sand vibration experiment

Seeing The Patterns In Sound

A pair of artists finds ghostly imagery in sound vibrations.

Vibrations of D. Credit: Louviere + Vanessa

In the late 18 th century, German physicist and musician Ernst Chladni demonstrated how vibrations could be used to create striking imagery. By spreading fine sand across the top of a metal plate and running a violin bow alongside, Chladni showed that the sand would settle into distinct patterns, depending on the frequencies of the sound waves produced by the bow.

Centuries later, in the 1960s, a Swiss physician named Hans Jenny built on Chladni’s experiments in an effort to study vibrational phenomena—what he called “ cymatics .” Visual artist Jeff Louviere happened upon the works of Jenny and Chladni while researching another project, and he and his partner, photographer Vanessa Brown, became inspired to conduct their own experiments to see what sound could look like. The resulting work became Resonantia (Latin for “echo”), a multimedia project centered around 12 images produced by vibrations.

To create the images, the pair (also known as Louviere + Vanessa ) built their own version of a Chladni plate in their New Orleans home. Louviere dismantled one of his guitar amps and separated the speaker, aiming it upwards. On top of the speaker, he placed a lined box and filled it with water and black food coloring. He then hooked the speaker up to an amp plugged into a frequency generator—that is, a computer program with an oscillator—that he could use to play musical notes at various frequencies. A bright ring light mounted over the box illuminated the water below.

As Louviere cycled through musical notes at different frequencies and volumes, from low to ear-piercing—“there was a point where it was so high we had to put the dogs outside so it wouldn’t hurt their ears,” he says—Brown took photographs through the ring light of the water formations produced by the vibrations.

“It was just constant shooting, and trying like every frequency we could stand,” Louviere says.

Brown took about 2,000 photographs in total, and the duo narrowed those down to a dozen, based on the 12 notes of the chromatic scale. They chose the images with the most complex or aesthetically pleasing patterns.

Louviere says he was surprised by some of the patterns they produced. “It’s the first time we’ve done a series of work where we didn’t know what the end result was going to look like,” he says. One of his favorites is the image for F sharp, which is “kind of a weird sound,” he says. The result looked “ like a puffer fish or an alien or something ; it’s got all these crazy lines in it. That one was pretty remarkable.”

And the image for G turned out to be even more eerie. Louviere had been researching the frequencies of various sounds like heartbeats and hurricanes when he read a conspiracy theory about a strange hum called the brown note —a low frequency that would supposedly cause people to lose control of their bowels. When Louviere tried to hit that frequency with their device, Brown captured a vibration pattern that looked like a demonic face.

“It looked like Satan,” Louviere says. “We were like, oh my god.”

Satanic visages aside, the images themselves are a creative example of physics at work. “It’s kind of a classic demonstration in acoustics,” says Trevor Cox, a professor of acoustic engineering at the University of Salford in England. “These are actual physical patterns.”

Every object has a characteristic frequency, or frequencies, at which it vibrates most, with the least input of energy. Those vibrations are associated with standing wave patterns called modes . When the Chladni plate, for instance, vibrates in one of its modes, a pattern appears in the sand on the plate.

“What’s happening is, the sand is moving away from the bits [on the plate] where it’s vibrating a lot” says Cox, and it’s settling in places where there are no vibrations (these places are called “nodes”). And, “if you up the frequency, you’ll find the patterns get really complicated,” because more of those nodes occur.

Cox, who isn’t affiliated with Resonantia , surmises that the patterns depicted in the images formed when the water vibrated in its natural mode. The bright light that Brown shone on the water illuminated the areas that rippled the most.

To achieve the vintage look of the final images, Louviere + Vanessa first printed each photograph onto kozo paper, which is thin and tissue-like, and lay that on top of a metal substrate covered in gold leaf. Then they poured resin over the paper, which turned transparent, allowing the gold leaf to shine through.

The prints have been on display at various galleries across the United States, including A Gallery for Fine Photography in New Orleans and the Verve Gallery in Santa Fe, New Mexico. You can also learn more about a record and music video that Louviere + Vanessa produced for Resonantia , based on the sounds and images, here .

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Chau Tu is an associate editor at Slate Plus . She was formerly Science Friday’s story producer/reporter.

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Sand and Sound Waves: A Stunning Sci-Art Video

We interrupt your regularly scheduled panic over Verizon, the National Security Agency, and PRISM for a few minutes of magnificent science-art.

Using just a tone generator, a speaker, and a metal plate, YouTube artist Brusspup shows us how certain frequencies can vibrate sand into wildly intricate patterns. The patterns increase in complexity as the frequency increases in pitch. Of course, it all has to do with math, specifically Chladni’s law . The unedited version lets you listen to the actual frequencies that make each pattern, but you’ll want to be sure to lower your volume.

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Chladni plates.

Accumulation of sand at nodes of vibrating plate reveals resonance patterns.

What It Shows

A Chladni plate consists of a flat sheet of metal, usually circular or square, mounted on a central stalk to a sturdy base. When the plate is oscillating in a particular mode of vibration, the nodes and antinodes that are set up form complex but symmetrical patterns over its surface. The positions of these nodes and antinodes can be seen by sprinkling sand upon the plates; the sand will vibrate away from the antinodes and gather at the nodes.

How It Works

We have four brass plates 1 mounted on a common wooden platform: two circular (diameters 8in and 10in), one square (10in), and one "stadium" (a 8in square with an 8in diameter semicircle at each end); all plates are roughly 1/16in thick, and each is bolted through the center to the wooden base by a 10cm brass rod.

The plates are driven using a cello or violin bow (for best results use plenty of rosin). Hold the plate with finger or thumb nail at a point on the edge—this point will automatically become a node—and draw the bow straight down across the edge. The plate will ring loudly if you manage to excite a mode of vibration, and sand will start gathering at the nodes to form a pattern. The distance between the bow and your finger will dictate which mode of vibration you excite.

Setting It Up

Firmly clamp the wooden base to the lecture bench. Use a video camera with a wide lens mounted to a benchtop stand. Sprinkle the sand on the plates so that it forms an even cover.

Good demo to show how complicated modes of vibration can get when we increase the number of dimensions.

1. E. H. Barton, Textbook on Sound (Macmillan, 1923) 2. E. F. F. Chladni, Acoustics: Historical and Philosophical Development , ed. R. B. Lindsay p.156 (Dowden, Hutchinson & Ross, 1972) 3. G. R. Graham, Physics Education 24 (1989) pp25-29 4. J. W. Strutt (Lord Rayleigh), Theory of Sound (Dover, 1945)

1 The origin of our plates is unknown, but similar examples are available from Cenco (70706) and Sargent-Welch (3314)

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WATCH: Sand Dances to Music And Forms Incredible Patterns

In the video above , watch as YouTuber brusspup sprinkles sand onto a metal plate attached to a speaker, and then turns up the volume to bring the whole thing to life in a pulsating, dance of intricate patterns.

Needless to say, it's beautiful and mesmerising all at the same time.

But the science behind the video is just as cool - this experiment is known as the Chladni plate experiment . As brusspup explains over on YouTube , it required a tone generator, a speaker and an attached metal plate.

