The Origin of Hogwallows and Gilgai Landforms - PART II

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The Origin of Hogwallows and Gilgai - PART I10/31/2013. This is a closer look at a theory I published in 1994 to explain these landforms. Included in this blog is a great photo of gilgai at ground level taken from Google Street View in Waxahachie Texas. This post was updated on 12/4/2018 and again on 2/2/2024.

PREBUCKLING STRESS AND DIFFERENTIAL REBOUND IN OVERCONSOLIDATED EXPANSIVE CLAYS

It may be that there has been some confusion about what buckling is and how it is applied in this case. Generally, buckling is a deformation produced by an axial load. It may happen in a linear member like a column or in a flat plate that is loaded in compression around the edge of the plate. In the first case, the load is axial. There is a critical load at which buckling produces a deformation. However, before the critical buckling load, there are internal stress changes that are the result of the applied load. These changes are magnified as the load builds. In this section, we will look at these pre-bucking changes in stress. It is important to understand the difference between a pre-buckling load (axial) that is not critical and a critical buckling load. The internal stresses associated with critical buckling do not just suddenly appear when the load becomes critical. So before a critical buckling load, the normal internal stresses are altered. Expansive soils react to this because they react to changes in confining (vertical) pressure. That is they swell more with less confining pressure and swell less as the confining pressure increases.

A deeply buried expansive soil will not expand if the confinement pressure (from the weight of the soil above) equals or is greater than the expansion pressure. As this confining pressure is decreased, the clay can expand more and more. The key idea is that before a critical buckling load, there are internal changes in stress that alters the normal confining pressure (in the horizontal direction) that then triggers differential rebound. Where mounds will appear the normal confining pressure is decreased and where depressions will occur the normal confining pressure is increased. These internal changes in stress, less than the critical buckling load can trigger differential heave and create the appearance of buckling. The evidence that gilgai are not caused by a critical buckling load are:

1. Farmers who have plowed gilgai flat report that gilgai will reappear in a few years this is supported by Goggle image histories of specific gilgai sites. I.e. if the movement rate is more like normal shrink-swell movements, then this is not a critical (sudden) buckling issue.

2. Gilgai only happen in expansive soils. If critical buckling was involved it would happen in other clays like Kaolinite, Illite and Chlorite.

So this means that the normal shrink-swell behavior of expansive clays appears to be the energy that is creating the gilgai. If you were to place some heavy lead plates on the ground in a pattern resembling gilgai depressions, in a few years there would be a differential rebound that would mimic gilgai with the plates in the depressions. In this case K_o >1 had nothing to do with the movement. However, K_o >1 but less than the critical buckling load can take the place of the lead plates. This is because an elastic member can carry a significant axial load up the critical buckling load but not without reacting to the load internally. This is what I call pre-buckling. When this happens expansive soil senses a change in vertical load just like there were lead plates on the surface of the ground. So in one sentence K_o >1 and shrink-swell behavior work together to produce differential rebound. I think we can say that once the buckling load represented by K_o approaches 25 to 50% of the critical buckling failure load then differential heave kicks in to create gilgai. But that is just a guess as to those percentages. The true analytics of the problem are quite complex because there are a lot of related properties that change with depth such as K_o, expansion potential and soil strength and others.

I will now show you in more detail how this works using a simplified model constructed from a long strip of elastic material that has self-weight and can buckle like a continuous sine wave. Think of this as a heavy very long column (an axially loaded member) that is lying down. It is fully braced in the z-direction (in and out of the page) due to self-confinement. Oddly, in this case, the material self-weight helps to brace the column, so for true buckling to occur it has to overcome the buckling strength of the material and it also has to lift the material as well. But there is a lifting influence prior to the critical buckling load.

I zoom in to look at a random segment of this longer strip in Figure 2. I have made several simplifications to show what happens internally and more importantly how the weight of the material is supported at the base of the material. A technically correct drawing would have roller supports along the sides and below. I have removed these for clarity. This drawing shows three levels of K_o in the material. This is the ratio of horizontal stress with the vertical stress. In the first drawing, the model has K_o =1 the horizontal loading on the side matches the weight of the material. In the second drawing K_o =Kcr (the critical buckling load) and the strip of material has buckled due to the higher horizontal loading. We don't know the actual value of K_o in this case, but we assume it is higher than the Rankin failure I show in Figure 1. So in this 2nd case, the material is a stronger material than a clay deposit for this behavior to occur. In the third drawing, there is less horizontal load but it is still higher than the vertical (self-weight due to gravity). Although the load is not high enough to produce buckling, changes in the internal stress are still there. You could say that the material it trying to buckle and producing a differential load (see support reactions) on the subsurface layers. This should trigger a differential rebound that would only occur in an expansive soil. The effect is the same as if you placed some heavy lead plates in locations of future depressions.

HOW MOUNDS TRANSFORM INTO MICRORIDGES (POLYGONS)

Figure 3 shows how mounds and depressions (a) change into more commonly seen polygon (c) shapes. My photo in PART I shows gilgai that are in transition (b) in-between. In mature gilgai, mounds are replaced by interconnected micro-ridges to create polygons. If you look at the aerial image at location (32.419913,-96.77876) dated 2-27-2001 you can see better developed polygonal gilgai in the yard behind the house. You can also see where contours have been plowed through the gilgai to help retain water and where the gilgai have been plowed flat in adjacent fields.

In 1994 I defined the term "shear joint" to describe the special subsurface fracturing that forms around gilgai mounds and micro-ridges. In the literature, you find these joints also called slickensides. However, the term slickensides has been used to describe lots of different shiny surfaces with different origins.  This is a special kind of fracture related only with gilgai and I think a special name should be used for these fractures. In Jackson Mississippi, I have seen shear joints that indicate that gilgai existed thousands of years ago and were eroded away leaving only the shear joints as remnants of gilgai. Joeckel (1999) calls this kind of fracture synformal slickensides. Williams et al (1998) excavated two sections through gilgai and described the subsurface fractures. These are the best descriptions I have seen for subsurface gilgai fractures.

The key concept of this final part of this theory shown in Figure 3 is that once mounds and depressions develop there is a slight loss of horizontal self-confinement. This then promotes additional lateral movement toward the mound. This squeezes the mounds into narrow ridges that eventually connect to create a continuous micro-ridge system or polygons. The development of shear joints around the perimeter of the mounds enables additional horizontal movement. The formation of linear gilgai on slopes occurs for the same reason that polygons form; the slope allows downhill creep to occur, this releases self-confinement in the downhill direction. This means that K_o >1 becomes directional occurring only perpendicular with the slope. This also means that K_o >1 is providing some of the energy into downhill creep that is well known in expansive clays. The very existence of linear gilgai proves that there are strong horizontal forces that are behind the formation of gilgai.

