T he Van N o r m a n Dam was holding back more than 10 million tons of water when the devastating Febru­

ary 9, 1971, ear thquake hit nearby San Fer­nando, California. The temblor cracked the dam and a concrete roadway crossing its top. The road and a massive chunk of the earthen dam slid into the water. (See " W h e n Soils Start To Flow," in this Mosaic.) N o one could determine if the dam would hold. Los Angeles County officials evacuated 80,000 people living in the path of the water. For four days, while engineers reduced the water behind the dam, the evacuees waited to see if their homes and possess ions wou ld be washed away.

People living near the Teton River Dam in southeastern Idaho on June 5, 1976, were not as lucky. N o ear thquake occurred, but that earthen dam collapsed suddenly. A tor­rent of water rushed through the breach,

The biggest. Originally designed for the space program, this 40-foot centrifuge is becoming the largest geotechnical centrifuge in the United States. National Aeronautics and Space Administration

2 MOSAIC July/August 1979

Geotechnical engineers seek—and find—ways to test massive structures to failure without waiting for them to fail.

Adaptations. Changes to the former space program centrifuge include an added disaster barrier and phase-one and phase-two model-support structures at the arm end. The six-foot figure, lower right, shows scale. National Aeronautics and Space Administration

flooding more than 300 square miles and causing damages estimated at more than $1 billion. The dam burst was in a sparsely settled area; nevertheless, 11 people lost their lives.

Such disasters illustrate a kind of "catch-22" in the engineering of such massive struc­tures as dams, offshore drilling platforms and the like. Until they fail, there is often no reliable information on the kinds of stresses that will cause them to fail.

Engineers have long sought ways to pre­dict reliably the stability of dams, deep mine tunnels, the sides of huge open-pit mines or formations from which groundwater or oil are to be withdrawn. But even at reduced scale, the prodigious dynamic forces of the kind produced by waves in the North Sea or earthquakes in California simply cannot be reproduced in a controlled way. To over­come the data lack, most massive structures are overdesigned. Engineering "fudge fac­tors" increase the margin of safety, but they

escalate costs and still fail to produce de­sired levels of certainty.

The generally adopted solution to this de­sign dilemma is to reduce the unwieldy forces and dimensions to numbers. A digit­ized structure can be simulated in a com­puter; it can then be shaken, rattled and rolled by a similarly digitized disruption.

Engineers did this in the early nineteen-fifties, before computers and modeling tech­niques had reached current levels of sophis­tication, when officials in Long Beach, California, asked how much the surface would sink when oil in formations under­lying the city was pumped out. As the story goes, the experts forecast a subsidence of 10 to 15 feet. When the ground sank 8 feet, they changed the prediction to 20. When the sink­ing totaled 18 feet, they revised their fore­cast to 25. The subsidence actually bottomed out at 30, when a program of repressuriza-tion by water injection took hold.

Computer simulations have improved,

but the moral remains: Some forces and structures cannot easily be reduced to num­bers. The behavior of multilayered soils sub­jected to dynamic loading is an example. The calculations escalate rapidly beyond a computer's capability (See "Solving for the Unsolvable," Mosaic, Volume 10, Number 1). They can be simplified, but at the cost of accuracy.

To surmount these limitations, geotech-nical engineers are putting new emphasis on devices that enable them to "create" land­slides and earthquakes, dam failures and mine cave-ins in a space no bigger than a laboratory closet at the end of a spinning centrifuge arm. These centrifuges rotate samples or models hundreds or thousands of times a minute, simulating increases in gravitational ("g") forces hundreds or thou­sands of times. For example, a foot-high model of an earthen dam can be centrifuged so that its weight simulates a structure 100 feet high. In this case, the speed required is one that produces an acceleration equiva­lent to 100 times the force of gravity at the earth's surface, or 100 g's. (The capacity of centrifuges can be expressed in g-tons, the product of the maximum g force and the weight of the specimen.)

Engineers thus have the ability to apply controlled forces in a laboratory setting. Samples or models of earthen dams, em­bankments, excavation supports, nuclear power plant foundations, offshore plat­forms, deep tunnels, submerged pipelines and a galaxy of other structures can be stressed to failure with relatively little cost or effort.

