Soil liquefaction occurs when a cohesionless saturated or partially saturated soil substantially loses strength and stiffness in response to an applied stress such as shaking during an earthquake or other sudden change in stress condition, in which material that is ordinarily a solid behaves like a liquid. In soil mechanics, the term "liquefied" was first used by Allen Hazen[1] in reference to the 1918 failure of the Calaveras Dam in California. He described the mechanism of flow liquefaction of the embankment dam as:
If the pressure of the water in the pores is great enough to carry all the load, it will have the effect of holding the particles apart and of producing a condition that is practically equivalent to that of quicksand... the initial movement of some part of the material might result in accumulating pressure, first on one point, and then on another, successively, as the early points of concentration were liquefied.
The phenomenon is most often observed in saturated, loose (low density or uncompacted), sandy soils. This is because a loose sand has a tendency to compress when a load is applied. Dense sands, by contrast, tend to expand in volume or 'dilate'. If the soil is saturated by water, a condition that often exists when the soil is below the water table or sea level, then water fills the gaps between soil grains ('pore spaces'). In response to soil compressing, the pore water pressure increases and the water attempts to flow out from the soil to zones of low pressure (usually upward towards the ground surface). However, if the loading is rapidly applied and large enough, or is repeated many times (e.g., earthquake shaking, storm wave loading) such that the water does not flow out before the next cycle of load is applied, the water pressures may build to the extent that it exceeds the force (contact stresses) between the grains of soil that keep them in contact. These contacts between grains are the means by which the weight from buildings and overlying soil layers is transferred from the ground surface to layers of soil or rock at greater depths. This loss of soil structure causes it to lose its strength (the ability to transfer shear stress), and it may be observed to flow like a liquid (hence 'liquefaction').
Although the effects of soil liquefaction have been long understood, engineers took more notice after the 1964 Alaska earthquake and 1964 Niigata earthquake. It was a major cause of the destruction produced in San Francisco's Marina District during the 1989 Loma Prieta earthquake, and in the Port of Kobe during the 1995 Great Hanshin earthquake. More recently soil liquefaction was largely responsible for extensive damage to residential properties in the eastern suburbs and satellite townships of Christchurch during the 2010 Canterbury earthquake[2] and more extensively again following the Christchurch earthquakes that followed in early and mid-2011.[3] On 28 September 2018, an earthquake of 7.5 magnitude hit the Central Sulawesi province of Indonesia. Resulting soil liquefaction buried the suburb of Balaroa and Petobo village 3 metres (9.8ft) deep in mud. The government of Indonesia is considering designating the two neighborhoods of Balaroa and Petobo, that have been totally buried under mud, as mass graves.[4]
The building codes in many countries require engineers to consider the effects of soil liquefaction in the design of new buildings and infrastructure such as bridges, embankment dams and retaining structures.[5][6][7]
Technical definitions
The Giddy House in Port Royal, Jamaica, which partially sank into the ground during an earthquake in 1907 which produced soil liquefaction, resulting in its distinctive tilted appearance.
Soil liquefaction occurs when the effective stress (shear strength) of soil is reduced to essentially zero. This may be initiated by either monotonic loading (i.e., a single, sudden occurrence of a change in stress – examples include an increase in load on an embankment or sudden loss of toe support) or cyclic loading (i.e., repeated changes in stress condition – examples include wave loading or earthquake shaking). In both cases a soil in a saturated loose state, and one which may generate significant pore water pressure on a change in load are the most likely to liquefy. This is because loose soil has the tendency to compress when sheared, generating large excess porewater pressure as load is transferred from the soil skeleton to adjacent pore water during undrained loading. As pore water pressure rises, a progressive loss of strength of the soil occurs as effective stress is reduced. Liquefaction is more likely to occur in sandy or non-plastic silty soils but may in rare cases occur in gravels and clays (see quick clay).
A 'flow failure' may initiate if the strength of the soil is reduced below the stresses required to maintain the equilibrium of a slope or footing of a structure. This can occur due to monotonic loading or cyclic loading and can be sudden and catastrophic. A historical example is the Aberfan disaster. Casagrande[8] referred to this type of phenomena as 'flow liquefaction' although a state of zero effective stress is not required for this to occur.