Mound squeezing explains several phenomena associated with gilgai mounds. Some of these are:

1. Tightly wrinkled shear joints inclined at steep angles under the mound perimeter. A photo of this can be seen in Figure 3-32 in Chapter 3 of the Soil Survey Manual. They do not relate these fractures with gilgai but these look the shear joints I have seen in the local Yazoo clay. Another image of this can be seen in Joeckel(1999). 

2. Features called chimneys where the subsurface strata appear to be pushed up under the mounds. These features have been compared with diapirs (Gustavson 1975).

Nature "turns off" or switches off gilgai when the K_o >1 soils become too deep or when expansive soils are replaced with non-expansive soils. This means that when you see a large field with polygons (c) around the perimeter you will occasionally see less mature forms (a) or (b) where nature is preventing the mature forms from developing. The transition is most often represented by the micro-ridges being wider. My guess is that this is most often happens when K_o >1 soils are buried by soils where K_o is equal to or less than one. Because the rate of erosion is slow, there is no reason for gilgai to be actively forming, at least in the southeastern United States unless surface soils have been removed by human activities and elevated K_o >1 expansive soils nearer to the surface. When we see the less mature forms of gilgai it shows that there is not enough expansive energy to push the gilgai into the mature stage.

The development of salt polygons in desert environments appears to occur by an almost identical process as I describe here, except in the case of salt polygons the horizontal force is maybe produced by the growth of salt crystals (see the textbook Geomorphology of Desert Environments (2009). This parallel process may be the best supporting evidence for K_o >1 theory of gilgai. 

Surface cracks vs Ko>1 theory

Surface cracks over gilgai mounds are a secondary effect produced by clay weathering, the deformation of the soil, and the release of horizontal stress near the surface that results from these processes. Self-mulching is also a secondary effect caused by erosion of surface material on top of mounds into the depressions. So the gilgai has to be developing or already present for these secondary effects to occur.
1. Surface cracks or shrinkage theories (this includes self-mulching)can't explain linear gilgai and those with polygonal shapes because the scale of gilgai never matches the scale of ordinary shrinkage cracks in a map view. Shrinkage cracks that form over gilgai mounds are not ordinary and are only seen after the appearance of gilgai and never before. Wavelengths of gilgai vary from about 12 to 30 feet. Shrinkage cracks formed in mud are usually less than 1 foot apart. Desiccation polygons that form in playas in the western U.S. appear at scales much larger than gilgai. For shrinkage crack theory to be valid there needs to be examples of large areas of shrinkage cracks at the same scale as gilgai. This does not exist.

2.  If gilgai resulted from surface cracks, it could be established by mapping the surface cracks as related to the topography or maybe by filling cracks with soil or by running water in the cracks in the field or by correlating moisture content with cracks. These kinds of studies have not shown correlations that support these theories. Two examples are Spotts (1974) and Kishne, Morgan and Miller (2009).

3. Surface cracks theories were proposed from 1840-1930 before modern soil mechanics discovered that horizontal stress naturally occurs in overconsolidated expansive clays. I think this negates these awkward attempts to generate horizontal thrust with a shrinkage crack.

4.  Shrinkage crack theories would not function under pavements, and pavement undulations have been associated with gilgai in several studies.

5.  Not all gilgai have surface cracks. Two sites in the Bienville National Forest in Mississippi don't have shrinkage cracks even during drought conditions. What causes these gilgai?

6.  The Ko>1 origin of gilgai can create gilgai of all forms with or without surface cracks. This is the only gilgai theory discussed in a peer-reviewed engineering journal. There are no valid published criticisms that have not been answered since this theory was introduced in 1994. l would be happy to respond any questions or criticisms.

7. The Ko>1 condition is well established in overconsolidated clays, if in the special case of expansive clays, that gilgai are not produced, then what does happen? How could an expansive clay ignore the presence of Ko>1 instability without reacting in some way that is out of the ordinary?

A FEW FINAL THOUGHTS

If you want to see gilgai in the field based on Google Earth images, you must realize that gilgai you see in aerial photos may not always be visible on the ground. The relief is typically less than 1 foot so if the grass or brush is higher than 1 foot, you may not be able to see the gilgai on the ground. So you need a fresh mowed field, yard or an actively used pasture to see gilgai on the ground. Your best bet is a pasture or land that is mowed regularly. Also occasionally owners plow the gilgai flat. In this case, the gilgai may come back but you may have to wait a few years. If you find this subject interesting and wish to read more please check out Riddell's two publications. His hogwallow descriptions are most interesting. I don't think his work has ever been referenced in recent gilgai research, so his work is herein being brought back in the history of gilgai research. Also, the paper by Mayne and Kulhawy is considered to be a classic in geotechnical engineering.

REFERENCES:

Gustavson, T. C. (1975). "Microrelief (gilgai) structures on expansive clays of the Texas coastal plain--Their recognition and significance in engineering construction." Bur. Econ. Geology--Geological Circular No. 75-7, University of Texas, Austin, Tex.

Hilgard, E. W. (1906). "Soils" New York, The Macmillan Company. 593 p.

Howard, A. (1932). "Crab-Hole, Gilgai and Self-Mulching Soils of the Murrumbidgee Irrigation Area" Pedology (Pochvovedeni), p.14-18.

Joeckel, R.M. (1999). " Paleosol in Galesburg Formation (Kansas City Group, Upper Pennsylvanian), Northern Midcontinent, U.S.A.: Evidence for Climate Change and Mechanisms of Marine Transgression." J Sedimentary Research. Vol. 69, No.3, p720-737.

Kishne, A. S., Morgan, C. L. S. and Miller W.L. (2009) "Vertisol Crack Extent Associated with Gilgai and Soil Moisture in the Texas Gulf Coast Prairie" SSSAJ: Vol. 73: No. 4. p. 1221-1230.

Maxwell, B. (1994). "Influence of Horizontal Stresses on Gilgai Landforms." J Geotech Eng., ASCE 120:1437–1444.

Mayne, P.W. and Kulhawy, F.H. (1982). "Ko-OCR Relationships in Soil." J Geotech Eng. ASCE 108 No. GT6:851-872.

Michalowski, R. L. (2005) "Coefficient of Earth Pressure at Rest." J Geotech Geoenv Eng., ASCE 131:11, 1429-1433.