Subsidence due to extraction of ground­water and oil, to gasification of coal or to underground burning of oil shale can be measured before the fact. Soviet researchers and at least one U.S. engineer use the tech­nique to simulate nuclear blasts, using fire­cracker-scale explosions. Other researchers have experimented with centrifuge modeling of continental drift and mountain-building processes.

A Soviet lead Although it utilizes space-age technology,

centrifuge modeling dates back to 1933, when a thoughtful mining engineer, Philip B. Bucky, started experimenting with it at Columbia University. He tested the stability of mine openings using small models accel­erated up to 2,000 g's in a machine with a diameter under 1.5 feet. Bucky discovered one fact that underlies the feasibility of much geotechnical research by centrifuge: In most cases, it is not necessary to scale the size of soil particles or other natural materials in a model. Within limits, experimenters can use

4 MOSAIC July/August 1979

The next biggest. The 700-g-ton centrifuge at Sandia Laboratories in Albuquerque, currently the largest in the United States, is used for some geotechnical work, Sandia Laboratories

the same clay, sand or granite as in the full-scale situation.

Work by a student of Bucky's, Louis Panek, on mine openings and rock bolts (used to hold the sides and roofs of mine tunnels and shafts in place) continued through the nine-teen-forties and nineteen-fifties.

But despite its potential, the technique never caught on in the United States. Digital computers made their appearance, and en­gineers decided the work could be done cheaper and faster with mathematical analy­sis. Comments George B. Clark of the Colo­rado School of Mines in Golden, "People never grasped the full potential of centri­fuge model testing."

The situation was different in the Soviet Union. G. I. Pokrovsky and I. S. Fyodorov started experimenting with the method about the same time as Bucky did. The Soviets continued centrifuge development, and the technique is in widespread use in the Soviet Union today. "The reason they are so far ahead in centrifuge testing," opines one researcher, "is that they are so far behind in computer development." At least five large centrifuges exist in the Soviet Union, one of which is the largest in the world. Located in Azerbaidzhan, it has, the Russians report, a capacity of 2,000 g-tons or more. According to Soviet literature, cen­trifugal testing is used routinely and pre­ceded such projects as the Moscow Metro, a canal to divert the Moscow River and a large hydroelectric power station at Kuibyshev on the Volga River.

In the early nineteen-sixties, a centrifuge was used in Sweden to simulate tectonic processes. British researchers started centri­fuge work a few years later. In England, machines of 65 and 280 g-tons have been constructed at the University of Manches­ter, and there is a 120-g-ton machine at Cambridge University. Researchers from the United States have participated in experi­ments at these facilities as well as on centri­fuges in Denmark, France and Japan.

In this country, at least seven relatively large working centrifuges are available. Though machines larger than 65 g-tons are used principally for defense and aerospace testing, the largest American centrifuge—

A minicrater. The crater produced by a 0.14-ounce charge, detonated at 450 g's in a centrifuge, simulates a crater produced by 400 tons of explosives. Boeing Company

MOSAIC July/August 1979 5

the 700-g-ton machine at Sandia Corpora­tion's Albuquerque laboratories—is used for some geotechnical work.

Smaller centrifuges for geotechnical research in the United States have been in more-or-less continuous use since the late nineteen-f if ties, when George Clark built a seven-foot-diameter machine at the Univer­sity of Missouri's Rolla campus. Much of his work involved the stability of under­ground openings at the slopes of open-pit mines. He constructed models a few centi­meters in size, imposed selected g-loads on them and stressed them until they failed. "We compared the results of such tests with theoretical predictions and with measure­ments made in the field, and they checked out beautifully," Clark observes. Strain gauges, cameras and other instruments re­cord a model's mechanical response as it rotates. "These experiments," Clark ex­plains, "allow us to study what happens when a structure fails but does not collapse— for instance, a mine support that partially fails but continues to support weight. This cannot be done with mathematical analysis.

"However, the use of the centrifuge and mathematics is not an either~or situation. The two techniques of modeling should be used in combination, not separately. One must be able to construct an exact model to get good results from a centrifuge test. In some cases, all the conditions in the field cannot be simulated, and numbers are needed to fill in the blanks. On the other hand, soil behavior or some other factor may not be reducible to numbers, and experiments are needed as a base for mathematical models that more faithfully reproduce the full-scale structure."