'Cyclic liquefaction' is the state of soil when large shear strains have accumulated in response to cyclic loading. A typical reference strain for the approximate occurrence of zero effective stress is 5% double amplitude shear strain. This is a soil test-based definition, usually performed via cyclic triaxial, cyclic direct simple shear, or cyclic torsional shear type apparatus. These tests are performed to determine a soil's resistance to liquefaction by observing the number of cycles of loading at a particular shear stress amplitude required to induce 'fails'. Failure here is defined by the aforementioned shear strain criteria.
The term 'cyclic mobility' refers to the mechanism of progressive reduction of effective stress due to cyclic loading. This may occur in all soil types including dense soils. However, on reaching a state of zero effective stress such soils immediately dilate and regain strength. Thus, shear strains are significantly less than a true state of soil liquefaction.
Deposits most susceptible to liquefaction are young (Holocene-age, deposited within the last 10,000 years) sands and silts of similar grain size (well-sorted), in beds at least metres thick, and saturated with water. Such deposits are often found along stream beds, beaches, dunes, and areas where windblown silt (loess) and sand have accumulated. Examples of soil liquefaction include quicksand, quick clay, turbidity currents and earthquake-induced liquefaction.
Depending on the initial void ratio, the soil material can respond to loading either strain-softening or strain-hardening. Strain-softened soils, e.g., loose sands, can be triggered to collapse, either monotonically or cyclically, if the static shear stress is greater than the ultimate or steady-state shear strength of the soil. In this case flow liquefaction occurs, where the soil deforms at a low constant residual shear stress. If the soil strain-hardens, e.g., moderately dense to dense sand, flow liquefaction will generally not occur. However, cyclic softening can occur due to cyclic undrained loading, e.g., earthquake loading. Deformation during cyclic loading depends on the density of the soil, the magnitude and duration of the cyclic loading, and amount of shear stress reversal. If stress reversal occurs, the effective shear stress could reach zero, allowing cyclic liquefaction to take place. If stress reversal does not occur, zero effective stress cannot occur, and cyclic mobility takes place.[11]
The resistance of the cohesionless soil to liquefaction will depend on the density of the soil, confining stresses, soil structure (fabric, age and cementation), the magnitude and duration of the cyclic loading, and the extent to which shear stress reversal occurs.[12]
Three parameters are needed to assess liquefaction potential using the simplified empirical method:
A measure of soil resistance to liquefaction: Standard Penetration Resistance (SPT),[13][14] Cone Penetration Resistance (CPT),[15] or shear wave velocity (Vs)[16]
The earthquake load, measured as cyclic stress ratio [17]
the capacity of the soil to resist liquefaction, expressed in terms of the cyclic resistance ratio (CRR)
Liquefaction potential: advanced constitutive model
The interaction between the solid skeleton and pore fluid flow has been considered by many researchers to model the material softening associated with the liquefaction phenomenon. The dynamic performance of saturated porous media depends on the soil-pore fluid interaction. When the saturated porous media is subjected to strong ground shaking, pore fluid movement relative to the solid skeleton is induced. The transient movement of pore fluid can significantly affect the redistribution of pore water pressure, which is generally governed by the loading rate, soil permeability, pressure gradient, and boundary conditions. It is well known that for a sufficiently high seepage velocity, the governing flow law in porous media is nonlinear and does not follow Darcy's law. This fact has been recently considered in the studies of soil-pore fluid interaction for liquefaction modeling. A fully explicit dynamic finite element method has been developed for turbulent flow law. The governing equations have been expressed for saturated porous media based on the extension of the Biot formulation. The elastoplastic behavior of soil under earthquake loading has been simulated using a generalized plasticity theory that is composed of a yield surface along with a non-associated flow rule.[18]
Pressures generated during large earthquakes can force underground water and liquefied sand to the surface. This can be observed at the surface as effects known alternatively as "sand boils", "sand blows" or "sand volcanoes". Such earthquake ground deformations can be categorized as primary deformation if located on or close to the ruptured fault, or distributed deformation if located at considerable distance from the ruptured fault.[19][20]
A liquefaction susceptibility map – excerpt of USGS map for the San Francisco Bay Area. Many areas of concern in this region are also densely urbanized.