When you play a tone through the speaker, specific frequencies cause the plate to vibrate in particular patterns - and some regions will vibrate in opposite directions, causing regions of no vibration called nodal lines. And when you add sand, the grains all "fall" into those areas, creating art-like geometric patterns.

As you can see, the location of these vibration-free regions change as the frequency varies resulting in a pulsating, resonance dance. In the above video , brusspup has tested the patterns of different tones, and set the whole thing to music.

Watch and be inspired . And see the full version of the video below , which features individual tones being played and the resonance pattern of each clearly displayed on the plate. You're welcome.

Source: brusspup

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Vibrations visualized with sand and sound.

Shake a metal plate covered in sand at certain frequencies and intricate patterns mysteriously appear. Jon Jacobsen, a mathematician at Harvey Mudd College, explains why this 200-year-old demonstration still captivates scientists and students.

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How to Make a Chladni Plate (vibrating Membrane)

Introduction: How to Make a Chladni Plate (vibrating Membrane)

• work with cheap off the shelf components
• use as much of my own kit as possible (my conventional audio amplifier etc.)
• avoid destroying the speaker
• use a plastic membrane that is cheaper and requires less power (less noise for my neighbours)

• It provides a great acoustic contact that bonds to plastic sheet, board, metal, glass
• creates a perfect seal between the speaker and the plate
• you have time to make the whole set-up level before the sugru cures
• can also create custom-made dampening pads for the contact with the table the rig sits on.
• I don't need to destroy my nice speaker since I can cut sugru and re-use my speaker once the experiment is done

Step 1: Build the Base

• Computer _ £ 0 (we assume you already have one)
• Sound amp _ £ 0 (we assume you already have one)
• Speaker (here I use a 10W car speaker) _ £10 at Maplins  (UK) / Radioshack (USA) If you want to use a more expensive speaker you already own, you can! Especially because it is easy to cut and remove sugru . 
• Paint bucket _ £2.5 at the local DIY paint shop
• Plastic membrane _ £3 
• Set of 4 x M5 (5mm) nuts and bolts _ £ 2.5
• Duct tape _ £2
• Rubber ring _ 0.10
• sugru 3x5 gr _£ 6.5
• Scrap wood board
• _TOTAL BUDGET  = £26.6 ( $ 41.25)
• Cordless drill + drill bit ø5mm
• Ruler / 90 angle
• Spirit level
• 1.5 hours to build with 2 people
• 6 hours for sugru to cure (overnight)
• 3 hours to play with tones

Step 2: Amplifying Cone

• So the idea is to roll some sugru in long rolls. 
• Install the long sugru rolls on the most outer ring of the speaker. 
• Make sure that the sugru is not interfering with any moving parts. 
• Flip the bucket upside down, opening facing downwards. 
• Install the speaker on top of the bucket bottom.
• Adjust the level roughly with 2 mini-spirit levels if you have them
• Prepare 4 or more contact points between the speaker and the platform. 
• Assemble the platform on top of the amplifying cone and speaker. 

Step 3: Install the Membrane

• Position the plastic sheet with A LOT of slack
• Hold the sheet in position with a rubber ring
• Create a "belt" of adhesive around the bucket, cut the slack
• just like when you adjust a traditional percussion, you want to adjust the tension on one side, and immediately adjust on the opposite side. 
• Eventually you can gently tap on the surface and find out if the tension is correctly distributed. The idea is that it would sound like a high pitch percussion drum. In fact, you could use an adjustable drum membrane to do this even more accurately, here an awesome video of how to adjust a darbuka head skin here (watch the end, spectacular!).   

Step 4: Assemble and Adjust

• it is level
• your neighbours do not mind low and high pitch loud sound to be played.  
• I recommend you use earplugs. Do not use noise cancelling headphones . 

Step 5: Software

Step 6: Play! /\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

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#sand #sound #video

The visual patterns of audio frequencies seen through vibrating sand, june 6, 2013, christopher jobson.

Youtube user Brusspup who explores the intersection between art and science just released this new video featuring the Chladni plate experiment . First a black metal plate is attached to a tone generator and then sand is poured on the plate. As the speaker is cycled through various frequencies the sand naturally gravitates to the area where the least amount of vibration occurs causing fascinating geometric patterns to emerge. There’s actually a mathematical law that determines how each shape will form, the higher the frequency the more complex the pattern.

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Inventors of Tomorrow

Hands-on science and engineering education for kids age 3 – 6, salt vibration: making sound visible.

You and your kids can use simple materials to create a DIY Chladni Plate – where you pour salt (or sand) onto a taut membrane, then play music and watch the salt move, making the vibration of sound waves visible to all. It’s easy, cheap, fun, and educational!

How to Make It

I discovered this mostly by accident. I’d started by following the directions on Classroom for “Visible Sound”

“Remove the top and bottom of the can with a can opener. Cut the bottom of the balloon off with scissors. Open the bottom of the balloon wide and slide it over one end of the can. Grab a small mirror and tape it to the balloon… Have [a] students place the open end of the tin can at his mouth. Now positions a flashlight so that the light reflects off the mirror. Ask the student to speak. Your students will be able to see the balloon move the mirror, which moves the light. They are seeing the effect of sound waves.”

I tried following this tutorial, but didn’t really have a small enough mirror and wasn’t that impressed with the effect.

Then I flashed back a couple days to when my husband and I saw the movie Wrinkle in Time. At the beginning of the movie, Meg’s dad shows her a plate with sand or salt vibrating on it in response to sound waves. A-ha!!

I made four additional devices:

The closed-end can and balloon . I only opened one end of this can. Covered it with a half balloon and taped it in place. I set the closed end of the can on top of the speaker. Advantage: this sort of deadens the sound of the speaker, which is nice in a classroom that’s already really loud, while keeping the full visual impact of the vibration. Disadvantage: You can see that the tip of the balloon makes sort of a “nipple” so the surface is not totally flat, so the salt patterns can’t form as well. I know it’s possible to get latex sheets (e.g. a dental dam, which is 6×6 or resistance bands) – those might be better.

The hot chocolate tin and saran wrap. I cut the bottom of the tin. Advantage: Bigger surface for the salt than a small can. You don’t have to tape the cling wrap… it just clings in place. Disadvantage: The saran wrap has a bit of a wrinkle in it.

The soda cup and plastic wrap . I cut the bottom off a 32 ounce cup. The plastic on this one is some plastic that was wrapped around some package we got. It was a little sturdier than the saran wrap.

The pot . This is the biggest pot I own, so the biggest surface I tested. I didn’t have rubber bands big enough to hold the saran wrap on, and it wouldn’t “cling” to the metal. So, I used two long skinny balloons to band it on. I just set the speaker in the bottom of the pot, which worked fine.

Testing the Devices

Music Choices : We tried lots of different types of music. You get the most response with: higher pitches (we liked All I Do Is Dream of You from Singing in the Rain… but be warned, keep the volume low for the dramatic opening of the piece, or it will bounce all the salt right off the table!), pieces with lots of organ vibration (think Toccata and Fugue in D Minor or Phantom of the Opera), pieces with lots of percussion (Angry Dance from Billy Elliott and Logo te Pate from Moana). My favorite was Mahna Mahna from the Muppets, and Flight of the Bumblebee is pretty delightful, as the salt dashing around wildly does look a bit like a swarm of insects!