Riddell, J.L. (1839) "Art. II.- Observations on the Geology of the Trinity Country, Texas. The American Journal of Science and Arts, Vol. 37, Nov., p. 211-217.

Riddell, J.L. (1840) "37. Hog Wallow Prairies.*--Extract of a letter to the Editors…May23, 1840." The American Journal of Science and Arts, Vol. 39, Oct., p. 211-212.

Spotts, J.W. (1974) "The role of water in gilgai formation." P.H.D. Dis. Texas A&M University, College Station, TX.

Williams, D. Wilding L., Lynn, W. Kovda, I. and Chervenka, G. (1998) "Slickenside arrangement in Burleson clay - a udic haplustert" 16th World Soils Congress. Vol.1, p. 89

The Origin of Hogwallows and Gilgai Landforms - PART I

INTRODUCTION

This is the definitive guide for gilgai landforms. Because of the length, this is a 2 part blog. I explain why self-mulching and all shrinkage crack theories are wrong in part 2. For the most part, gilgai and hogwallows in the literature are the same thing. They are a naturally occurring temporal landform called microrelief that only occurs in expansive clays mostly in the wet seasons. The higher areas have been called microknolls, mounds, and microridges, and the lower areas are called depressions, micro-lows, or micro-depressions. According to Gustavson (1975) the maximum relief produced by these landforms is about 18 inches. The three basic forms are mounds and depressions, the more mature polygons (with microridges), and linear ones that are elongated in the direction of downslope. The expression "hogwallows" appeared first (in print) in the United States in about 1839 but the Australian expression "gilgai" has become the more commonly used word since 1930's. These landforms are caused by montmorillonitic expansive soils. The study of these landforms is compelling because the resulting micro-topography is anomalous concerning surface moisture and the expected shrink-swell behavior. Low spots collect water, this should make these areas heave and disappear. So we would expect expansive soils to dampen out low areas, but the exact opposite occurs with these landforms. This means that there must be a special mechanism or process that starts and maintains these landforms. At stake is some process that produces extraordinary differential movements in expansive clays. This post was updated on 12/4/2018, 4/25/2020, and again on 2/11/2024.

There is a similar class of microrelief that are sometimes called gilgai or hog wallows that are not related to expansive soils. These landforms are distinctly different because they have a flat or tableland area between the microknolls without clearly defined microlows. In other cases, there are apparent sinks or microlows separated by flat or tableland without any defined microhigh areas. These similar landforms can also have a much higher relief than gilgai and are more appropriately called pimple mounds, mima mounds, hillocks, prairie mounds, nebkhas, and hummocks. In Texas, there are pimple mounds in the same general area as gilgai. However, studies of these similar types do not reveal a connection with expansive clays.

In 1994 I published a new theory that shows a connection between these landforms and overconsolidated (OC) expansive clays. If this theory is correct we have to use the language and concepts developed by geotechnical engineers to fully understand these landforms. More specifically the explanations of horizontal stress as used in this text come from the science of unsaturated soil mechanics. With this concept, gilgai are one result of the natural weathering process of OC expansive clays. Before weathering these clays are massive and unfractured. Weathering breaks down the massive structure into smaller and smaller peds. This is the only theory that explains how gilgai develop under pavements and this theory also explains all the cracks, joints, and shapes of these landforms. Since 1994 I have found several hundred sites in Mississippi and Alabama and several thousand sites in Texas using Google Earth, Bing Maps, and sometimes Yahoo Maps. In 2016 a map that I produced was published (The Geology of Mississippi by Dockery and Thompson) showing dozens of gilgai sites occurring inside the Jackson Group (Yazoo clay). This map is located on page 28 of this classic textbook. In my next publication, I will show all the known gilgai sites in Mississippi and their associated geologic formations. Maps like my map in The Geology of Mississippi are important because they show that once these OC clays become buried by silts then gilgai no longer occur. Maps like this of Texas and Alabama are still needed to further show this established connection between OC expansive geologic deposits and these landforms. However, Hilgard without the benefit of Google Earth or aerial photography first made this connection 158 years ago. In 1860 he wrote, "..the Hog-Wallow prairie region, in which only the clay marls of the Jackson Group are to be looked for." Most of the expansive clay deposits from Texas to Alabama and Mississippi related to gilgai are either Eocene or Cretaceous age. This results in an approximate age in the range of 34 to 145 Million years. These deposits have had hundreds of feet of sediments eroded from above. This creates the condition of overconsolidation that sometimes results in gilgai landforms. Even the more recent Pleistocene era Beaumont Formation of Texas has been shown to have properties of unloading that produce overconsolidation and a naturally occurring horizontal stress. The result is instability that promotes weathering, shearing, and the formation of gilgai landforms. This blog (Part I) is a close look at the meaning of overconsolidation and how the related (higher) horizontal stress is connected.

Thirty years later I still stand by the solution I proposed in 1994, mainly because there have been no flaws or arguments raised against this concept since it was first published. Structural and geotechnical engineering concepts were used to solve this problem in geomorphology which has been scientifically recognized since 1840. That year John Leonard Riddell published the first surface crack theory about hogwallows in Texas. Riddell speculated that rains would wash earth into shrinkage cracks and convert "them into little valleys, and leaving intermediate hillocks."Amazingly the hogwallows that Riddell first saw in April and May of 1839 are still there 185 years later! Unfortunately, there are no clear online images.  But if you carefully study other sites in Texas and this area you can tell that there are gilgai at this site. I direct you to Google Earth at Lat. 31.338337 and Long. -95.729792.  To see these landforms look at the 1-22-1995, 3-8-2011, and 12-24-23 images at an elevation of about 2350 feet. These images have poor resolution (compared with other locations below) but those are Riddell's hogwallows. You can find several clusters of hogwallows totaling over 200 acres in this neighborhood that he might have seen. This site is associated geologically with the Claiborne Group which includes the Cook Mountain Formation. I located these hogwallows by using Riddell's description which was eighteen miles above Robbins Ferry on the Trinity River. The location of this ferry can be determined from a historical marker at 31.074917, -95.701623. Note you can copy and paste these locations into the GE search box.

In Texas gilgai are so common, they sometimes appear in Google Street View as on Broadhead Road in Waxahachie Texas. This amazing photo was taken at 32.419913,-96.77876. Another good street view image of gilgai could be once seen at 32.642325, -96.522785. Unfortunately, the updated image does not show gilgai, but they can still be seen in this neighborhood in historic images in Google Earth most years between December and March.

