The Acoustic Cushion

Huascarán and Why Falling Mountains Flow Like Water

Dry broken granite has a coefficient of sliding friction near $\mu = 0.6$. That hard mechanical limit requires any ordinary rockslide to grind to a halt as soon as a mountain slope flattens below thirty-one degrees. Yet at 3:23 p.m. on May 31, 1970, a fifty-million-cubic-meter slab of glacial ice and granodiorite rock broke off the vertical western face of Mount Huascarán in the Peruvian Andes. It defied that friction limit across sixteen kilometers of gentle valley floor. Triggered by a Magnitude 7.9 subduction earthquake off the coast of Chimbote, the falling mass dropped 1,000 meters down the steep glacier before entering the shallow, seven-degree slope of the Llanganuco gorge and the Santa River valley.

Instead of piling up at the base of the cliff where the slope flattened, the debris accelerated to an average velocity of 280 kilometers per hour. Eyewitnesses standing on high ridges above the valley felt the ground vibrate like a drumhead. They watched boulders weighing thousands of tons skim across the landscape. One survivor who watched the avalanche bear down on the provincial capital of Yungay reported that the mountain did not slide like stone grinding upon stone, but rushed down the valley with hurricane speed and the fluidity of water. A lobe of the racing debris leaped straight over a 200-meter-high bedrock ridge that had sheltered Yungay from smaller historic mudflows. It buried the entire city under ten meters of rock and mud in less than three minutes.

Nearly a century earlier, after an 1881 rockfall destroyed the Swiss village of Elm, Alpine geologist Albert Heim had documented this same anomaly. He named such long-runout rock avalanches sturzstroms—fall-streams. Whenever the volume of a dry rockfall exceeds roughly ten million cubic meters, its effective coefficient of friction (measured as the ratio of vertical drop $H$ to horizontal runout $L$) plummets from the normal laboratory value of $\mu \approx 0.6$ down to 0.1 or less. Early geologists proposed that falling mountains rode on a trapped cushion of compressed air or steam. That hypothesis collapsed when lunar photographs from the Apollo missions revealed identical long-runout landslides inside airless, bone-dry craters on the Moon.

In 1979, geophysicist Jay Melosh solved Heim's paradox. He demonstrated that a massive rock avalanche generates an internal field of high-frequency acoustic vibrations that relieves the weight of the overlying rock. In standard Coulomb friction, the shear stress $\tau$ resisting motion equals the friction coefficient $\mu$ multiplied by the normal stress $\rho g h$ pressing rock grains together. Inside a rushing sturzstrom, however, violent collisions between boulders generate intense elastic pressure waves $p_{\text{acoustic}}(t)$ that bounce back and forth between the bedrock floor and the free upper surface:

Because the vast bulk of the rock mass traps this vibrational energy faster than internal damping can dissipate it as heat, acoustic pressure fluctuations grow until their peak amplitude matches the overburden weight $\rho g h$. During each rarefaction half-cycle of the sound wave, adjacent rock fragments are momentarily pushed apart. That acoustic unclamping drops normal contact stress to zero and allows the overburden to slip forward under minimal shear stress. The avalanche flows like a liquid not because the stone melts, but because trapped sound waves continuously unclamp the grain contacts. Out of twenty thousand residents in Yungay, only three hundred people survived by running up the stone steps of the municipal cemetery built atop an ancient pre-Columbian artificial mound.