Single Frequency:  If  you had a perfectly designed device, with a perfectly flat membrane on top, you’d get a really cool effect. Different musical frequencies make different patterns in the sound. Each pitch is associated with a characteristic shape. (See a slideshow of this effect:  https://skullsinthestars.com/2013/05/02/physics-demonstrations-chladni-patterns/#jp-carousel-7352 or a video of it here:  www.youtube.com/watch?v=YedgubRZva8 ) or this one (make sure your volume isn’t high before watching this!)

I tested my devices at different frequencies. (To find recordings, just go to YouTube and search for “frequency test speakers” to get recordings of a wide range of frequencies, or just search for one particular frequency, such as 20 khz (high), 250 hz (mid-range) or 20 hz (sub-bass). You’d type into the search “250 hz test tone” to find videos that play one note for a minute or two at a time. Or you can use a tuner app on your phone.

Since none of my membranes were perfectly smooth and flat, I didn’t get really detailed patterns. But, I definitely got different patterns for different tones. But, my dog hated this experiment, and my housemates shouted down the stairs “Whatever you’re doing, would you just cut it out??”

A few days later, we finished off a container of Swiss Miss Hot Chocolate. I took the plastic lid off the top, turned it over, put it on top of the speaker, and sprinkled salt on the flat metallic bottom. Better results than on the plastic surfaces!

Volume : The louder the music, the more movement you’ll get. Sometimes you need to control for this… if the music is too loud, the salt all just bounces off immediately, and it’s not that interesting… so plan to adjust the volume up and down as you go for the best effect.

This Science Buddies article recommends a step-by-step testing process that would be fun too. They built their device by putting wax paper or parchment paper atop a glass bowl.

Using this in Class

We used this for our Five Senses theme , when we studied Hearing . At the end of our group time, I told kids that sound travels in waves. I asked them if they’d ever seen sound. They all said no. I said that sound waves can make things vibrate – I asked if they’d ever felt the vibration of sound. Some had. My co-teacher Cym showed them her harp – she played a note, and we all saw how the string vibrated as long as the note was playing, but if we stopped the vibration, we stopped the sound. Then, I pulled out the cocoa tin and the speaker and showed them how it worked. They were all totally captivated. After a few minutes of watching, we told them that anyone who wanted to could leave group time and return to station exploration and art projects, but many stayed watching the salt. For the next 30 minutes, I had kids rotating in and out of watching the salt dance.

Note: you’ll want to put the device on top of a tray, to contain the salt mess, because over time, the salt all bounces off and you have to keep sprinkling more and more salt on.

Learning More about the Science and the History

After class, I realized I didn’t really know what to call this device, or the scientific device I’d seen in Wrinkle in Time, so I went searching.

Da Vinci noticed that if a table was struck and vibrated, the dust on it would settle in typical patterns and Galileo noticed that brass filings would settle into patterns when a plate was scraped with a chisel. ( Source ) In 1680, Robert Hooke  covered a glass plate with flour, then ran a violin bow along the side of the plate to create a vibration. He saw typical nodal patterns appear.  In the 1780’s, Ernst Chladni used metal plates and sand. (Image from Wikipedia .) To learn more about the history and science of visualizing sound waves, read this article on Cymascopes .

This vibrating device is similar to how our ears hear sound: Our eardrum is a thin membrane. When sound waves hit the eardrum, they make it vibrate, like the sound is vibrating the balloon or plastic on these devices. Those vibrations are transferred to the cochlea, a fluid filled chamber in our ear. Then the vibrations are interpreted by the brain. ( Source )

Another way kids can feel sound vibrations: have them hold a balloon in their hands, near a speaker playing music. ( Details .)

You could make a much more sophisticated device using this Instructable  or this Make tutorial .

Here’s a lesson plan on Chladni plates for older kids – maybe middle school?  http://sciencenetlinks.com/lessons/making-sound-waves-visible-exploring-chladni-plates/

Here’s a video of a Chladni plate responding to sung tones:  https://munrovian.wordpress.com/2010/03/16/curiosity-chladni-plates/ .

Here’s how to make a tonoscope to sing into:  https://www.youtube.com/watch?v=jhL933QoK_Y , and a video of someone singing Mozart into a tonoscope:  https://www.youtube.com/watch?v=KU84ckD1AcA .

A modern Cymascope device shows much more sophisticated patterns:

Entertaining sidenote: After I went through the process of building this device, testing with kids and THEN researching it, I ran across this post from Frugal Fun for Boys , where she shares that she did almost the same thing! Check out her post as well.

If you make one of these, let us know about your experience in the comments!

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[…] Making Sound Visible: Build a Chladni plate / salt vibration device and watch the salt dance to music! Find the whole tutorial and the history of cymascopes here: https://inventorsoftomorrow.com/2018/03/28/salt-vibration/ […]

[…] made visible with a Chladni plate made from a can, saran wrap, rubber band or tape and some salt. Salt vibration tutorial. (We use this in Five Senses […]

[…] Salt vibrations – It’s easy to make one of these devices, using a can or a plastic cup, put on plastic wrap or a balloon and tape it or rubber band it in place. Then sprinkle salt on it and play music – the salt will dance with the vibrations of the music. […]

[…] can make a Chladni plate with a metal can or plastic cup, a balloon, and tape. Put it on top of a speaker and sprinkle some […]

Thanks so much for this post. Def going to make a tonoscope using a speaker with my daughter’s 3rd grade class. I found a bunch online but this page filled in all the gaps. Well written, wide ranging, what the internet SHOULD be. (IMHO)

Thanks again!

[…] can find the whole tutorial here. If you have a device your child can use effectively to choose different music to play, you could […]

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Artist Uses the Power of Sound to Turn Sand Into Mesmerizing Patterns

Kanazawa Kenichi— Sound's ability to bring order out of chaos from r/BeAmazed

Do you know what sound looks like? Japanese artist Kenichi Kanazawa makes the invisible visible. He studies cymatics —the art of visualizing sound vibration—by experimenting with sand on a steel tabletop. In a recent video posted on Twitter , Kanazawa is captured creating “a visual demonstration of the power of sound to create order out of chaos.”

Kanazawa starts by sprinkling white sand on the tabletop, before using a small mallet to rub the metal surface to create sound vibrations. Just like magic, the sand starts to move and a geometric pattern starts to take shape. He then picks up a larger mallet that produces lower vibrations, and the pattern begins to change. A third mallet changes the course of the sand yet again, creating a final star-like motif from grains of sand.

Originally a sculptor by trade, Kanazawa began experimenting with steel and sound in 1987 after collaborating with the late sound artist Hiroshi Yoshimura. Today, he continues to explore the fascinating possibilities of cymatics with colorful sand, steel, and mallets.

Check out Kanazawa’s cymatics demonstrations below.

Cymatics artist Kenichi Kanazawa visualizes sound vibrations with sand, a steel table, and mallets.

A visual demonstration of the power of sound to create order out of chaos. pic.twitter.com/9zVSyi0ujg — Ted Gioia (@tedgioia) November 14, 2020

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Sound in sand: complex visualizations of audio frequencies.

