooling mechanisms of the three measures are different, the complementary thermal regulation mechanism formed by them in the composite structure effectively improves the thermo-mechanical stability of the embankment.

Heat transfer and cold energy capacity properties of crushed-rock layer in cold sandy regions

Addressing the impact of climate warming and anthropic activities, crushed-rock layer (CRL) is a zero-carbon emission technology by using natural cold air to protect infrastructures in permafrost regions. But in cold sandy environment, the issue of its cold energy capacity on account of aeolian sand clogging needs to be solved. Based novel field experiments on Tibet Plateau, the dynamic evolution law and its controlling factors of natural cold energy accumulation of the CRL are quantitatively figured out. Results show that the initially open CRL had a strong forced convection of air in the first two winters, while the cooling effect was failure after the third winter. The filling of aeolian sand caused heat transfer mode of the CRL to change from forced convection to natural convection in cold season, losing the ability of “thermal semiconductor” aimed to mitigate permafrost degradation. The closed CRL represented weak natural convection in cold season and thermal insulation in warm season, which had better long-term cooling effectiveness than other conditions in the aeolian environment. As the thickness of the aeolian sand filling increased, the maximum Rayleigh number and natural convection time of the closed CRL decreased. Accumulation of cooling energy in cold season and thermal insulation in warm season were positive correlation with thickness of porous media layer. It was not recommended to solely adopt crushed rock embankment or crushed rock revetment in aeolian sand environment and regions with higher annual average temperature. The findings solved the scientific evaluation issue of cold energy storage capacity of CRL, and provided constructive engineering implications for its efficient application.

Investigating characteristics of the long-term settlement of railway embankments in warm permafrost areas

Introduction: The embankment in the permafrost zone of the Qinghai–Tibet Railway (QTR) faces the problem of permafrost degradation, especially in the warm and ice-rich permafrost areas. The settlement deformation of the embankment is more serious in these areas.Methods: This study systematically investigates the settlement deformation characteristics during 16 operational years of three types of typical roadbed structures. The traditional embankment (TE), U-shaped crushed-rock embankment (UCRE), and crushed-rock revetment embankment (CRRE) are the roadbed structures. The long-term monitoring ground temperature and deformation data of the embankment section along the QTR in warm permafrost areas from 2005 to 2020 are utilized in analysis.Results and Discussion: This study focuses on the influence law of the roadbed structure form, shady–sunny slope effect, and temperature field change on the settlement of the roadbed. The results indicated that the two types of the crushed-rock embankment (CRE) of the long-term cumulative settlement are less than 50% of the cumulative settlement of the TE, and the impact on controlling the settlement is significant. The annual settlements of the three types of embankment structures are related to the artificial permafrost table (APT) and influenced by cyclical climate change at the regional scale. The annual growth rate of the settlement at the left and right shoulders of the UCRE as a result of the effect of the shady–sunny slope does not vary considerably as the number of operational years increases. The impact of the shady–sunny slope on the CRRE for the various settlements before 2008 was negligible. After 2008, the thermal disturbance to the embankment temperature field induced by the preconstruction and the effect of shady–sunny slopes decreased gradually as the number of operational years increased. In some years of operation, a thawed interlayer in the TE and CRRE greatly affected the embankment settlement acceleration. The settlement growth rate of the TE is related to the decline of the artificial permafrost table (APT). During the operational years, there was no thawed interlayer in the UCRE. The development of the settlement rate is unaffected by the temperature field for either the left or right embankment shoulder.

