By Dov Leshchinsky
The history of humankind indicates that most people, arguably, embrace magic. Adding exotic ceremonies turns magic into voodoo.
While magic is based on uncritical thinking, relying on it in engineering is undesirable because it could lead to overly expensive structures or, worse, unsafe practice. Hence, designers use rules stemming from mechanics that follow the laws of physics. Often these rules are augmented by practice that originates in art.
“Art” here should not be equated with “guessing,” but with “experience.” As an example, experience may imply maximum vertical spacing between geosynthetic layers or maximum height of a reinforced structure. While the mechanics may be applicable to any spacing or height, experience indicates that large spacing may lead to poor construction or that tall walls/slopes may undergo compression leading to unaccounted parasitic loads. Hence, art is part of engineering but it is not a substitute for mechanics.
In the realm of geosynthetic reinforced walls and steep slopes, one often realizes that the measured force or, more correctly, strain, in the reinforcement is far smaller than expected. “Expected” means predicted by mechanics, i.e., statics.
To an engineer this disagreement could be puzzling. If one adopts such data uncritically, considering it as a Rosetta stone, one is embracing magic over mechanics. Adopting unexplained behavior of reinforced soil essentially shortcuts engineering and may lead to failures.
The purpose of this article is to examine an apparent magic related to measured reinforcement force. A variation of a cliché could be, “If the magic is published, it becomes a fact.” It is important to critically review the apparent magic before it becomes a “fact” adopted in design.
Soil is strong in compression but has virtually no strength in tension. Geosynthetics are relatively strong in tension. Combining the two materials produces a composite structure that is strong under both compression and tension.
This means that reinforced earth structures can be constructed steeply and act as retaining structures. In fact, dry noncemented sand alone cannot be steeper than its internal angle of friction, typically less than 40°. Mechanics agree with this measured limit on steepness of dry sand slopes. Often this limit is termed “angle of repose.”
Sandcastles serve as an example in which—at face value—the rule of angle of repose is invalidated. Sandcastles are formed with steep slopes, even negative batters and overhanging cliffs that are realistically sculptured. This magical phenomenon is observed in wet sand, a cohesionless material and without inclusion of reinforcement.
Those who question the apparent reality of sandcastles would wonder how one can sculpt details in unreinforced, cohesionless material that is in conflict with basic mechanics. This apparent conflict with mechanics is a serious issue, well beyond child’s play, because mechanics provide the foundation for geotechnical design.
One more important observation: Sandcastles collapse when moisture content increases with high tide or heavy rainfall. Sandcastles are not durable structures!
Real geotechnical structures
Shown is an excavator on top of an unreinforced steep sandy slope during the deconstruction of the Indian River Inlet Bridge (IRIB) approach embankments in Sussex County, Delaware. This photo was taken in 2007, near the location where strains in geogrid panels were measured. The height of the unreinforced sandy slope is about 6m and its inclination is roughly 75°. The slope is comprised of medium sand with less than 5% passing sieve 200.
Following mechanics and the rule of angle of repose, this cohesionless slope cannot remain stable even without the heavy, constantly vibrating excavator on its top. We now observe in a large-scale structure the same phenomenon as in sandcastles—a steep unreinforced slope.
One can attribute the observed phenomenon in Figures 1/1a to magic. However, there is a physical explanation that can dispel the apparent magic. Soil matrix suction due to moisture in the sand effectively produces apparent cohesion. This cohesion keeps sandcastles and even larger structures stable. In fact, this phenomenon has been studied using centrifugal modeling. Such studies show that increase in the sand’s moisture content (e.g., due to rainfall) diminishes the cohesion resulting in collapse of the sandy steep slope.
Imagine that geosynthetic layers had been installed in the unreinforced slope in Figures 1/1a. Considering that the unreinforced slope seems stable, the expected mobilized strains in the installed layers would be zero, as it is not needed for stability.
In reality, perhaps small values of strains may exist at random locations along reinforcement layers, likely induced by compaction and differential movements of backfill during construction. However, substantial strains, in the order of 3–5%, were measured in the geogrids embedded in the adjacent reinforced sand wall.
Unlike the slope, over which the excavator operated for a few hours, where no precipitation occurred, the reinforced wall was subject to many rainfall events in its life. These events caused the moisture content in the sand to increase and the apparent cohesion to vanish. The dormant reinforcement was activated, resulting in substantial mobilization of its strength. Most importantly, the wall structure remained intact because its design did not rely on magic.
The observation related to the Indian River Bridge is commonly noticed in construction. It is presented not to warn designers to ignore cohesion, as this should be an obvious practice in design of geogrid-reinforced walls. It is presented to warn engineers who monitor gages in walls to realize that smaller-than-expected measured forces are not necessarily because the reinforcement is excessively strong but because an apparent cohesion renders a stable system where the reinforcement is dormant.
Any significant increase in moisture may diminish the apparent cohesion, making the small force observation inherently unreliable in the context of design. What appears as magic is actually due to apparent cohesion, which is dependent on the moisture content of the backfill.
Impact of apparent cohesion
The reality observed in Figures 1 & 1a was attributed to an apparent cohesion of sand.
Using an acceptable slope stability method, log spiral analysis, one can relate the apparent cohesion required to render a “stable” slope, albeit without the surcharge induced by the excavator.