Article by SA Rogers , filed under Installation & Sound in the Art category

Grains of sand arrange themselves into complex geometric patterns according to audio frequencies in these fascinating resonance experiments by Youtube user Brusspup . The sand is sprinkled onto a black metal plate attached to a tone generator, which emits a series of increasing frequencies. The higher the frequencies, the more intricate the designs become.

This experiment is based on the Chiadni plate , invented by German physicist Ernst Chiadni in the 18th century. Chiadni used a violin bow along the edge of a glass plate covered with sand to create visualizations of sound. The plate is divided into regions vibrating in opposite directions, bounded by lines of zero vibration called nodal lines.

The plate was bowed until it reached resonance, at which point the vibration causes the sand to concentrate along the nodal lines where the surface is still. This technique is still used in the design and construction of acoustic instruments like violins and guitars.

Brusspup often experiments with the intersection of science and art. Previous projects have included running water through sound waves to produce incredible zig-zagging shapes, and a sound-based camera trick that makes water appear to travel backwards.

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Watch audio frequencies visualised in sand

When a plate sprinkled with sand vibrates at certain audio frequencies, it creates beautiful, intricate patterns.

(Screenshot by Michelle Starr/CNET Australia)

If you've never heard of the Chladni plate experiment , the principle is very simple. Sound frequencies create patterns. If you can make a metal at certain frequencies, acoustic resonance will cause those plates to vibrate with those patterns.

Normally, you can't actually see this — unless you sprinkle something granular over the top. Which is exactly what YouTube user Brusspup has done in his latest video. Using a metal plate attached to a speaker, he drove frequencies through it using a tone generator to create intricate configurations of sand.

"Certain frequencies vibrate the metal plate in such a way that it creates areas where there is no vibration," he said. "The sand 'falls' into those areas, creating beautiful geometric patterns. As the frequency increases in pitch, the patterns become more complex."

The patterns, called Chladni figures, are fascinating to watch as Brusspup changes the frequency; and, if you have the equipment, this one is absolutely safe to try at home.

Via www.thisiscolossal.com

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Sand sprinkled on the Chladni plate will gather on nodal lines when vibrated, dramatically revealing the intricate patterns.

• 1x Square Chladni Plate (24 cm sides)
• 1x Circular Chladni Plate (24 cm diameter)
• 1x Sand, extra fine (1 kg)
• 1x Sand Shaker

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• Published: 22 August 2024

Field study on vibration characteristics of geocell-reinforced aeolian sand subgrades

• Jie Liu 1 , 2 , 3 ,
• Jiadong Pan 1 , 2 , 3 ,
• Bin Gao 4 ,
• Jiahui Liu 5 ,
• Changtao Hu 2 &
• Haoyuan Du 4  

Scientific Reports volume  14 , Article number:  19564 ( 2024 ) Cite this article

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• Civil engineering

Constructing highways in deserts is expensive due to the difficulty of acquiring materials; utilizing aeolian sand effectively has become a problem, especially in the Xinjiang region, where the desert widely occurs. This paper aims to investigate the vibration response of a geocell-reinforced aeolian sand subgrade under traffic loading based on field tests of highways in deserts. The vibration acceleration response of geocell-reinforced aeolian sand and gravelly soil upper roadbed structures is tested. The field test results illustrate the effects of dynamic loading on geocell-reinforced aeolian sand roadbeds, and the thickness substitution ratio between geocell-reinforced aeolian sand roadbeds and conventional gravelly soil roadbeds is determined and verified based on the vibration acceleration monitoring values. The results show that the vibration response induced by the test vehicle is concentrated within the 30 Hz frequency band, and the higher the vibration frequency, the faster the vertical decay in the road. The vibration damping capacity of the reinforced aeolian sand roadbed is better than that of the gravelly soil roadbed; when replacing the gravelly soil roadbed with the reinforced aeolian sand roadbed, the substitution ratio is 0.31–0.42. It is verified that half thickness of gravel soil on roadbeds can be replaced by geocell-reinforced aeolian sand under different working conditions. The results of this study can provide reference data for the design of highway subgrades in deserts.

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Introduction.

With the construction of the core area of the Silk Road Economic Belt in Xinjiang, many highways in deserts have been built in rapid succession. The S21 Awu Highway Project is the most essential and convenient channel between Urumqi and northern Xinjiang, with a total length of 342.5 km and a 120 km/h design speed. This project is vital for enhancing the connection between Urumqi and Altay, shortening the interregional distance, and promoting regional economic and social development. In the design and construction of highways in deserts, gravelly soil is generally chosen as the upper roadbed filler to transfer vehicle loads. In desert areas, the long transportation distance of raw materials and construction difficulties make the upper roadbeds of highways in deserts expensive to build. Due to its low surface activity, looseness, obvious non-plasticity, notable non-hydrophilicity, and high collapsibility, aeolian sand is unsuitable for direct use as an upper roadbed filler on desert expressways 1 , 2 , 3 . Therefore, using reinforced aeolian sand instead of gravelly soil as the upper roadbed filler is economically feasible.

Geosynthetics have been widely used in highway engineering, with geocells utilized primarily for load-bearing and reinforcement purposes 4 . On the other hand, considering that aeolian sand particles are small and non-cohesive, reinforcing them with three-dimensional geosynthetics is more effective 5 , 6 , 7 . Geocells have the advantages of being lightweight and having high strength, convenient transportation, and easy construction. Geocells save road construction materials and optimize road performance by increasing the strength, stiffness, and durability of the structural layer to reduce the thickness of the subgrade 8 , 9 , 10 , 11 , 12 . After geocell reinforcement, roads can carry higher traffic volumes. The geocell's reinforcement mechanism indicates that it can be used as a reinforcing element within the soil to promote stress redistribution and limit soil deformation. The closed geocell around the reinforced soil has a lateral restraining effect, and there is a friction effect between the geocell and the soil in the generation of relative displacement, which significantly improves the roadbed's bearing capacity 13 , 14 , 15 , 16 . In addition, geocells have the advantages of light weight and high strength, convenient transportation and easy construction. Therefore, the use of geocells to reinforce aeolian sand is an ideal means to enhance the performance of aeolian sand.

Many scholars have used various experiments and numerical simulations to illustrate the enhancement of highway performance using geocells 17 , 18 , 19 . Particularly, there have been many studies on the static properties of geocell-reinforced aeolian sands. For example, Singh 20 conducted plate loading tests using geocell-reinforced and unreinforced sand and compared the results from these laboratory tests with field test results. The experimental results showed that geocell reinforcement significantly increased the strength and stiffness of the sand. Using a large-scale triaxial test, Song 21 demonstrated that geocells were more effective than loose sandy soils in reinforcing compacted sandy soils. Using a block resonance test, Hasthi and Hegde 22 found that the use of geocell-reinforced aeolian sand resulted in a 61% reduction in the displacement amplitude. Nevertheless, these findings only reflect the static properties of geocell-reinforced aeolian sand and do not consider the dynamic response of the subgrade under traffic loading. Therefore, more mobile wheel load field tests are needed to investigate the effect of geosynthetic reinforcement in the subgrade.