To find these landforms you usually have to look at historical images taken between December and March because during this period gilgai may be holding water and this makes them more visible in aerial photography. This is fairly typical of aerial photos in the southeastern United States. Higher-resolution images are also a requirement. There is also a chance the ground surface will be dry even it the images are made during the optimum period. Presently the extreme rural areas of Mississippi and Texas do not have adequate photographic coverage to map and to fully define the distribution. This is unfortunate because these landforms could help map unknown areas where damaging expansive clays exist.

An example of gilgai near Macon Mississippi can be seen at 33.118497,-88.507111 and near Marion Alabama at 32.613375, -87.424533. I could not find these gilgai in Alabama until new aerial photos were taken during the wet season in January of 2013. Both of these sites are associated with the same geological units, the lower Demopolis and the Mooreville which are chalky Cretaceous deposits. Maybe the most interesting gilgai are near Denton Texas like at 33.179328, -97.220062 (see image 2-27-2001). At a hilltop, there are polygonal gilgai but it appears that 2 or 3 depressions (darker spots) are usually grouped together. Here linear gilgai are stretched out in the downhill direction (around the hill) but still have the occasional depression in the valleys below. The elongated or linear gilgai were mentioned by Riddell in 1840 and also by Gustavson in 1975 but there are no theories to explain this form of gilgai until now (see PART II of this blog).

E. W. Hilgard (1906) the former state geologist of Mississippi added an element of expansion (from expansive clay) with "the heavier and more continuous rains wet the land fully, also causing the consolidated mass in the crevices to expand....the result being that the intermediate portions of the soil are compelled to bulge upward, sometimes for six or more inches." In 1932 or maybe 1939 A. Howard wrote "…further penetration of rain will only take place in isolated points where root channels, burrows, etc. have broken down the natural impermeability. When the B1 and B2 horizons become saturated in these isolated spots, the swelling due to the high clay content causes a mound to form."  My 1994 paper was titled Influence of Horizontal Stresses on Gilgai Landforms. In this paper, I proposed a whole new concept to explain the origin of these landforms. This paper was referenced in a textbook titled Geomorphology of Desert Environments (2009). J.C. Dixon wrote the chapter that includes gilgai. This is the best review of gilgai theory that I have read. But there was a paper with the title: Structure development in surficial clay soils: A synthesis of mechanisms by Kodikara, Barbour, and Fredlund (2002). These writers stated," Maxwell (1994) suggested that continuum buckling due to lateral swelling pressures might be responsible for gilgai undulations." I was surprised when I read this because in my paper I state "It is proposed that at a lower level of stress (than buckling stress), there are changes in vertical stress in a prebuckling mode… This effect could then induce a differential rebound with a buckled appearance." I also stated that "measured horizontal stresses in OC (overconsolidated) expansive clays are far below a critical buckling load."  To me, differential rebound is clearly not the same as buckling, but if this has been misunderstood, I feel I must clarify this concept. So this blog is inspired by this issue and I will attempt to fill in the gaps and expand this theory as I published in 1994 in the Journal of Geotechnical Engineering. Because this is a long blog I have left out some of the general information about gilgai and focused on aspects related to this theory and split the blog into two parts. I will explain the three parts of this theory in detail, but here is a quick summary:

1.  THE ORIGIN OF K_o >1: K_o is called the (at rest) lateral earth stress coefficient or the ratio of horizontal (effective) stress with the vertical (effective) stress. OC expansive clays have naturally occurring horizontal stress (K_o >1) that creates the instability needed to form gilgai. I will explain the origin of this stress state as a result of its geologic history where it is loaded and unloaded. Because of horizontal self-confinement, K_o increases during unloading (created by normal erosion) this along with an increase in shear strength results in a pre-buckling stress (item 2) that alters the natural confinement pressure in the soil profile.

2.  DIFFERENTIAL REBOUND IN A PREBUCKLING MODE: In part II of this blog, I will contrast the difference between a prebuckling internal stress and a buckling internal stress and show how a prebuckling stress creates differential rebound and the initial mounds and depressions. The key point here is to recognize that expansive clays are load-reactive much like a spring. When you mix this reactivity with K_o >1 near the ground surface gilgai landforms are the result. A simplified linear model can be produced by compressing a long spring that is confined in the lateral horizontal direction. Here as with gilgai, the self-weight of the material affects the wavelength. As you increase the self-weight the wavelength gets shorter. Eventually, the reaction is suppressed altogether when the self-weight becomes excessive. We see this real-world effect where gilgai appear and disappear when there is excessive material above the expansive clays that is not expansive. In part II of this blog, I will also introduce a more comprehensive elastic gilgai soil model than the spring model used here.

3.  HOW POLYGONS AND LINEAR GILGAI FORM: I will then show how mounds and depressions change into the more commonly seen polygons. This happens because the initial mounds and depressions cause a release of self-confinement at the surface and allow more lateral movement. This causes shear joints to form around gilgai mounds. I will also show how linear gilgai form on slopes from the same process. I have developed this since 1994 so this is new information.

THE ORIGIN OF Ko>1; I.E. THE HORIZONTAL STRESSES THAT CREATES GILGAI

An OC clay is a clay that has had more stress (or load) applied to it in the past than presently exists. This creates a telltale negative pore pressure and an altered stress state of the clay deposit that can be measured with geotechnical instruments. In my paper I explained the origin of K_o >1 as follows: "Horizontal stresses larger than the vertical in OC clays are primarily residual consolidation stress" and "when these clays rebound from unloading, internal friction causes a lag in the release of horizontal stress induced during consolidation."  To show this in more detail, I have modified the classic stress history chart that shows the origin of K_o >1. The following interpretation of the chart is my own understanding of what is happening in the rebound of expansive clays. This chart shows how unloading produces increasing positive values of K_o as unloading progresses. There are ways to measure the horizontal stress of a clay during compression or consolidation and then under a later cycle of erosion or unloading as the clay becomes overconsolidated. Mayne and Kulhawy (1982) state that "any reduction of the effective overburden stress results in overconsolidation of the soil." The vertical stress or the effective overburden stress is simply the effect of the weight of the material above corrected for the effect of pore pressure. Thus the changes in horizontal and vertical stress created by changes in load can be plotted as a stress history. The combined cycles of virgin (first) loading and subsequent unloading are referred to as the stress history of a clay.

A simplified stress path or stress history of an expansive clay is shown in Figure 1. An expansive soil deposit like in the Eocene or the Cretaceous has a much more complex loading and unloading history than is shown by this chart. Whenever there is an unconformity in the deposits above an expansive clay we know that there was a period of unloading, reloading and then a final unloading. This creates loops in the path, but the end effect when the clay is finally unloaded should be essentially the same as the unloading path shown in this chart.