Subsidence and crafersng At present, Clark has a Department of

Energy contract to study subsidence over geothermal reservoirs. He places models of the reservoir rock in the machine at Rolla. Slabs of lead represent overlying rock, and accelerations of as much as 1,000 g's simu­late the weight.

Tests at Rolla are preliminary to work on larger models in the 700-g-ton Sandia centri­fuge. "We intend to determine the sequence of events as hot water is withdrawn and the weight of the overburden breaks down the fabric of the rock," Clark explains. "The same type of tests can be used to predict subsidence due to in-situ removal of coal by gasification or of oil by underground burn­ing of oil shale."

Clark's experiments point to another use of centrifuge modeling—determining the size of craters made by large chemical or nuclear explosions. Modeling a kiloton or megaton

explosion, such as might be used in digging a new Panama Canal, can be done relatively easily and inexpensively on a centrifuge, according to Clark, Soviet researchers do this routinely, he says. An ounce of an explo­sive detonated at 1,000 g's can model a blast crater produced by some 25,000 tons of explosive. Doing this type of modeling, Robert M. Schmidt of the Boeing Company in Seattle has successfully represented in a centrifuge cratering caused by a 500-ton-equivalent nuclear blast.

Centr i fuge scal ing In a centrifuge, all dimensions of a model

needed to represent a full-sized structure de­crease directly with the increase in g's. Simu­lated forces increase as the square of the g factor; energy increases as the cube. At 100 g's, one pound of force on the model of an offshore platform is equivalent to a load of 10,000 pounds on the full-sized object. A gram of explosives at 100 g's generates a force of a million grams, or a metric ton of explosives. Even time can be compressed. Events that take 10,000 days, such as deposition and con­solidation of sediments, can be completed in one day at 100 g's.

In other work, Hon-Yim Ko of the Univer­sity of Colorado at Boulder uses a centrifuge there to simulate the loading forces on piles used to support offshore platforms and other structures. "If you reduce the linear dimensions of a pile by a factor of 100, then the force you need to apply at 100 g's de­creases by 1002," he explains. To test a 10-foot-diameter pile with a 50-ton capacity, he uses a model 1.2 inches in diameter and applies a force of 11 pounds. "I place the models in sand or clay from the actual con­struction site," he explains, "so there is no need to make complicated calculations of soil properties."

"Of course," Ko says, "such a system has its limits. The soil grains cannot be too large in relation to the model size. If the model pile is 4 inches in diameter and the grains average 0.04 inch, the pile 'sees' the soil as a continuum. But if the pile is only 0.04 to 0.12 inch in diameter, the soil may act like an aggregation of boulders instead of the soil it is supposed to simulate. In this case, we would model the actual soil with one having smaller grain size. You have to be careful when doing this, because the sub­stitute soil may have different properties, such as permeability. If that happens, and we are modeling a soil with a certain water content, we can substitute a liquid with a different viscosity."

James A. Cheney of the University of

California at Davis uses a four-foot-diam­eter drum centrifuge to model overconsoli-dated clay slopes. Houses built on such slopes in southern California slip into canyons, ravines and even the ocean when the clay fails. In October 1978, 25 houses were de­stroyed in Laguna Beach as the result of an early morning earthslide.

"Natural forces such as the weight of overlying sediment, rock layers or glaciers compact the clay," Cheney states. "Erosion, melting or some other process later removes the pressure. As long as the slope remains completely dry, it will not slip. However, rain fills cracks in the clay with water, caus­ing expansion, then failure." A long period of dry weather followed by heavy rains in the winter of 1978-79 triggered the Laguna Beach slides. "The slopes would have failed whether houses had been built on them or not," Cheney adds. "But poor construction practices can increase the problem."

"To simulate the failures on the drum centrifuge," he explains, "we use 650 g's to consolidate a clay from a slurry. Then we stop the machine and cut a slope. The ma­chine is restarted, and the g-level increased until the slope fails."