Investigation of Wind Characteristics and Cooling Effects of Crushed-Rock Embankment with Different Pavement Widths in Permafrost Region

A crushed-rock embankment (CRE) with a high porous crushed-rock layer (CRL) can effectively cool the underlying permafrost through natural ventilation within the layer. However, in addition to the ambient conditions, the ventilation efficiency of the CRL and its cooling effect are significantly affected by the pavement width. In this study, the local wind flow around an embankment section was first analyzed based on field monitoring data. Then, considering climate warming, a 2-D coupled model of heat and mass transfer was established to investigate the wind characteristics and the cooling effects of the CRE with different pavement widths. The results showed that the pavement width exerted considerable impacts on the wind characteristics and cooling effects of the CRE. These impacts were evaluated via variations in the wind speed, the permafrost table, and the soil temperatures. An increase in pavement width can lower the wind speed within the CRL, which is adverse to the long-term thermal regimes of the embankment and the underlying permafrost. In addition, due to differential wind flows around the embankments, an asymmetric distribution of the soil temperatures beneath the windward and leeward sides of the embankments existed. Overall, it is hoped that the results of this study can provide informative references for the Qinghai–Tibet expressway that is constructed in permafrost regions.

Optimizing embankment structures in a snowy permafrost region of the pan-Arctic based on a coupled numerical model

In pan-Arctic permafrost regions, snow drift may lead to more snow accumulation around the road, which prevents the heat release from the underlying soil in winter and aggravates the permafrost degradation beneath the road. However, the study of snow distribution patterns around the road is insufficient, which makes it difficult to accurately evaluate the long-term stability of the road. To investigate the thermal regime of the road and optimize the road structure in permafrost regions under the effect of snow drift, based on heat transfer and multiphase flow theories, a coupled numerical model is presented. The model includes snow transportation around the embankment, natural convection of air in the crushed-rock layer, and heat conduction in soil and snow layers. The results of model simulation show that an embankment with a height of 4 m leads to heavier snow accumulation on both sides of the embankment in winter compared to an embankment with a height of 3 m, which accelerates permafrost degradation. The full crushed-rock embankment with a height of 3 m can be used to counteract the permafrost degradation caused by snow accumulation to some extent, while the soil temperature beneath the toe of the embankment slope is still noticeably higher. By contrast, when the U-shaped crushed-rock embankment (UCRE) with a height of 3 m and 1:6(vertical: horizontal) side slopes is used, the snow accumulation around the embankment is greatly reduced, the embankment slope delivers better cooling performance. Considering the climate warming at a rate of 0.067 ℃ year−1 in pan-Arctic regions, the thermal stability of the UCRE can still be ensured after 20 years of its construction. These results provide a valuable reference for road construction in pan-Arctic snowy permafrost regions.

Risk assessment of the crushed rock structure embankments of the Qinghai-Tibet Railway under a warming climate

On the Qinghai-Tibet Plateau, transportation infrastructure has been greatly affected by permafrost degradation owing to the increasing air temperature caused by climate change. This study presents a risk assessment model for evaluating the viability of the crushed rock embankment under the scenario of climate warming. The results demonstrate that the service life of an embankment is determined by the time it spends at the lowest or low levels of failure risk. At the failure probability threshold of 0.1, the service lives of open crushed rock-based and U-shaped crushed rock embankments are longer than 100 years, those of closed crushed rock-based embankments are about 66 years, and those of crushed rock revetments are less than 40 years. In essence, the longer an embankment has been in service, the stronger its ability to resist climate warming. Based on these results, U-shaped crushed rock and crushed rock-based embankments are the most capable of offsetting the effects of climate warming on permafrost and should account for a higher proportion of independent embankment structures. The same cannot be said for crushed rock revetments, which should only be used as auxiliary engineering measures. Despite this recommendation, regular maintenance should be conducted on the open system crushed rock embankments because the high winds on the Qinghai-Tibet Plateau fill the embankments with sand, which has a negative effect on the long-term stability of the embankments.