Since the state of geosynthetic reinforcement under actual conditions needs to be considered in practical applications, compared with the results of laboratory and unpaved tests, the results of field tests are more reliable for highway practice. For instance, White 23 showed that the lateral confinement effect of geomaterials on the fill under dynamic loading can improve its performance. At the same time, axle weight and vehicle speed are the main factors affecting the dynamic response of the railroad subgrade. Latha et al. 24 investigated the effect of geosynthetic reinforcement on increasing bearing capacity and reducing rutting depth through systematic field tests. Their test results showed that the geotextile effectively increased the number of vehicle passes from 17 to 100, and the rut depth of the geotextile-reinforced section was significantly smaller than that of the unreinforced section. Pokharel 25 conducted a large-scale traffic test of geocell reinforcement of weak roadbeds. The geocell reinforcement reduced the deformation of the subgrade and the roadbed, saved 13 cm of subgrade material, and increased the service life by 3.5 times. Yang et al. 26 conducted a large-scale traffic test on a geocell-reinforced weak subgrade. Through geocell reinforcement, the subgrade and subgrade deformation decreased, 13 cm of subgrade material was saved, and the service life increased by 3.5 cm. In addition, Imjai et al. 27 investigated the effectiveness of geosynthetics for reinforcing flexible pavements through a foot-scale field test in which the geosynthetics were placed at different depths to measure the structural response in the field. The results showed that the vertical static stresses in the subgrade were reduced by 66%, and the dynamic stresses were decreased by 72%. Geosynthetic reinforcement significantly reduced the vertical stresses transmitted to the subgrade and the roadbed. Singh et al. 28 investigated the performance of geosynthetics for the reinforcement of unpaved roads using mobile wheel load tests. The test results showed that the surface deformation was reduced by 44.89% in the geotextile-reinforced test section and 28.57% in the geogrid-reinforced test section. Luo 29 compared the dynamic deformation modulus of geocell-reinforced and unreinforced roadbeds using a roadbed reinforcement test and suggested that geocell-reinforced roadbeds can increase the dynamic deformation modulus by 27% and reduce the soil pressure by 30.1 to 37.2%. In addition, geocell reinforcement can reduce the surface bending subsidence of the roadbeds by 26.4 to 29.2%. The above research shows that the dynamic response of subgrades determines the critical dynamic characteristics and working properties, which is important for designing subgrade structures and reducing project costs 30 , 31 .

Several scholars have carried out field test studies on the dynamic and static structural properties of geosynthetic-reinforced soils. Due to the limitations of the test conditions, conventional field tests for traffic loading can only be carried out on unpaved roads, which cannot accurately express the dynamic properties of the road when it is in service. Because the state of geosynthetic reinforcement under natural conditions needs to be considered in practical applications, field tests are more reliable for highway practice than are laboratory and unpaved road tests. At present, there is still a lack of field tests on the dynamic characterization of geocell-reinforced aeolian sand; therefore, the actual reinforcing effect of geocell-reinforced aeolian sand under the action of a driving load cannot be effectively illustrated, which affects the further promotion of geocell-reinforced aeolian sand in highways in deserts. This paper investigates the vibration attenuation performance of geocell-reinforced aeolian sand roadbeds under a moving wheel load test. Two road test sections were constructed in the field to achieve this goal, with geocell-reinforced aeolian sand and gravelly soil as the upper roadbed. The mobile wheel load performance of the geocell-reinforced aeolian sand test section was compared with that of the gravelly soil test section. The vibration acceleration index was used to evaluate the vibration attenuation of geocell-reinforced aeolian sand, and the bearing capacity index of aeolian sand was verified to determine the proportion of geocell-reinforced aeolian sand replacing gravelly soil. This paper aims to verify the effectiveness of geocell-reinforced aeolian sand replacing traditional gravel soil in roadbed fill by studying the dynamic characteristics of aeolian sand roadbeds under vehicle dynamic loading. The research results can provide a design basis for constructing highways in deserts.

Field testing

Case study description.

The field test site is located in the hinterland of the Gurbantunggut Desert along the S21 line, namely, the first highway in the deserts within the Xinjiang Uygur Autonomous Region. The total length is 342.5 km, and the design speed is 120 km/h. The test section of this study is selected from Huanghuagou to Urumqi, K233 + 600 to K233 + 750, with a total length of 150 m. This section is a separated subgrade, and the width of one side is 13.25 m. Two schemes are designed for this test section to compare the vibration characteristics of geocell-reinforced aeolian sand and gravelly soils as the upper roadbed. Scheme 1 entails the use of woven fabric + gravelly soil to fill the upper roadbed. Through dynamic triaxial tests of reinforced and unreinforced aeolian sand, it is found that the hysteresis curve of geocell-reinforced aeolian sand is denser and the plastic deformation is smaller, which indicates that the geocell can better restrict the development of the soil plastic zone 32 . Therefore, Scheme 2 involves the use of woven fabric and geocell-reinforced aeolian sand to fill the upper roadbed. The gravelly soil and aeolian sand filler were taken from the local area, and the grading curves of the two filler materials are shown in Fig.  1 . The thickness of the asphalt layer was 12 cm, the cement-stabilized gravel subgrade was 36 cm, and the thickness of the natural gravel subbase was 18 cm in both scenarios. The physical properties of the gravelly soil and aeolian sand are shown in Table 1 . The geogrid used in the field test is a plug-in integral high-strength geocell, and the material is polypropylene resin. To ensure that the strip and the connection point exhibit high strength and consistent strength matching, the grid belt connection is interwoven by U-shaped steel nails. The U-shaped nails exhibit a diameter greater than 2.5 mm, and they are subjected to galvanized anti-corrosion treatment. The physical and mechanical parameters of the polypropylene resin geocells are shown in Table 2 .

The grading curves of the filler scale.

Monitoring program

The reinforcing effect of geocells on aeolian sand roadbeds under traffic load conditions is reflected explicitly in the performance and spatial attenuation of dynamic stress, dynamic velocity, and dynamic acceleration at different locations when the test vehicle passes through the test section. The vibration acceleration is closely related to the vehicle's driving speed, loading, and material properties of the subgrade. Vibration acceleration is an essential parameter for determining the effect of energy generated by vehicle loading on road structures 33 . To study the spatial attenuation trend of the vibration acceleration along the vertical direction of the geocell-reinforced aeolian sand subgrade and the traditional gravel soil subgrade, the vibration reduction performance levels of these two different forms of subgrade structures were compared, and the sensor layout was consistent between the two subgrades. Five monitoring points were established in the sections of the two roadbeds, which were evenly arranged on the surface of the pavement, between the pavement and the upper roadbed, between the upper and lower roadbeds, and within the aeolian sand roadbed. Due to the varying thicknesses of the roadbed structures, the buried depth of the sensor differs. The layout depths of geocell reinforced aeolian sand roadbed sensors are 0 m, 0.66 m, 0.81 m, 1.26 m and 1.71 m respectively. The depth of gravel soil roadbed sensors is 0 m, 0.66 m, 0.96 m, 1.41 m and 1.86 m respectively. The layout position is shown in Fig.  2 . Measurement was conducted by a pressure point vibration accelerometer, model JMCZ-2091, with a range of 1 to 1.4 kHz, an acceleration up to 100 g , a charge sensitivity of 2060 PC/g, and the signal output as the voltage output. A standard vibration source that can generate 10 cm/s 2 acceleration was used for calibration and scaling before burial. JMCZ-2091 vibration accelerometers were placed along the vertical direction during road construction. After the sensors were pre-buried at predetermined positions in the test section, the surrounding aeolian sand was compacted via jump tamping. The acquisition analyzer is a sixteen-channel dynamic acquisition module modeled as JMDY-1016, which can collect the dynamic acceleration value of the measurement point in real time and directly convert it into a time curve.