Cheney's colleague, C. K. Shen, uses a 5-g-ton centrifuge at Davis to model a re­inforced lateral earth support system that strengthens and prevents collapse of soils surrounding excavations. The system con­sists of a facing wall and reinforcing ten­dons drilled and grouted into the soil. Shen has used the centrifuge model to verify his analytical solutions. He also checked the model against a full-sized system used in an excavation for a hospital building in Port­land, Oregon, and he reports that agreement was "very good."

Shen and Cheney feel that centrifuge mod­eling can contribute profoundly to under­standing of real soil behavior—an essential in the formulation of analytical approaches to a range of geotechnical engineering prob­lems. "We go back and forth between the mathematical model, centrifuge tests and measurements made on full-sized structures to keep refining predictions of what kinds of loads the structures can withstand," ob­serves Shen.

Doubts and resistance The biggest obstacle to centrifugal model-

testing in the United States is the size of the machines. "The small size does not permit us to model all the important details of full-scale structures in many cases," Ko says. "Also, the models frequently are too small to instrument completely."

American geotechnical engineering is about to take a quantum jump in centrifuge

6 MOSAIC July/August 1979

size, however, with the adaptation of a giant machine at Ames Research Center, near Palo Alto, California. This centrifuge was built, but never used, by the National Aeronautics and Space Administration for the testing of astronaut reentry systems. The National Science Foundation has provided $1.5 mil­lion to convert the facility into a center for geotechnical research. The Ames centrifuge arm will be adapted ultimately to accept a 20-ton payload at 100 g's. This will bring its rating to 2,000 g-tons, a rating matched in the world only by the Soviet Union's Azer-baidzhan centrifuge.

The Ames facility, says Cheney, who will direct its operation, should solve many of the U.S. engineers' scaling problems. "The larger capacity," he declares, "will allow more accurate modeling of full-sized struc­tures and more extensive instrumentation to make comprehensive measurements of stress and strain distribution."

Not everyone agrees. "The technique still meets resistance in the geotechnical and mathematical communities," Clark points out. "Not everyone is convinced that the scaling relationships have been proved be­yond doubt, that data obtained in a model faithfully predicts what will happen in a full-sized structure."

"There is a significant absence of attempts at corroboration between data obtained by centrifugal tests and measurements made on full-scale structures," says Ronald F. Scott of the California Institute of Technol­ogy. "You build a model of a prototype, wind it up in the centrifuge and load it until it fails. But you cannot compare the data to a real structure because you cannot fail the prototype.

"This is not to say that centrifuge model-testing does not have great potential, or that it is not valuable as far as it goes," Scott explains. "Say you test a model of an off­shore platform by placing it in real soil, spinning it up, then simulating the action of wave forces. They do this now at the Univer­sity of Manchester, Platforms are built using this data, and they do not fail. Certainly this is very useful for specific structures. However, we have not proven the general concept. We cannot say that the scaling relationships for size, energy, time and other quantities are valid in all cases."

Scott has attempted to prove the tech­nique by modeling two piles that were in­strumented and tested in the sand of Mustang Island, Texas. Two 24-inch-diameter, 60-foot-long piles were installed and subjected to a variety of loading conditions. Scott obtained the data, then modeled the same loads in an experiment in his 5-g-ton centri­fuge at Caltech. When he compared the two

At Davis. Cylinders beside the experimental bucket in a 5-g-ton centrifuge (top) contain piezoelectric shakers to simulate earth­quakes. Clay-slope failure is studied in the four-foot-diameter drum centrifuge (left). James Cheney (right) checks overcon-solidated clay in a centrifuge bucket.

University of California, Davis

MOSAIC July/August 1979 7

Spinner in a tank. The 75-g-ton, 7-foot-diameter centrifuge at the University of Missouri spins up to 720 revolutions a minute in a partially evacuated tank, a technique that reduces power requirements. University of Missouri-Rolla

sets of data, they agreed only to within 30 to 50 percent.

"Either the technique has deficiencies or the soil model was not correct," Scott com­ments. "There is no good way to simulate exactly the Mustang Island sand, because it has been deposited and compacted over a 20,000-year span. Therefore, I'm inclined to think that this is the explanation. If we had used a better model, we would have gotten better results.