The other common observation is land instability – cracking and movement of the ground down slope or towards unsupported margins of rivers, streams, or the coast. The failure of ground in this manner is called 'lateral spreading' and may occur on very shallow slopes with angles only 1 or 2 degrees from the horizontal.
One positive aspect of soil liquefaction is the tendency for the effects of earthquake shaking to be significantly damped (reduced) for the remainder of the earthquake. This is because liquids do not support a shear stress and so once the soil liquefies due to shaking, subsequent earthquake shaking (transferred through ground by shear waves) is not transferred to buildings at the ground surface.
Studies of liquefaction features left by prehistoric earthquakes, called paleoliquefaction or paleoseismology, can reveal information about earthquakes that occurred before records were kept or accurate measurements could be taken.[21]
Soil liquefaction induced by earthquake shaking is a major contributor to urban seismic risk.
The effects of soil liquefaction on the built environment can be extremely damaging. Buildings whose foundations bear directly on sand which liquefies will experience a sudden loss of support, which will result in drastic and irregular settlement of the building causing structural damage, including cracking of foundations and damage to the building structure, or leaving the structure unserviceable, even without structural damage. Where a thin crust of non-liquefied soil exists between building foundation and liquefied soil, a 'punching shear' type foundation failure may occur. Irregular settlement may break underground utility lines. The upward pressure applied by the movement of liquefied soil through the crust layer can crack weak foundation slabs and enter buildings through service ducts and may allow water to damage building contents and electrical services.
Bridges and large buildings constructed on pile foundations may lose support from the adjacent soil and buckle or come to rest at a tilt.
Sloping ground and ground next to rivers and lakes may slide on a liquefied soil layer (termed 'lateral spreading'),[22] opening large ground fissures, and can cause significant damage to buildings, bridges, roads and services such as water, natural gas, sewerage, power and telecommunications installed in the affected ground. Buried tanks and manholes may float in the liquefied soil due to buoyancy.[22] Earth embankments such as flood levees and earth dams may lose stability or collapse if the material comprising the embankment or its foundation liquefies.
Over geological time, liquefaction of soil material due to earthquakes could provide a dense parent material in which the fragipan may develop through pedogenesis.[23]
Existing buildings can be mitigated by injecting grout into the soil to stabilize the layer of soil that is subject to liquefaction. Another method called IPS (Induced Partial Saturation) is now practicable to apply on larger scale. In this method, the saturation degree of the soil is decreased.
Quicksand forms when water saturates an area of loose sand, and the sand is agitated. When the water trapped in the batch of sand cannot escape, it creates liquefied soil that can no longer resist force. Quicksand can be formed by standing or (upwards) flowing underground water (as from an underground spring), or by earthquakes. In the case of flowing underground water, the force of the water flow opposes the force of gravity, causing the granules of sand to be more buoyant. In the case of earthquakes, the shaking force can increase the pressure of shallow groundwater, liquefying sand and silt deposits. In both cases, the liquefied surface loses strength, causing buildings or other objects on that surface to sink or fall over.
The saturated sediment may appear quite solid until a change in pressure, or a shock initiates the liquefaction, causing the sand to form a suspension with each grain surrounded by a thin film of water. This cushioning gives quicksand, and other liquefied sediments, a spongy, fluidlike texture. Objects in the liquefied sand sink to the level at which the weight of the object is equal to the weight of the displaced sand/water mix and the object floats due to its buoyancy.
Quick clay, known as Leda Clay in Canada, is a water-saturated gel, which in its solid form resembles highly sensitive clay. This clay has a tendency to change from a relatively stiff condition to a liquid mass when it is disturbed. This gradual change in appearance from solid to liquid is a process known as spontaneous liquefaction. The clay retains a solid structure despite its high-water content (up to 80% by volume), because surface tension holds water-coated flakes of clay together. When the structure is broken by a shock or sufficient shear, it enters a fluid state.