Diagrammatic drawing of sensor placement.

Test program

The test program mainly considers the effects of vehicle type, weight, and speed. Based on available statistics on highway traffic volume data and representative vehicle types 34 , 35 , the dynamic acceleration test takes three different types of vehicles, namely, two-axle trucks, three-axle trucks, and buses, to pass through the test and control sections of the geocell-aeolian sand subgrade at different speeds (Fig.  3 ). The mass of the trucks was controlled by loading them with aeolian sand before the test. Prior to the test, the quality of the different models was accurately measured, and the error was controlled within 1% to ensure the rigor of the test. The test was designed for 60 working conditions. These working conditions are listed in Table 3 . In addition, to ensure that the test vehicle can pass through the range of 20 m before and after the test section at a uniform speed, there is 1 km in front of the test section for the vehicle to accelerate in advance. During the test, the rear wheel center track line overlapped with the marking line directly above the sensor. The test was repeated in 3 groups for each working condition, and the data with similar excitation were selected from the test results.

Preparation and testing arrangements at the site: ( a ) geocell laying; ( b ) aeolian sand filling; ( c ) two-axle truck; and ( d ) three-axle truck.

Field test results and analysis

Vibration analysis of the upper roadbed on gravelly soil.

When a vehicle passes on the gravelly soil upper roadbed, accelerometer G1 records the vertical acceleration-time diagrams of different models passing at different speeds when unloaded (Fig.  4 ). In the graphs, the different colored curves represent the different driving speeds of the test vehicles. As the vehicle travel time and the distance from the monitoring point change, the collected response acceleration signals first increase and then decrease, with apparent peaks. The waveforms of passenger cars and trucks are different, and the waveforms of the two-axle and three-axle trucks are similar. In addition, a smaller peak occurs before the peak when the passenger car passes at a driving speed of 20 km/h. When traveling at a slower speed, the front and rear axles of the test vehicle act on the test section separately. The axle load of the rear axle is more significant than that of the front axle, so two wave peaks are formed with a large front and a small back. At faster speeds, the front and rear axles are closer in time, so they overlap into a single peak.

Time–history characteristics under different traffic loads: ( a ) Buggy; ( b ) two-axle truck; and ( c ) three-axle truck.

Figure  5 shows the frequency domain characteristics of the vertical attenuation of the excitation of an unladen two-axle truck passing over a gravelly soil upper roadbed road at 20 km/h. While a vehicle travels along the road, the wheels of the vehicle travel on the road with a specific frequency and amplitude of bouncing due to the unevenness of the road surface. The vertical vibration is mainly caused by the excitation generated by the vehicle body bumps. As shown in Fig.  5 , the vibration response shows a trend of attenuation with increasing depth, and the vibration frequency ranges from 0 to 50 Hz, with the main components concentrated from 0 to 30 Hz. This indicates that the vibration caused by the vehicle traveling on the site is mainly low-frequency. Spectral analysis revealed that the high-frequency and low-frequency vibration attenuation speeds are slow during the vibration attenuation process. This is because the high-frequency vibration in the propagation process is fast; due to the large soil body damping effect, the attenuation speed is more rapid. Low-frequency vibration attenuation is slower, so the propagation distance is greater than that of high-frequency vibration. In addition, as the depth of the monitoring point increases, the amplitude of the acceleration signal decreases significantly, which shows that the monitoring results are reliable.

Frequency domain features along the depth direction.

Characteristics of the vibration acceleration amplitude with vehicle speed and vehicle weight

The changes in the vibration acceleration amplitude with vehicle speed and weight are shown in Fig.  6 . The vibration response caused by a passenger car is highly sensitive to changes in speed; the vibration acceleration amplitude of the passenger car at a speed of 20 km/h is 3.9 times greater than that at a speed of 120 km/h. For a 2.7 t passenger car, the speed increased from 20 to 60 km/h, and the acceleration amplitude of the subgrade increased from 0.32 to 0.44 cm/s 2 , which is an increase of 28%. For a 10 t two-axle truck, the speed increased from 20 to 60 km/h, and the acceleration magnitude of the road surface increased from 0.77 to 1.04 cm/s 2 , which is an increase of 26%. For a 16 t three-axle truck, the speed increased from 10 to 30 km/h, and the acceleration magnitude of the road surface increased from 2.79 to 3.46 cm/s 2 , which is an increase of 19%. The above analysis demonstrates that the vibration acceleration decreases with increasing depth when different vehicles pass at varying speeds, and there is a mutation point in the process of reducing the vibration acceleration under most working conditions. With increasing vehicle speed and vehicle weight, the acceleration at different depths of the subgrade increases, and the closer to the vibration source, the more significant the acceleration change is. This indicates that the change in the vehicle speed and vehicle weight influences the attenuation characteristics of acceleration along the depth direction of the subgrade. Since the tests were conducted on the same test section with the same pavement structure, flatness, and inherent vibration characteristics, it can be seen that the increase in speed affects road vibration.

The curve of vibration acceleration with vehicle speed and vehicle weight: ( a ) buggy; ( b ) two-axle truck; ( c ) three-axle truck; and ( d ) both trucks.

The impact of changing the test vehicle load on the road vibration response is also pronounced, and the vibration response of the two-axle truck is more sensitive to changes in vehicle weight. For every 1 t increase in the weight of a two-axle truck, the vibration velocity amplitude increases by 0.16 cm/s 2 , with an average increase of 15%, and for every 1 t increase in the weight of a three-axle truck, the vibration velocity amplitude increases by 0.04 cm/s 2 , with an average increase of 1.8%. When the vehicle weight is 15 t, the vibration response of the three-axle truck is slightly greater than that of the two-axle truck, which is caused by the superposition of the same vibration source of the rear two axles 36 .

Vibration attenuation laws for different upper roadbed structures

The vibration attenuation laws of different roadbed forms are significantly different. Therefore, the dynamic characteristics of roadbed structures under different vehicle weights, speeds, and models have specific research value. Figure  7 shows the vibration attenuation curves of two-axle and three-axle trucks with a vehicle weight of 16 t. For two-axle and three-axle trucks with the same mass, the vibration acceleration amplitude in the vertical direction shows a different attenuation trend. The attenuation of two-axle and three-axle trucks is closer on the geocell-reinforced aeolian sand side. The attenuation is most apparent in the geocell-reinforced aeolian sand layer, with an attenuation rate above 20%. On the gravelly soil side, the vibration attenuations of the two-axle and three-axle trucks are more disparate. The attenuation rate of the two-axle truck in the gravelly soil layer is 15%, and the attenuation rate of the three-axle truck in the gravelly soil layer is only 6%.

Vibration attenuation curves of different vehicle models with a weight of 16 t.