"As it is, being within 50 percent at the start means we're doing something right. We've got to keep trying to prove the tech­nique; its potential is so great."

Scott is one of a number of geotechnical engineers who feel that this kind of problem should be solved before the leap is made to a machine the size of the one at Ames. "At present," he argues, "in the United States there is no one with any developed expertise in carrying out large centrifuge research....A very large machine for the first attempts seems a poor training ground."

He has argued unsuccessfully for the development first of a number of more flex­ible, middle-sized machines, in the 100- to 200-g-ton size range, on which experience could be gained and graduate students trained. Experiments on the Ames centri­fuge are likely to be sufficiently demanding, he notes, that its use in the education of the next generation of geotechnical engineers is likely to be limited.

Modeling models Nevertheless, the arguments for the large

machine are persuasive—an approach to providing the needed scaling relationships, for instance, known as "modeling of models," that requires a large machine.

"You start with tests on a 1:100 model of, say, an earthen dam," explains Ko. "Then you do the same tests on a larger model, say 1:50, decreasing the g factor as the size in­creases. Ideally, the final tests would be made on the full-scale structure. Results dealing with all the quantities—area, volume, time, mass, etc.—are compared to determine if they agree closely. This has not been done because the centrifuges are not large enough to hold big models, and it is difficult to obtain data on full-sized structures."

The first, problem would be solved by successful operation of the Ames centri­fuge. The second may be alleviated by a dam safety program instituted by the Bureau of Reclamation in the wake of the Teton River Dam collapse. Existing dams and those to be built will be instrumented to monitor stress distribution and deformation. "The Bureau has to analyze a few hundred existing dams, determine which ones may cause problems,

8 MOSAIC July/August 1979

then instrument them," notes Ko. "New dams will be instrumented from

the first day of their existence," he says. "This will give us the kind of field data on prototype structures that we never before obtained. Previously, we took measure­ments on full-scale structures only when they cracked or showed signs of failure. But earthen dams and their prototypes deform under their own weight after they are built, whether they actually fail or not. No records exist of such deformities or the stresses that produce them."

Ko believes that centrifugal testing can prevent disasters, such as the one at Teton River Dam, if the geology of the dam site can be accurately modeled.

Kandiah Arulanandan of the University of California at Davis agrees. "If we could have built a good model of the Teton Dam, we could have predicted its failure," he says.

One of the consultants on erosion to a panel of engineers investigating the collapse, Arulanandan and Andrew N. Schofield of Cambridge University used a centrifuge to verify the most accepted theory of its cause. Seepage, which normally flows through all earthen dams, apparently backed up when filters on the structure clogged. Water pres­sure built up and caused fracturing of core material in the center of the dam. As cracks opened, water moved in, increasing the frac­turing and erosion. To simulate a hydraulic fracture leak, Arulanandan and Schofield placed compacted Teton Dam core material in the 5-g-ton centrifuge at Davis. They started the machine, then pumped water into bore holes in the model. A videotape clearly showed hydraulic fracturing taking place.

Near disaster Engineers probably never will pinpoint

the cause of the Teton River Dam collapse to everyone's satisfaction. The structure was not instrumented, and no data exist on stress and strain distribution prior to collapse. There is more information available on the Van Norman Dam; the 1971 San Fernando earth­quake was labeled at the time, "the best monitored earthquake in U.S. history." Scott believes the Van Norman and two other dams upstream of it would be good subjects for centrifuge modeling. "If we could reconstruct what happened, we could go a long way toward validating the tech­nique," he says.

"Upstream from Van Norman," Scott

At Caltech. The 6-foot fork/arm of the 5-g-ton centrifuge at Caltech is set up to test the holding power of an anchor (top) and a model pile bedded in sand and instru­mented for a vibration test. Caltech

MOSAIC July/August 1979 9

continues, " t w o other dams survived the temblor. The center of one shifted a few feet downstream, but the sides held. A third dam, newer than the others, received no damage. If we could successfully model the three—a failure, an almost failure and a nonfailure—-we would have the first good agreement between model results and what happened on full-sized s t ruc tures ."