Quick clay has been the underlying cause of many deadly landslides. In Canada alone, it has been associated with more than 250 mapped landslides. Some of these are ancient, and may have been triggered by earthquakes.[26]
Submarine landslides are turbidity currents and consist of water-saturated sediments flowing downslope. An example occurred during the 1929 Grand Banks earthquake that struck the continental slope off the coast of Newfoundland. Minutes later, transatlantic telephone cables began breaking sequentially, farther and farther downslope, away from the epicenter. Twelve cables were snapped in a total of 28 places. Exact times and locations were recorded for each break. Investigators suggested that a 60-mile-per-hour (100km/h) submarine landslide or turbidity current of water-saturated sediments swept 400 miles (600km) down the continental slope from the earthquake's epicenter, snapping the cables as it passed.[27]
An earthquake – also called a quake, tremor, or temblor – is the shaking of the Earth's surface resulting from a sudden release of energy in the lithosphere that creates seismic waves. Earthquakes can range in intensity, from those so weak they cannot be felt, to those violent enough to propel objects and people into the air, damage critical infrastructure, and wreak destruction across entire cities. The seismic activity of an area is the frequency, type, and size of earthquakes experienced over a particular time. The seismicity at a particular location in the Earth is the average rate of seismic energy release per unit volume.
Geotechnical engineering, also known as geotechnics, is the branch of civil engineering concerned with the engineering behavior of earth materials. It uses the principles of soil mechanics and rock mechanics to solve its engineering problems. It also relies on knowledge of geology, hydrology, geophysics, and other related sciences.
In materials science, liquefaction is a process that generates a liquid from a solid or a gas or that generates a non-liquid phase which behaves in accordance with fluid dynamics. It occurs both naturally and artificially. As an example of the latter, a "major commercial application of liquefaction is the liquefaction of air to allow separation of the constituents, such as oxygen, nitrogen, and the noble gases." Another is the conversion of solid coal into a liquid form usable as a substitute for liquid fuels.
The cone penetration or cone penetrometer test (CPT) is a method used to determine the geotechnical engineering properties of soils and delineating soil stratigraphy. It was initially developed in the 1950s at the Dutch Laboratory for Soil Mechanics in Delft to investigate soft soils. Based on this history it has also been called the "Dutch cone test". Today, the CPT is one of the most used and accepted soil methods for soil investigation worldwide.
Quicksand is a colloid consisting of fine granular material and water. It forms in saturated loose sand when the sand is suddenly agitated. When water in the sand cannot escape, it creates a liquefied soil that loses strength and cannot support weight. Quicksand can form in standing water or in upward flowing water. In the case of upward flowing water, forces oppose the force of gravity and suspend the soil particle.
Soil mechanics is a branch of soil physics and applied mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids and particles but soil may also contain organic solids and other matter. Along with rock mechanics, soil mechanics provides the theoretical basis for analysis in geotechnical engineering, a subdiscipline of civil engineering, and engineering geology, a subdiscipline of geology. Soil mechanics is used to analyze the deformations of and flow of fluids within natural and man-made structures that are supported on or made of soil, or structures that are buried in soils. Example applications are building and bridge foundations, retaining walls, dams, and buried pipeline systems. Principles of soil mechanics are also used in related disciplines such as geophysical engineering, coastal engineering, agricultural engineering, hydrology and soil physics.
Quick clay, also known as Leda clay and Champlain Sea clay in Canada, is any of several distinctively sensitive glaciomarine clays found in Canada, Norway, Russia, Sweden, Finland, the United States and other locations around the world. The clay is so unstable that when a mass of quick clay is subjected to sufficient stress, the material behavior may drastically change from that of a particulate material to that of a watery fluid. Landslides occur because of the sudden soil liquefaction caused by external sollicitations such as vibrations induced by an earthquake, or massive rainfalls.
Earthquake engineering is an interdisciplinary branch of engineering that designs and analyzes structures, such as buildings and bridges, with earthquakes in mind. Its overall goal is to make such structures more resistant to earthquakes. An earthquake engineer aims to construct structures that will not be damaged in minor shaking and will avoid serious damage or collapse in a major earthquake. A properly engineered structure does not necessarily have to be extremely strong or expensive. It has to be properly designed to withstand the seismic effects while sustaining an acceptable level of damage.
Paleoliquefaction is any liquefaction features attributed to seismic events occurring before measurements or written records were kept of earthquakes. The study of these features can reveal a great deal about the seismicity of regions where large earthquakes happen infrequently. This is a subset of the broader field of paleoseismology.