Figure  8 shows the vibration attenuation curves of passenger cars and trucks at different speeds. Due to the lower axle weight of the passenger car, road vibration in the pavement structure at the loss of larger, transmitted to the roadbed when the vibration acceleration amplitude is reduced to 0.2 cm/s 2 or less. The decrease is greater than 60%, with the maximum decrease reaching 87%. For two- and three-axle trucks under different driving speed conditions, the vibration acceleration decreases with increasing depth. On the geocell-reinforced aeolian sand side, the attenuation rate of vibration acceleration in the geocell-reinforced aeolian sand layer increased significantly. However, the attenuation rate of the vibration acceleration on the gravelly soil side does not show any particular change in the gravelly soil layer. The vibration attenuation of the geocell-reinforced aeolian sand layer is greater than that of the gravelly soil layer.

Vibration attenuation curves at different speeds: ( a ) buses and ( b ) two-axle and three-axle trucks.

Figure  9 illustrates the vibration response attenuation curves for different vehicle weights. The vibration attenuation of both upper roadbed structures becomes more pronounced as the vehicle weight increases. Additionally, vehicle weight affects geocell-reinforced aeolian sand slightly more than gravelly soil. A combination of the results in Figs.  8 and 9 reveals that changing the vehicle weight and driving speed has an effect on the attenuation of vibration in the road structure. In addition, the attenuation rate of the vibration acceleration of the geocell-reinforced aeolian sand upper roadbed is greater than that of the gravelly soil upper roadbed under different working conditions. This is because the polypropylene resin geocell improves the dynamic elastic modulus as well as the damping of the aeolian sand; therefore, it changes the compression and deformation properties of the aeolian sand under traffic loading, restricts the lateral deformation of the soil, inhibits the development of the shear zone in the soil, and strengthens the load-bearing capacity of the soil, thus improving the vibration suppression performance 37 .

Vibration response attenuation curves under different vehicle weights: ( a ) two-axle truck and ( b ) three-axle truck.

Analysis of the vibration attenuation effect of different upper roadbeds

To analyze the attenuation of vibration acceleration in different upper roadbeds under traffic loading, the proportion of vibration acceleration attenuation per unit height is defined as the dynamic acceleration attenuation coefficient \({K}_{a}\) :

where \({a}_{u}\) is the vibration acceleration of the upper layer, \({a}_{d}\) is the vibration acceleration of the lower layer, and \(\Delta h\) is the height difference between the upper and lower layers.

According to the above equation, the attenuation coefficients of the dynamic acceleration of roadbeds under different working conditions can be calculated (Fig.  10 ). The attenuation coefficients of gravelly soils at different test speeds are much lower than those of geocell-reinforced aeolian sand, and the influence of the driving speed on the attenuation coefficient is small. Under the most unfavorable working conditions, the driving speed of the bus is 120 km/h. Under the most unfavorable working conditions, the driving speed of a two-axle truck and three-axle truck is 60 km/h, and the average attenuation coefficient of geocell-reinforced aeolian sand at this time is 3.2 times that of gravelly soil. Figure  10 b shows that the attenuation coefficient of the vibration acceleration increases with increasing vehicle weight, and the increase in the gravelly soil is slightly greater than that in the geocell-reinforced aeolian sand. This is because gravelly soils under heavy loads produce greater micro-deformation, consuming a portion of the energy into internal energy, and the nature of vibration transfer is the transfer of energy. Hence, the attenuation coefficient of the gravelly soil is more significant. The most unfavorable working condition of a two-axle truck occurs when the truck weight is 22 t. The most unfavorable working condition of a three-axle truck occurs when the truck weight is 52 t.

Attenuation coefficient curves for different vehicle ( a ) speeds and ( b ) weights.

This paper mainly explores the influence of geocell-reinforced aeolian sand upper roadbeds on the vibration response of aeolian sand subgrades to show that the dynamic characteristics of geocell-reinforced aeolian sand subgrades are better than those of traditional subgrade forms. The results of this study can provide practical reference data for highways in deserts at the design and construction stages. In addition, by comparing the attenuation coefficients of the most unfavorable working conditions, the thickness of geocell-reinforced aeolian sand needed to replace the traditional gravelly soil upper roadbed can be calculated.

An analysis of the vibration attenuation effect of different upper roadbeds shows that the impact of geocell-reinforced aeolian sand changes with changing test vehicle mass and speed; the most unfavorable working conditions for two-axle trucks are a truck weight of 22 t and a traveling speed of 60 km/h. The most unfavorable working conditions for three-axle trucks are a truck weight of 52 t and a traveling speed of 60 km/h.

Considering the different test models and upper roadbeds, the field data are normalized to compare the vibration attenuation laws under other working conditions. The normalization process is as follows:

where \({a}_{i}\) is the vibration acceleration amplitude of the measurement point and \({a}_{0}\) is the vibration acceleration amplitude of the road measurement point.

The attenuation curves of the vibration acceleration at each measurement point under the most unfavorable working conditions of different test vehicles and the attenuation curves after normalization are shown in Fig.  11 . Figure  11 shows that under the most unfavorable working conditions, the vibration attenuation effect of geocell-reinforced aeolian sand on the vibration acceleration is greater than that of a road surface, gravelly soil, or aeolian sand. This occurs because the vertical tendons in the three-dimensional cellular side-limiting structure of the geocell play a role in the lateral restraint of the soil body as well as generate a profound foundation effect; this substantially increases the apparent cohesion of the soil body and the integrity of the structural layer, thus increasing the attenuation of vibration acceleration 38 .

Normalized attenuation curve: ( a ) attenuation curve and ( b ) normalized curve.

The substitution ratio of the geocell-reinforced aeolian sand upper roadbed to the gravelly soil upper roadbed can be calculated based on the vibration attenuation coefficient as follows:

where C is the proportion of substitution, \({h}_{l}\) is the thickness of the gravelly soil upper roadbed, \({h}_{t}\) is the thickness of the equal-proportion substitution of the geocell-reinforced aeolian sand upper roadbed, \({K}_{al}\) is the vibration attenuation coefficient of the gravelly soil, and \({K}_{at}\) is the vibration attenuation coefficient of the geocell-reinforced aeolian sand.

Figure  12 shows the variation curve of the substitution ratio with vehicle weight, which shows that the substitution ratio increases with increasing vehicle weight. This finding also confirms the need to increase the thickness of geocell-reinforced aeolian sand under heavy load conditions. Under the action of two-axle trucks, the substitution ratio is in the range of 0.18–0.42. Under the action of three-axle trucks, the substitution ratio is in the range of 0.15–0.31. The substitution ratio used in the field is 0.5, which can theoretically satisfy the vibration acceleration requirements in all the test cases.

Geocell-reinforced aeolian sand replacement gravel/soil ratio curve.

Finally, the substitution ratios between the geocell-reinforced aeolian sand upper roadbed and the gravelly soil upper roadbed are calculated. When the highway subgrade filling height is low, the bearing capacity of the roadbed material does not meet the allowable bearing capacity requirements because the traffic load is not effectively spread through the subgrade. Theoretically, the sum of the dynamic stress and static stress attenuated by each working layer of the subgrade should meet the requirements of the allowable bearing capacity of the subgrade holding layer as follows:

where \({\sigma }_{D}\) is the dynamic stress value (kPa) at the top of the bearing layer; \({\sigma }_{S}\) is the static stress value (kPa) at the top of the bearing layer; and \(\left[{f}_{0}\right]\) is the allowable bearing capacity of the bearing layer (kPa).