To do such modeling requires both bigger centrifuges and a shaker or earthquake sim­ulator compact enough to fit in the instru­men ted cent r i fuge bucket . Engineers at Sandia deve loped a hydrau l ic shaker for centrifuges, but it has been used only with small models. To shake larger payloads, re­searchers have taken another page from the book of space technology. They are studying the possibility of generating miniquakes with panels of squibbs—small explosive charges l ike those used to b low away covers or separate the stages of space vehicles. Placed on either side of a dam model, they could be p r o g r a m m e d to de tona te al ternately and produce a quakelike shaking. Arulanandan, in collaboration with NASA's Angelo Gio-vannet t i and others, is developing a shaker consisting of stacks of piezoceramic disks. W h e n a force strains this material, it gener­ates a small electric voltage. Conversely, elec­tric signals fed into the disks would produce displacements that could vibrate a model. T h e inves t iga tors are exper iencing diffi­cul ty , however , A r u l a n a n d a n repor t s , in maintaining the accelerations at the centri­fuge's higher g levels.

The big machine Arulanandan will coordinate initial re­

search on dams and shaker systems at the Ames centrifuge facility. He also will chair a committee that will advise on research needs and priorities. Shen will coordinate an initi­ating program on tie-back systems. In addi­tion to his duties as director of the facility, Cheney will coordinate research on founda­tions and subsidence. The facility will be open to all geotechnical investigators who can justify the use of its large capacity in their work.

Cheney and his associates at Davis argued for a big machine and supported the conver­sion of the N A S A centrifuge for geotech­nical work from the beginning. A new facility with the same capability would have cost $10 million, they estimate. Of the $1.5 mil­lion NSF grant, $1.25 million will be used for conve r t ing the machine and the re­mainder for the design and coordination of experiments.

A new rotating arm and model-holding buckets will be fitted to the present 18,000-horsepower motor. "We propose that models

or models and shaker systems weighing u p to 6,000 pounds each would rotate at the end of the 40-foot a rm," Cheney remarks.

The maximum size of the model and asso­ciated equipment will depend on the bucket shape, which has not been decided. It prob­ably will be 6 feet square by 3 feet high in a square design, or 15 feet long and 3 feet wide and high in a tear-drop shape. The motor would spin the models at 210 revolu­tions per minute, or about 300 miles an hour, to obtain an acceleration of 300 g's. "Under these condit ions," notes Cheney, "a 6,000-pound model has an effective weight of 1.8 million pounds or 900 tons. After we oper­ate successfully at 900 g-tons, we plan to add two buckets with a 2,000-g-ton capacity (20 tons at 100 g's each). This upgrading should cost an additional $258,000."

Future plans also call for installing tubes on the machine to carry sand, clay and other material into the buckets as they rotate. Such " inf l ight" modeling would give geotechni­cal engineers the ability to simulate actual construction of earthen dams, embankments and other structures and monitor the inter­nal s t resses caused by s t ruc tu re weight . Measurements could be made to show how loads build up on supports and abutments dur ing construction. Centrifuge users also would like to have the capability for in­flight excavations, but this is further in the future as far as the Ames facility is concerned.

A 120-foot-diameter rotunda houses the centrifuge at Ames. Six thousand pounds whirling around at 300 miles an hour would, if it tore loose, create a disaster of the kind to be s imula ted in the b u ck e t s . There fore , $100,000 has been included to build an addi­tional safety barrier. N A S A will operate the facility and supply up to $20,000 in power. Cheney hopes to obtain operating funds beyond the NSF grant by means of general suppor t from the University of California and other agencies and institutions "wi th national concerns amenable to centrifuge model ing."

" T h i s centrifuge, which will come on line in 1981, will not solve all the problems of geotechnica l eng inee r ing , " C h e n e y says . " N o r is the technique itself a panacea. It is another tool to help us get better answers, or answers we cannot get by other methods.

" A t the Ames Geotechnical Centrifuge, we intend to create a facility where research­ers with a range of engineering and earth science backgrounds can do experiments to find these answers, many of which involve problems of national concern." •

National Science Foundation support of the research reported in this article is through its Geotechnical Engineering Program.

10 MOSAIC July/August 1979