Pore water pressure refers to the pressure of groundwater held within a soil or rock, in gaps between particles (pores). Pore water pressures below the phreatic level of the groundwater are measured with piezometers. The vertical pore water pressure distribution in aquifers can generally be assumed to be close to hydrostatic.
The effective stress can be defined as the stress, depending on the applied tension and pore pressure , which controls the strain or strength behaviour of soil and rock for whatever pore pressure value or, in other terms, the stress which applied over a dry porous body provides the same strain or strength behaviour which is observed at ≠ 0. In the case of granular media it can be viewed as a force that keeps a collection of particles rigid. Usually this applies to sand, soil, or gravel, as well as every kind of rock and several other porous materials such as concrete, metal powders, biological tissues etc. The usefulness of an appropriate ESP formulation consists in allowing to assess the behaviour of a porous body for whatever pore pressure value on the basis of experiments involving dry samples.
A direct shear test is a laboratory or field test used by geotechnical engineers to measure the shear strength properties of soil or rock material, or of discontinuities in soil or rock masses.
Soil consolidation refers to the mechanical process by which soil changes volume gradually in response to a change in pressure. This happens because soil is a three-phase material, comprising soil grains and pore fluid, usually groundwater. When soil saturated with water is subjected to an increase in pressure, the high volumetric stiffness of water compared to the soil matrix means that the water initially absorbs all the change in pressure without changing volume, creating excess pore water pressure. As water diffuses away from regions of high pressure due to seepage, the soil matrix gradually takes up the pressure change and shrinks in volume. The theoretical framework of consolidation is therefore closely related to the concept of effective stress, and hydraulic conductivity. The early theoretical modern models were proposed one century ago, according to two different approaches, by Karl Terzaghi and Paul Fillunger. The Terzaghi’s model is currently the most utilized in engineering practice and is based on the diffusion equation.
Geotechnical investigations are performed by geotechnical engineers or engineering geologists to obtain information on the physical properties of soil earthworks and foundations for proposed structures and for repair of distress to earthworks and structures caused by subsurface conditions; this type of investigation is called a site investigation. Geotechnical investigations are also used to measure the thermal resistance of soils or backfill materials required for underground transmission lines, oil and gas pipelines, radioactive waste disposal, and solar thermal storage facilities. A geotechnical investigation will include surface exploration and subsurface exploration of a site. Sometimes, geophysical methods are used to obtain data about sites. Subsurface exploration usually involves soil sampling and laboratory tests of the soil samples retrieved.
A triaxial shear test is a common method to measure the mechanical properties of many deformable solids, especially soil and rock, and other granular materials or powders. There are several variations on the test.
There have been known various classifications of landslides. Broad definitions include forms of mass movement that narrower definitions exclude. For example, the McGraw-Hill Encyclopedia of Science and Technology distinguishes the following types of landslides:
Shear strength is a term used in soil mechanics to describe the magnitude of the shear stress that a soil can sustain. The shear resistance of soil is a result of friction and interlocking of particles, and possibly cementation or bonding of particle contacts. Due to interlocking, particulate material may expand or contract in volume as it is subject to shear strains. If soil expands its volume, the density of particles will decrease and the strength will decrease; in this case, the peak strength would be followed by a reduction of shear stress. The stress-strain relationship levels off when the material stops expanding or contracting, and when interparticle bonds are broken. The theoretical state at which the shear stress and density remain constant while the shear strain increases may be called the critical state, steady state, or residual strength.
Arthur Casagrande was an American civil engineer born in Austria-Hungary who made important contributions to the fields of engineering geology and geotechnical engineering during its infancy. Renowned for his ingenious designs of soil testing apparatus and fundamental research on seepage and soil liquefaction, he is also credited for developing the soil mechanics teaching programme at Harvard University during the early 1930s that has since been modelled in many universities around the world.
Offshore geotechnical engineering is a sub-field of geotechnical engineering. It is concerned with foundation design, construction, maintenance and decommissioning for human-made structures in the sea. Oil platforms, artificial islands and submarine pipelines are examples of such structures. The seabed has to be able to withstand the weight of these structures and the applied loads. Geohazards must also be taken into account. The need for offshore developments stems from a gradual depletion of hydrocarbon reserves onshore or near the coastlines, as new fields are being developed at greater distances offshore and in deeper water, with a corresponding adaptation of the offshore site investigations. Today, there are more than 7,000 offshore platforms operating at a water depth up to and exceeding 2000 m. A typical field development extends over tens of square kilometers, and may comprise several fixed structures, infield flowlines with an export pipeline either to the shoreline or connected to a regional trunkline.