The static stress is the sum of the stress of the test vehicle axle load and each structural layer as follows:

The dynamic stress can be calculated by combining the parameters of the vibration accelerometer as follows:

where \(\phi \) is the instrument parameter, which is 356 according to the field situation.

The ultimate bearing capacity of single-layer geocell reinforced aeolian sand measured by static load test is 456 kPa 39 , and the measured value is basically consistent with the previous studies 40 . In addition, according to the calculation formula of bearing capacity of geocell reinforced foundation studied by Li Chi 40 and Lei Shengyou 41 (Eqs.  7 – 9 ), the calculation is carried out according to the parameters in static load test:

where p u is the bearing capacity of pure aeolian sand foundation calculated according to Terzaghi formula; Δ p u is the increment of bearing capacity of aeolian sand foundation after geocell reinforcement.

where γ is the gravity of aeolian sand, the value is 16.4 kN/m 3 ; the bearing capacity coefficient N r is 93.16; b is the width of the loading plate in the static load test, the value is 0.3 m; q is the overlying load, because the thickness of the overlying soil is 0, the value of q is 0; The cohesion is small, the value is 0; the calculation can be obtained as 178.87 kPa.

where T is the tension of the geocell, the single-layer tension is 15 kN; s is the final settlement, the value is 0.045 m; r is the radius of the round on both sides of the foundation, generally 3 m; β is the angle between the tension and the horizontal plane, and β is 12.68° calculated by the settlement; The bearing capacity coefficient N q is 40; After calculation, the incremental value of bearing capacity is 250.75 kPa. According to the above calculation, the bearing capacity of single-layer geocell reinforced aeolian sand subgrade is 429.62 kPa.

To ensure safety, the allowable bearing capacity \(\left[{f}_{0}\right]\) is taken as 380 kPa, and according to the literature 42 , and the actual measurement, the average rear wheel static stress σ 0 of a 22 t vehicle can be calculated as 108 kPa. The average rear wheel static stress σ 0 of a 52-t vehicle is 201 kPa. An assessment of the load-carrying capacity for the most unfavorable conditions is provided in Table 4 .

The most unfavorable working condition is when the ratio of the vibration attenuation coefficient of gravel soil to the vibration attenuation coefficient of geocell-reinforced aeolian sand is the smallest, i.e., the substitution thickness is the largest, so the substitution ratio under the most unfavorable working condition is the maximum value. The most unfavorable working conditions are when the test vehicle weight is the greatest; then, the static stress generated by the vehicle is also the largest. When the most unfavorable working conditions are satisfied, other working conditions can be introduced. Therefore, we can verify the reasonableness of the substitution ratio by calculating the load-carrying capacity under the most unfavorable working conditions.

In this paper, the dynamic characteristics of the geocell-reinforced aeolian sand subgrade under traffic load conditions are investigated. The results show that the damping capacity of the geocell-reinforced aeolian sand roadbed is greater than that of the traditional gravel soil roadbed. The obtained conclusion is similar to that reported in previous studies. Gao et al. 43 conducted a field test by embedding a vibration velocity measuring device inside a geocell-reinforced aeolian sand roadbed. The results indicated that the attenuation of the vibration velocity of the geocell-reinforced aeolian sand roadbed is less than that of gravel soil, but the attenuation curve is smoother. In addition, the depth of the working area of the geocell-reinforced aeolian sand subgrade is smaller, which also shows that the dynamic attenuation characteristics of the geocell-reinforced aeolian sand roadbed are better than those of gravel soil. Ya 44 used ABAQUS to study the dynamic stress attenuation of geocell-reinforced aeolian sand subgrade and the deformation of the geocell under traffic load conditions. When a vehicle travels over the geocell, the geocell will be deflected and is tilted, and the deformation will gradually recover after the vehicle leaves. Through the analysis of the dynamic stress attenuation coefficient, it is shown that the geocell-reinforced aeolian sand roadbed reduces the vibration, improves the long-term service performance of the roadbed, and homogenizes and reduces the peak stress. In addition, there will be a net effect after the geocell-reinforced aeolian sand roadbed is applied, which reduces the settlement. In this paper, the dynamic response of the geocell-reinforced aeolian sand subgrade is studied by the field test method, and valuable results are obtained. However, there are still shortcomings in this research. Next, numerical simulation, microscopic mechanism and field test results should be combined to study the mechanism of action between the geocell and aeolian sand.

In this study, moving wheel load tests were carried out on roadbeds composed of two structures, namely, a geocell-reinforced aeolian sand upper roadbed and a gravelly soil upper roadbed, to assess the effect of the vibration response of a subgrade with geocell-reinforced aeolian sand. The attenuation coefficients of the two forms of subgrades were also compared to derive a thickness replacement formula for the conventional gravelly soil upper roadbed and the geocell-reinforced aeolian sand roadbed. Based on the above analysis, the conclusions are summarized as follows. The test vehicle's vibration response is mainly dominated by low-frequency vibration, and the vibration frequency is concentrated within 30 Hz. Spectral analysis reveals that during the vibration decay process, the high-frequency vibration in the road structure decays fast vertically, and the low-frequency vibration decays slowly. The vibration acceleration amplitude increases with the increase in the vehicle speed and vehicle weight. When the vibration sources are closer, the acceleration is superimposed, increasing the amplitude. The attenuation effect on the vibration of the geocell-reinforced aeolian sand upper roadbed and gravelly soil upper roadbed increases with increasing vehicle weight, in which the degree of increase in gravelly soil is slightly greater than that in geocell-reinforced aeolian sand. The mobile wheel load field test results reveal that in the different models, the effects of vehicle weight, driving speed, and geocell-reinforced aeolian sand on the vibration attenuation ability are greater than those of the gravelly soil, and under other working conditions, one-half the thickness of the geocell-reinforced aeolian sand upper roadbed can be used instead of the gravelly soil upper roadbed. In addition, considering the most unfavorable conditions, the attenuation coefficients are compared to calculate the thickness substitution ratio of the geocell-reinforced sand roadbed and the traditional gravel soil roadbed under different conditions. Notably, half of the thickness of the geocell-reinforced sand layer roadbed can be used to replace the traditional gravel soil roadbed.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

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Acknowledgements

This study was funded by the enterprise commissioned science and technology project of the Xinjiang Traffic Design Institute Company (No. KY2021100901).

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Jie Liu & Jiadong Pan

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Jie Liu: Writing—review and editing. Jiadong Pan: Writing—original draft, Writing—review and Editing Pictures and Tables. Bin Gao: Writing—original draft. Jiahui Liu: Writing—original draft. Changtao Hu: Writing—review and editing. Haoyuan Du: Writing—original draft. All authors reviewed the manuscript.

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Liu, J., Pan, J., Gao, B. et al. Field study on vibration characteristics of geocell-reinforced aeolian sand subgrades. Sci Rep 14 , 19564 (2024). https://doi.org/10.1038/s41598-024-69683-y

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DOI : https://doi.org/10.1038/s41598-024-69683-y

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