Effect of Complex Environment on Soil Thermal Regime Alteration Under Crushed-Rock Embankment Structures in Permafrost Region on the Roof of the World

Effect of Complex Environment on Soil Thermal Regime Alteration Under Crushed-Rock Embankment Structures in Permafrost Region on the Roof of the World

The Thermal and Settlement Characteristics of Crushed-Rock Structure Embankments of the Qinghai-Tibet Railway in Permafrost Regions Under Climate Warming

The temperature difference at the top and bottom of the crushed-rock layer can drive the heat convection inside. Based on this mechanism, crushed-rock structures with different forms are widely used in the construction and maintenance of the Qinghai-Tibet Railway as cooling measures in permafrost regions. To explore the stability of different forms of crushed-rock structure embankments under climate warming, the temperature and deformation data of a U-shaped crushed-rock embankment (UCRE) and a crushed-rock revetment embankment (CRRE) are analysed. The variations in temperature indicate that permafrost beneath the natural sites and embankments is degrading but at different rates. The thermal regime of ground under the natural site is only affected by climate warming, while that under embankment is also affected by embankment construction and the cooling effect of the crushed-rock structure. These factors make shallow permafrost degradation beneath the embankments slower than that beneath the natural sites and deep permafrost degradation faster than that beneath the natural sites. Moreover, the convection occurring in the crushed-rock base layer during the cold season makes the degradation of permafrost beneath the UCRE slower than that in the CRRE. The faster degradation of permafrost causes the accumulated deformation of the CRRE to be far greater than that of the UCRE, which may exceed the allowable value of the design code. The analysis shows that the stability of the UCRE meets the engineering requirements and the CRRE needs to be strengthened in warm and ice-rich permafrost regions under climate warming.

Multi-scale Experimental Investigations on the Deterioration Mechanism of Sandstone Under Wetting–Drying Cycles

The repeated wetting–drying (WD) cycles can cause the deterioration of rock and thus affect the service performance of the related rock engineering, e.g., the crushed-rock embankment and the reservoir. The study comprehensively investigated the deterioration mechanism of sandstone under the WD cycles based on a series of multi-scale experiments, including the microstructure, the meso–micro pore characteristics, and the macroscopic physical and mechanical properties. The results indicate that the content of dissolved minerals and the permeability are two key factors that determine the deterioration effect caused by the WD cycles. During the WD cycles, the pore size range of sandstone becomes wider due to the formation of new small pores and the connection of original pores. Thus, low-density area forms within the samples, which causes the increasing of density dispersion. The structure deterioration weakens the physical and mechanical properties of the samples. The ultrasonic test indicates that the decreasing rate of the P-wave velocity is larger than that of the S-wave velocity, especially in the first 5 cycles. Besides, the exponential equations of uniaxial compressive strength and elastic modulus with the number of WD cycles are established to describe the deterioration of mechanical characteristics.

Wind field and thermal performances of an expressway constructed with two separated crushed-rock embankments in high-altitude permafrost zones

The crushed rock layers (CRLs) with a satisfactory cooling effect has been widely used to mitigate permafrost thaw beneath road embankments in cold regions. However, whether the CRLs can still work as well for an expressway constructed with an integral embankment is still under discussion, it is generally accepted that the expressway with wide asphalt pavement should be constructed with two separated embankments rather than one integral embankment in permafrost zones. In that case, wind field around the two embankments would be of great importance as it would impact the work conditions of the CRLs considerably. Here, a coupled computational fluid dynamics and heat transfer model was developed to numerically investigate and quantify the characteristics of wind field and thermal performances of an expressway constructed with two separated crushed-rock embankments (SCREs) with different separating strip widths (SSWs). The model was validated by the field observed data of wind flows and ground temperatures around an experimental expressway. The simulated results indicated that the two SCREs can ensure the long-term thermal stability of permafrost subgrade in the projected climate warming scenario. However, due to different distribution of wind field around the two SCREs, permafrost thermal regimes beneath them differed considerably under different SSWs. The SSW exerted a significant impact on the cooling effect of the rear embankment, while less significant to that of the front embankment. To ensure that the two SCREs have close thermal performances, the SSW between them should be not less than 15 times of the embankment height. In addition, the local warming effect, which is caused by low wind speed, can result in severe permafrost degradation when the separating strips were narrow.