Any straight line through the origin (0) is a line of constant K_o with K_o increasing counterclockwise. In the middle of the chart is the K_o =1 line. This would be the path of a hypothetical frictionless material (like a compressible fluid) during any loading or unloading. Above this line K_o >1, below this line K_o <1. The stress path varies from K_o =1 only because of internal friction. So this chart shows how internal friction causes values of K_o to vary. The internal friction does not change during the loading cycle so K_o is a constant value (a straight line). This value is called the virgin loading and is expressed as K_o here but K_onc  has also been used in the literature where the nc stands for "normally consolidated." At the end of the virgin loading cycle (point B) there is an increase in internal friction or shear strength caused by a dropping pore water pressure. This then causes K_o to increase throughout the unloading cycle. So this plot contrasts the difference between the virgin loading cycle and the unloading cycle under the influence of internal friction that begins to change when unloading starts at point B. These two cycles of the stress history are described in more detail as follows:

THE CONSOLIDATION OR LOAD PATH (A TO B): Initially a deposit of clay is a soft mixture of clay and water particles. As more deposits accumulate above, the clay is subject to more compression. The clay becomes denser because water is squeezed out with positive pore pressures. This effect causes the transfer of the vertical compressive force into the horizontal direction at a constant rate. K_o is less than one and constant during the whole loading cycle. The actual number usually varies between .4 and .8 and the value depends on the clay.

THE UNLOADING PATH (B TO C): The overconsolidated coefficient of earth pressure at rest has been represented by different symbols in the literature. Some of these are K_ou , K_o(oc), and K_o^oc. An Equation was proposed for this coefficient by Mayne and Kulhawy (1982). More recently Michalowski (2005) reviewed the proposed K_o functions for loading and unloading. Note that this paper is available online. As the clay is unloaded it becomes unsaturated and overconsolidated and as the vertical load decreases a negative pore pressure increases. This causes the clay to gain strength and develop more resistance against the particles from sliding past each other. If you could freeze the material and lock the particles together at point B the unloading path would be horizontal and the horizontal stress would not change. So any drop in horizontal stress during unloading is allowed by interparticle shifting. This is what I call “unloading shear.”

Because of the increase of internal friction at the beginning of unloading, the stress path shifts horizontally when unloading begins and the horizontal stress drops slower than then the vertical stress. This causes K_o to steadily increase as unloading progresses. K_o >1 and a negative pore pressure now identifies the clay as being overconsolidated. As K_o increases the clay becomes more unstable. The dryer inter-particle shifting must create fractures or distort the clay to relieve horizontal stress. The process of losing horizontal stress during rebound is herein named “unloading shear” and it is this process that produces gilgai and the associated shear joints in expansive clays.

In my paper, I use Rankine theory to compute a maximum value of K_o. This is shown as point C (the end of the unloading path) in Figure 1. For an average friction angle, K_o is limited to a value of about 3. I don't know the smallest value of K_o that could produce gilgai, but it might be as low as 1.5 in ideal conditions. It depends on the state of the surface soil. I think often the surface soils would be highly weathered and have K_o close to unity. When this happens these soils can't participate in forming gilgai and surface cracks can appear. Two gilgai sites in Mississippi on public land do not have any significant surface cracks even in drought. In the photo above there are no surface cracks visible, but the ground is dry. I interpret this as meaning that K_o must be greater than one very near the surface. These are sites where a surface crack origin would not work and provide evidence that surface crack theories are not correct. It is important to realize that K_o and instability steadily increase during the unloading cycle and the formation of gilgai with the related shear joints is an important (horizontal) stress release mechanism. This process contributes to the weathering of expansive clays. Shear joints initially form in the subsurface around the perimeter of gilgai mounds and are explained in more detail in part II of this blog. I will also perform a more detailed comparison between this theory and the older surface crack theories.

Here is a link to part II of this blog:

The Origin of Hogwallows and Gilgai - PART II  The conclusion of this blog.

Extreme Building Damage Caused by Yazoo Clay


Every time I look at this picture I can't help but compare it with earthquake damage. The end result can be very similar. Geologic deposits like the Yazoo clay are often called "highly active" and the movement is not sudden like an earthquake. You get a little bit every day and some days you get a retraction where cracks close, a door that would not close last month suddenly works fine. But when you get heaving (or uplift) in high-rise construction, the second floor tries to resist the movement and the first floor behaves like it's being squeezed in a giant vice.

Extreme damage to structures can result from expansive soil movements. This photo is a reproduction of a Polaroid that I took before I went to the University of Texas. It shows the first floor of a high-rise building in Jackson Mississippi. This might be the most dramatic photograph of interior building damage from expansive soils ever taken. Each floor of the building was a flat plate structural slab (self-supporting). The first-floor slab was constructed with an undrained 6-inch open void underneath. However, by the time the building was 8 years old, the void had closed and the first floor had heaved as much as 8 inches. The problem was that the expansion potential (uplift) of the Yazoo clay was seriously underestimated. 


Expansive soil damage to the first floor of a high rise
building in Jackson Mississippi.

The floor of this room on the 1st floor was a structural slab that was supported by the same concrete columns that supported every floor. When it was built this slab had a 6" inch void underneath. But 10 years later heaving of the slab caused the structural slab to disconnect from the columns in an odd reverse punching shear failure. A punching shear failure is when a structural slab shears away from a supporting column. Normally the slab falls down; but in this case, the slab moved up (in reverse) from the expansion of the clay. The columns were supported by deep drilled piers and were not damaged. Fortunately, this part of the building structure was stable.

Damage seen in this photo is the result of crushing metal stud partitions (in compression) that were constructed from the first floor to the bottom of the second floor slab. The damage was so severe that most interior doors had been removed on the first floor. In the left side of the photo is a door that has been replaced by tapping sheets of brown wrapping paper over the opening (a common solution). The door near the center of the photo and the one on the right has been removed. In the room in the foreground partitions have failed by rupturing the wallboard. In the background the wallboard buckled and disconnected from the studs.

In Central Mississippi, this kind of construction represented the first efforts by engineers to isolate the bottom floor (using structural self-supporting slabs) from the expansive soils in the 70s, and early 80s. Numerous buildings were built just like this. I doubt that any of them still exist like they were originally built. We now know that a typical rate of heave for a normal soil profile with Yazoo clay is about ¾ inch per year. So a 6-inch void like this building couldn't last more than 8 years in a typical setting. In this particular case, the expansive clay was exposed at the surface, there was poor drainage, and it potentially heaved at a rate of more than double the amount from a typical condition. That is the highest heave rate that I know of in Central Mississippi.  One end of the building was built several feet below the surrounding natural grade. So construction required the removal of natural inactive soils above the clay. This created an unloading condition that promoted rebound of the expansive clay. This construction also created a condition of poor drainage around the structure.  Surface drainage that was constructed rapidly deteriorated from heaving that occurred in the ground around the building.