Table 1 shows the minimum required cohesion considering different frictional strengths values for 90° and 75° slopes, all 6m high having unit weight of 20kN/m3. The sand at the IRIB was dense and likely had relevant frictional strength of about 45°. Hence, for a 75° slope the required minimum apparent cohesion is 7kPa (about 150psf). Such value of cohesion due to suction in sand is feasible but should be considered completely unreliable and ignored in design.
While Table 1 indicates significant effect of slope angle, even for a vertical slope the required apparent cohesion is feasible. Refer to Figure 2 for an example of unbraced vertical cut, roughly 2m high, in moist, unreinforced sand. For a 2m cut, the required cohesion for stability is about 4.3kPa (about 90psf).
It is no wonder that some geotechnical engineers consider cohesion as “the invention of the devil” (i.e., a little cohesion can make even a sandy, steep slope stable). Its unreliability, however, can lead to a disaster if one depends on it.
Fortunately, the alternative to apparent cohesion is geosynthetic reinforcement. It has an equivalent impact to cohesion; however, this manmade material is predictable, reliable, durable, and easy to integrate into existing geotechnical analysis. Unlike apparent cohesion, there is no magic with geosynthetics, just sound geotechnical engineering.
Apparent cohesion in sand may sound oxymoronic. When using the term “cohesionless soil,” one will typically refer to sand as a good example. Cohesion existence in “cohesionless” soils is a result of soil matrix suction, which is often associated with capillary suction.
Soil matrix suction is a subset of soil physics and soil mechanics. Its effects on soil behavior (e.g., compaction, strength) can be significant. In fact, behavior of unsaturated soils is an important emerging research area. In general, due to its surface tension, water molecules in the interparticle voids bond the soil grains at their interface with the air that is present in the voids and where menisci develop—see Figure 3.
The smaller the grain size, the greater the bonding or apparent cohesion. For example, suction effects on uniformly graded gravel would be negligible while the effects on well-graded gravel could be significant. Saturation or complete dryness causes loss of this bond. Increase in moisture content causes rapid loss of cohesion.
Even a small amount of fines in sand can result in measurable cohesion. In the context of reinforced walls and slopes, the research on the behavior of unsaturated soils may lead to better interpretation of field data. However, one doubts if it will lead to a change in design methodologies as this apparent cohesion is an unreliable long-term parameter.
Design should produce structures that are safe and economical for a set life span.
Often, field measurements indicate that the load in geosynthetic reinforcement used in constructed walls and slopes is significantly smaller than predicted in design. One well-known element in design that contributes to overestimation of load is a significant underestimate of the backfill’s frictional strength. That is, tan(f) used in design is typically as low as half when compared with the actual value.
Such a discrepancy produces the impression that the mechanics used in design are overly conservative, contributing to the mystery of low-measured loads. Apparent cohesion, however, has much greater impact than friction. While apparent cohesion stabilizes in a similar process as geosynthetics, it is unreliable and should not be used in design.
The presence of cohesion may lead to smaller loads measured in reinforcement. Such apparent cohesion can be formed by soil matrix suction. Ignoring suction in interpreting measured field data may lead to unsafe conclusions. It replaces mechanics with magic because it ignores cohesion but attributes its impact to the presence of geosynthetics.
Unfortunately, it is daunting to consider suction in interpreting field measured data. Furthermore, suction will vary with moisture content; hence, it is not a reliable design parameter considering a structure’s life span. Underestimating frictional strength and disregard of existing apparent cohesion leads to a paradoxical conclusion where magic is real and basic rules of mechanics are unreal!
Reports on measured force that are smaller than predicted are often mentioned to reflect “at working” condition. This condition is explained by the absence of a slip surface in the backfill soil. Design that considers a limit state in determining the strength (and length) of the geosynthetic is overly conservative, as the premise of failure is not realized. This explanation also serves as a reason for uncritical acceptance of measured data in lieu of mechanics.
However, existence of apparent cohesion and higher than assumed frictional strength can prevent the formation of continuous slip surface (e.g., Figures 1/1a), providing an equally compelling and physically sound explanation for the “at working” conditions. Such conditions underestimate the required strength of the geosynthetic should the apparent cohesion diminish or should the designer use the actual frictional strength of the backfill.
Paradoxically, to prevent the formation of slip surfaces by stiff geosynthetic layers alone, it has to be stronger than the load that causes the slip surface to fully develop. That is, they have to be able to resist backfill movements, therefore preventing the soil from mobilizing its frictional strength. To ensure stability, the reinforcement has to compensate for the smaller contribution of resistance from the “restrained” soil. Hence, the “at working” condition does not explain the magic of low measured force; the unaccounted soil strength does. Proper use of soil strength leads to design that is sound and compatible with statics.
Finally, the design of geotechnical structures nearly always considers the safety against collapse. Apparent cohesion is ignored in design, as it should be.
Determining the required reinforcement strength based solely on measured field data while ignoring the apparent cohesion may result in a structure that is inherently unsafe. Globally there could be a substantial deficit in the sum of resistance of all layers of reinforcement relative to what is statically needed to stabilize the cohesionless reinforced structure.
Static global equilibrium must be a considered as a benchmark when assessing experimental data. Indeed, the current reduction factor for creep could be excessive and may make up for a magic-based unconservative approach.
However, counting on two wrongs to make one right promotes magic associated with the use of geosynthetics in reinforced soil. Moreover, since engineering is not science fiction, magic in design is a step in the wrong direction. Soil reinforcing is a subarea of slope engineering for which well-established, sound designs already exist.