River bank failure can be caused when the gravitational forces acting on a bank exceed the forces which hold the sediment together. Failure depends on sediment type, layering, and moisture content.
References
↑ Hazen, A. (1920). "Hydraulic Fill Dams". Transactions of the American Society of Civil Engineers. 83: 1717–1745.
↑ International Code Council Inc. (ICC) (2006). International Building Code. Birmingham, Alabama: International Conference of Building Officials, and Southern Building Code Congress International, Inc. p.679. ISBN978-1-58001-302-4.
↑ Casagrande, Arthur (1976). "Liquefaction and cyclic deformation of sands: A critical review". Harvard Soil Mechanics Series No. 88.
↑ Youd, T. L.; Member, Asce, I. M. Idriss, Chair; Fellow, Asce, Ronald D. Andrus, Co-Chair; Arango, Ignacio; Castro, Gonzalo; Christian, John T.; Dobry, Richardo; Finn, W. D. Liam; etal. (2001). "Liquefaction Resistance of Soils: Summary Report from the 1996 NCEER and 1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils". Journal of Geotechnical and Geoenvironmental Engineering. 127 (10): 297–313. doi:10.1061/(ASCE)1090-0241(2001)127:10(817). S2CID8299697.{{cite journal}}: CS1 maint: multiple names: authors list (link)
↑ Robertson, P.K., and Fear, C.E. (1995). "Liquefaction of sands and its evaluation.", Proceedings of the 1st International Conference on Earthquake Geotechnical Engineering, Tokyo
↑ Robertson, P K; Wride, CE (Fear) (1998). "Evaluating cyclic liquefaction potential using the cone penetration test". Canadian Geotechnical Journal. 35 (3): 442–59. doi:10.1139/t98-017. S2CID129256652.
↑ [Cetin, K.O., Seed, R.B., Armen Der Kiureghian, M., Tokimatsu, K., Harder, L.F. Jr., Kayen, R.E., Moss, R.E.S. (2004) SPT-Based Probabilistic and Deterministic Assessment of Seismic Soil Liquefaction Potential, Journal of Geotechnical and Geoenvironmental Engineering, American Society of Civil Engineers, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 130, No. 12, December 2004, pp. 1314-1340. http://ascelibrary.org/doi/abs/10.1061/%28ASCE%291090-0241%282004%29130%3A12%281314%29 ]
↑ [I.M. Idriss, Ross W. Boulanger, 2nd Ishihara Lecture: SPT- and CPT-based relationships for the residual shear strength of liquefied soils, Soil Dynamics and Earthquake Engineering, Volume 68, 2015, Pages 57 68, ISSN 0267-7261, https://doi.org/10.1016/j.soildyn.2014.09.010.]
↑ [Robb E.S. Moss, Raymond B. Seed, Robert E. Kayen, Jonathan P. Stewart, Armen Der Kiureghian, and K. Onder Cetin (2006) "CPT-Based Probabilistic and Deterministic Assessment of In Situ Seismic Soil Liquefaction Potential" Journal of Geotechnical and Geoenvironmental Engineering 132(8) 1032-1051. http://ascelibrary.org/doi/abs/10.1061/%28ASCE%291090-0241%282006%29132%3A8%281032%29]
↑ [Kayen, R., Moss, R., Thompson, E., Seed, R., Cetin, K., Kiureghian, A., Tanaka, Y., and Tokimatsu, K. (2013). ”Shear-Wave Velocity–Based Probabilistic and Deterministic Assessment of Seismic Soil Liquefaction Potential.” J. Geotech. Geoenviron. Eng., 139(3), 407–419. http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0000743 ]
↑ Scalenghe, R., Certini, G., Corti G., Zanini E., Ugolini, F.C. (2004). "Segregated ice and liquefaction effects on compaction of fragipans". Soil Science Society of America Journal. 68 (1): 204–214. Bibcode:2004SSASJ..68..204S. doi:10.2136/sssaj2004.2040.{{cite journal}}: CS1 maint: multiple names: authors list (link)
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