To repair the building, the entire first floor, and the slab was completely removed and replaced when this building was about 9 years old. As a result, this building is still in service today. The repair involved increasing the void space size to 30 inches. However, clearances under plumbing in the crawl space had to be recently dug out again in part of the crawl space. At the other end of the building, the new crawl space was still intact and some shrinkage had actually increased the crawl space by a few inches.

Unfortunately, buildings on drilled piers like this one today are still having issues with Yazoo clay in Central Mississippi. My studies of these newer buildings indicate these primary issues:

1. Inadequate clearances specified for utilities or specific elements of the foundation.

2. Inadequate retainage to prevent soil flow into the crawl space or voids under grade beams.

3.  Inadequate drainage of the void spaces or crawl spaces.

4.  Inadequate construction review of void or crawl spaces.


All rights reserved by Britt Maxwell P.E.

Historical Meteor Shockwave Events That Destroyed Structures

This blog is Part II of a three-part series about possible meteor shock wave damages to structures. It was updated on 8/18/2019. Part I is about "Google Earth Photos taken the same day as the Chelyabinsk meteor event on February 15, 2013. This blog (Part II) is about structures that have been destroyed (as a result of meteor events) as reported in news since 1900. Part III will be an analysis the Chelyabinsk Zinc Plant Warehouse collapse. I started out to just blog about the warehouse collapse but I decided to put this event in historical context with other meteor events reported in the news.

Before I start, I should explain some of the terminologies. A meteoroid is an object like an asteroid but smaller than 1 meter. A meteor is the visible streak of light seen in the sky made by a meteoroid as it impacts the atmosphere. A meteorite is a fragment of a meteoroid that has hit the surface of the Earth. This blog was inspired by the historic meteor event at Chelyabinsk Russia where a substantial industrial building collapsed under the influence of a shock wave. I began research to see if there were other similar events. I was surprised to find five events with reports of the destruction of houses that were apparently caused by meteors since 1900. In these reports, there was an understanding that a meteor was involved, but that somehow a meteorite must have hit the structure, although no meteorites were found with any of these events. In three reports the damage is related to the word meteorite, but no meteorite was found, and in two of the reports the phrase "meteoric stone" or "meteoric shower" is used, but again no meteorite was found. Two of these events were criticized as "meteorite events" and I think appropriately so, and I provide links to these criticisms. Where's the meteorite if these structures were destroyed that way? It is important to realize that when the first 4 events happened there was no scientific understanding about meteor airbursts, so a meteorite was the only possible explanation. Airburst science was not developed until the 1950s and early '60s. I think that these events I list below are all shock wave damage events and these events only make sense if they are interpreted in that way. So I want to make it clear that this is my interpretation of these events. 

Prior to the historical meteor event at Chelyabinsk Russia in February, I think some scientists discounted these accounts of meteor events where houses were destroyed. Maybe they still do. One problem is that in only a single account (where a structure was destroyed) prior to Chelyabinsk were scientists were reported to be involved in the investigation. Because of the event at Chelyabinsk in February and the event at Tunguska in 1908 we have some first-hand accounts of the effects of destructive meteor shock waves that represent real events. We also can look at well-documented accounts of meteorite impacts with houses and other structures where the meteorite is found. There are lots of these events. Most recently on April 19, a meteorite crashed through the roof of a house in Wolcott Connecticut. That is the third meteorite to penetrate a roof in Connecticut since 1971. The two previous meteorites in Connecticut damaged houses 1.64 miles and eleven years apart. One thing seems clear in these events and is that the damage was light enough so that the house could be quickly repaired and more importantly the meteorite in these cases was fairly easy to find. Halliday, et al. (1985) states that "it is clear that an impact on a building greatly increases the probability of recovery of the meteorite since only a small percentage of falls will strike buildings, whereas half of the recent recoveries have such involvement." In a couple of instances that I found, the meteorite penetrated the whole house and was found in the crawl space. 

If we compare these real meteorite events with the events I list below, we must conclude that they are shock wave events, because the damage is much greater than would be expected from a typical meteorite and yet no meteorite is found.

An important test of a shock wave event is that someone saw a bright meteor and reported a loud bang or a series of bangs that are commonly associated with cannon fire by witnesses in older accounts. Based on that test only 2 or 3 of the 6 events (I list below) where structures are destroyed would pass; an event in Mississippi, Chelyabinsk and maybe the Jakarta event. But as a structural engineer, I see a potential public safety issue that I feel we need to look at, so I want to err on the conservative side consider all reports of structures being destroyed that have not been proven to be false. There is another potential problem and that is, prior to 1900 there were unscrupulous newspaper accounts of meteors that were made up to help sell papers. I could not find any evidence of this happening after 1900 so I decided to start the inventory of meteor events in the year 1900.  Scientific papers written on structural damage from meteors have been made by Fessenkov, 1955, La Paz, 1958, Graham et al., 1985 and Yau, K., Weissman, P., & Yeomans, D. (1994) listed 10 reports of structural damage in China from 588 to 1879.

The following is an account in the New York Times of what I think is a shock wave that destroyed a large house in 1900 in Mississippi. This event and the event in Shiraz in southwestern Iran are not included in any lists of historic meteorite events that I have seen. I think they were excluded because if it is stated in the report that no meteorite is found then the event is not relevant. But I could not find where anyone has ever compiled an exclusive list of meteor events where structures were reported as being destroyed. Someday I will expand this list to before 1900 and include hut structures that were knocked down in a separate category. 

METEORITE IN MISSISSIPPI. Visitor from the Heavens Explodes and Wrecks a House. Special to The New York Times. NEW ORLEANS, La., July 12.—The little village of Bellefontaine, in Webster County, Miss., thirty miles in the interior from this place, was the scene last night of the fall of an aerolite, or meteoric stone, which completely wrecked the large storehouse of Hodge & Mabry, and destroyed the stock of goods contained in it. The fall of the aerolite occurred between 9 and 10 o clock, during a perfectly clear moonlight night. The destruction of the building was preceded by the appearance of a ball of fire passing swiftly through the air. It gave off during its passage enough light to greatly increase the light from the moon. As it came near a loud explosion was heard and a shower of fire burst forth from all sides of the blazing mass, having the appearance of hundreds of falling stars. The storehouse was wrecked simultaneously with the explosion. The explosion of the aerolite caused a report like the sound of distant thunder or the roll of far-away cannon. The debris of the house is being cleared away in search of the aerolite... Many cinders of a gray gritty metal appearance have been found in the wreckage.

ANALYSIS of the Bellefontaine Event: This event is listed as a "Meteor Wrong" on the internet, but my research shows that this really happened. This expression is a kind slang term for rocks that look like meteorites but are not. Because Webster County Mississippi has good genealogical records, I was able to find the full name of one of the store owners and then verify that the event happened from a living granddaughter. The store owner was, George Clark Mabry (1874-1952). This is one of the better meteor airburst descriptions that I have read. If anyone can contribute information about this event or other listed events (below) please contact me.

Here is an account of 5 other events (2 with very limited information) since 1900 where houses and one building have been reported to be destroyed by meteor events:

!  In the publication of the Meteoritical Society (Meteoritics 29, 864-871) 1994 there is this report: Sept. 5, 1907, Hsin-p’ai Wei in Weng-li, China meteorite caused a house to collapse, killing a family; “the whole of Wan Teng-Kuei's family was crushed to death.” ANALYSIS: An event scrutinized by the Meteoritical Society, should be a credible event. In a paper by Yau, K., Weissman, P., & Yeomans, D. (1994) it is stated: "The Wan family probably died from the collapse of the house, rather than from a direct fall of the meteorite."

!  The Straits Times (A Malaya Newspaper) on May 17, 1946, reported: Mexico City, Thurs. –The Government announced today that a meteorite destroyed the hamlet of Santa Ana in Nuevo Leon state of Mexico. Eight people were killed and 26 injured. – Reuter. Also in the New York Times 5-17-46 and listed by John Lewis in Rain of Iron and Ice.

!  August 15, 1951, Teheran, Iran near. Sixty-two houses were destroyed by a meteoric shower. Twelve people were killed and nineteen injured. In addition, 300 livestock animals were killed. The event was reported by Iranian newspapers and the United Press. This event is reported to have been published in the Lowell Sun (Massachusetts) on the next day (p.19) but I have not as of yet seen the archives.

!  An event on April 29, 2010, at 4:30 in the afternoon in Durensawit, East Jakarta according to news reports by the Jakarta Globe was investigated by The Institute of Aeronautics and Space (LAPAN) and the National Police's Ballistics and Metallurgy Center (BMC). The head of the BMC said that tests had ruled out a bomb or a gas-canister explosion and said the object was similar to the one that hit in Bone in South Sulawesi on October 8, 2009. "LAPAN ruled out the possibility that the object may have been space debris…" Sri Kaloka Prabotosari estimated the meteorite was 30 centimeters in diameter and had an impact velocity of 10 kps. According to Berita Jakarta, a government website, Thomas Djamaluddin with LAPAN said: "it was not detected by a transmitter, possibly because of its small size."  The blast has only left dust with the color of a bit grayish (as translated). The homes of Sunarti, Sudarmojo, and Marzuki were damaged in the incident with Sudarmojos house taking the brunt of the impact. It blasted a hole in the second floor of the house, sending furniture falling to the first floor, and tore big holes in walls. No one was home when this happened. ANALYSIS: Getty Images owns twelve high-resolution photos of the damage made by Romeo Gacad originally posted on May 4, 2010. Unfortunately, these photos have recently been removed from their website. One, however, was re-posted at WSJ BLOGS(scroll down 14 images). All the photos appear to be of the same Sudarmojo residence. Photos show the roofing material is completely missing above at least 2 adjoining rooms, most of the wood roof framing is still in place but a few pieces are broken and a few appear to be missing and there are piles of clay tile roofing fragments on the floors. One photo shows a large wood (glass?) frame knocked down inside the house. This area appears to be a very high-density living area and it is odd that the damage was limited to only 3 adjacent structures. I looked for photographic evidence for an explosion outside vs inside. I think an inside explosion of this magnitude would have removed significant roof framing and left few, if any, roof tiles inside the structure. Photographic evidence suggests a small air burst above the roof at a low altitude but above the roof, that shattered the roof tiles and knocked them down into the house. Witnesses saw a localized flash at about 4:30 in the afternoon but not a fireball. Investigators shied away from using the expression "shock wave" but compared this event with the larger shock wave event at Sulawesi (6 down in TOP TEN table below) the year before. This was the first event in this list where shock wave science appears to be involved, but the estimated velocity of the impact object is 1.2 km/s slower than the 11.2 km/s the theoretical lower limit of meteors. A blog questioning this event was made by Ian O'Neill.  More on this subject after the following event.

!  February 15, 2013, the Chelyabinsk meteorite was visible in the early morning as a brilliant superbolide that created a series of shock waves that damaged some 7,200 buildings and according to the official Chelyabinsk website, 1613 people were injured in the region and 69 people were hospitalized. It also apparently triggered the collapse of about 1050 square meters or 11,300 square feet of roof at the Chelyabinsk Zinc Plant (see part I of this blog series). The building described as a concentrate storage facility was constructed with concrete columns and a precast concrete roof deck. This is the most substantial building ever destroyed by a shock wave. My previous blog and my next blog after this one will provide more details about this building collapse so I have cut this short.

Principles of physics limit the range of velocities of asteroids and meteoroids when they first enter the Earth's atmosphere. The escape velocity of Earth controls the lower limit (personal communication with Gareth Collins) and the full range is between 72 and 11 km/s (161,000 to 25,000 mph). Hills and Goda (1998) state that "asteroids with diameters smaller than 50-100 m that collide with the Earth usually do not hit the ground as a single body; rather they detonate in the atmosphere." A shockwave can be generated when the combined forces on the meteoroid cause it to break apart. A potentially damaging shock wave can be produced when the object is a larger meteoroid or asteroid. John Lewis (1996) states that the density of air roughly doubles for every 5 kilometers of altitude. He also states that "our normal intuition would suggest that the faster a projectile is moving the more deeply it will penetrate its target. But the exact opposite is true for meteors: the fastest moving meteors produce the highest pressures and are crushed to dust at higher altitude." Because of the high speed of the meteoroid, a pocket of high air pressure in front of the meteoroid is created. When the pressure differential becomes higher than the strength of the meteoroid it breaks apart. When this happens it is sometimes called a bolide or an airburst. The shock wave energy released is dissipated with distance. So a shockwave that begins high in the atmosphere loses most of its energy by the time it gets to the ground. But at the same time, it distributes the energy over a larger area on the ground. These events often have sound effects that can be heard. The larger events rattle windows and the even larger events break windows. On July 23, 2001, a bolide meteor shattered windows in towns west of Williamsport Pennsylvania (see Meteorites Don't Pop Corn).  In the reports I have reviewed (above), we might consider that the smallest meteoroid capable of destroying a structure to be roughly about 30 centimeters in diameter (Jakarta event). However, there is a nifty online "Earth Impact" tool to compute the effects of different size meteoroids with different masses, traveling at different speeds and traveling at different angles. This tool created by Collins, Melosh, and Markus, makes assumptions and approximations that limit the accuracy of the result, particularly for smaller objects. To get more accurate results full computer simulations must be run. So for what it's worth, I used this program to see what the smallest meteoroid was that would produce a damaging shock wave. I went through numerous iterations  and I found the following object:

1.5 meters (4 feet 11 inches) in diameter, a density of 7907 kg/m³,  impact velocity of 11.2 km/s, and an impact angle of 85 degrees. The resulting meteor burst occurred at a height of only 170 meters (559 feet) with an energy of .21 kilotons producing a peak overpressure of 17.4 psi at ground zero. The overpressure drops to 3.7 psi at .5 kilometers from ground zero. This event if it were to happen would be very serious but over a fairly small area. All wood-framed structures would be destroyed over an area of about 2 square miles or (5.4 square km). However, there are two versions of the impact tool and the new version computes different results without an airburst for the same inputs. So one or maybe both tools have an error. So a mini-shockwave event like this may not be real when you include all the physics. But the original tool indicates that the object needs to impact at the low end of possible velocities and needs to be strong and have a density close to that of an iron meteorite. These factors allow the meteoroid to penetrate deeper in the atmosphere before it explodes. The Chelyabinsk meteor, by comparison, was an object estimated to be 17-20 meters (55.8-65.6 feet) and hit at an angle just under 20 degrees and was initially traveling at about 30 km/s (67,100 mph). It only had a 10% meteoric iron content and it slowed to 18.6 km/s (41,600 mph) when it burst at a height of 23.3 km (14.5 miles).

A list of air burst events has been listed on the internet at en.wikipedia.org. I have reproduced this table showing only the top ten events and sorted them according to the average estimated yield. By doing that the Chelyabinsk event shows to be #3 and it has widely been reported as being #2. The problem is that there is a very wide range of estimates for the Curuçá River event. A Tunguska type event is believed to occur once every 1000 years and events like the Sikhote-Alin occur every 2 years somewhere on Earth.

                                   TOP TEN SHOCKWAVE EVENTS

EVENT	DATE	YIELD (kiloton's)	AVG.YIELD
Tunguska	6/30/1908	10,000-15,000	12,500
Curuçá River	8/13/1930	100-5,000	2,550
Chelyabinsk	2/15/2013	500	500
Offshore, S Africa	8/3/1963	176-356	266
Arroyomolinos de Leon	12/8/1932	190	190
Sulawesi Indonesia	10/8/2009	31-50	40
Eastern Mediterranean	6/6/2002	12-20	16
Queen Maud Land	9/4/2004	12	12
Marshall Islands	2/1/1994	11	11
Sikhote-Alin, Russia	2/12/1947	10	10

By studying the videos and pictures in the area of Chelyabinsk we can see the effects of shockwave damage. The exterior of a structure that protects it from wind and rain from a structural perspective is called the envelope. Once the envelope is damaged (from doors blown open or by windows blown out) by a shockwave, pressure changes occur inside the building. Interior doors can then be blown open and drop ceilings can be damaged by the pressure changes. Once the envelope is compromised, flexible walls, ceilings or floors can act as a membrane and bounce under the impact of a shock wave. This matches the description of the energy of the impact at Jakarta.

SUMMARY

The following is a summary of the events listed above that I think are shockwave events that mostly occurred before the science was developed:

                                     POSSIBLE SHOCKWAVE
            EVENTS SINCE 1900 THAT DESTROYED STRUCTURES

			NUMBER OF
EVENT	DATE	FATALITIES	STRUCTURES
			DESTROYED
Bellefontaine Mississippi	7/12/1900	0	1
Hsin-p’ai Wei, China	9/5/1907	a family	1
Santa Ana, Mexico	5/17/1946	8	a hamlet
Shiraz, Iran	8/15/1951	12	62
Jakarta, Indonesia	4/29/2010	0	1
Chelyabinsk, Russia	2/15/2013	0	1

We don't know the number of structures destroyed in the 1946 event and we don’t know the number of people killed in the 1907 event. But if we add all the occurrences together, we get a total of 6 events since 1900 with an average occurrence of a meteor with a shock wave that destroys at least one structure every 19 years. In 67% of these events, only a single structure was destroyed but in the remainder, maybe 3 to 62 houses were destroyed. On average about 11 to 15 structures will be destroyed by the event, and the fatality rate per event (when structures are destroyed) is 4 to 5. We can compare these possible shock wave events with known damage from meteorites. Halliday et al. (1985) estimated that 16 buildings per year could receive some damage from meteorites that weigh at least 500 grams (1.1 pounds). Adjusted to the population of Earth in 2013 this becomes 23 buildings per year damaged by meteorite impacts. They used a 20 year period in North America as a sample interval.

The fatality rate from meteors, in general, is a little higher because only events destroying structures were included (above). But if we add in all meteor events since 1900 we get maybe 2 or 3 more fatalities. There are conflicting reports of one or two deaths related to the Tunguska event in 1908 and a male guest was killed in a bridal party in Zvezvan Yugoslavia while riding a carriage in 1929 by a 40-centimeter meteorite according to a New York Times article. If we add up all the fatalities and assume 3 were killed in 1907 we get a total of 24 or 25 deaths since 1900 with one person killed every 4 ½ years on average. Every one of these fatalities except maybe the one in Yugoslavia I think are the result of shock waves and not being struck by a meteorite. But the occurrence rate of destroyed structures and fatalities must be related to the population of Earth that is now over 4 times as high was it was in 1900. Also note that in the Mississippi, Chelyabinsk and Jakarta events no one was killed, but probably because there was no one in the structures when the shock wave hit. Yau et al., 1994 used data from China to compute that a fatal incident will occur somewhere on Earth every 3 ½ years, adjusted for Earths population change that would be an incident every 2.8 years today. For comparison, I find 5 incidents worldwide since 1900 where someone was killed that is an average of once every 22.5 years. If I normalize that for a 4x population increase, we might predict an incident with at least one fatality every 9 years.

CONCLUSIONS

I have reviewed 5 events of destruction to residence type structures reported to be caused by meteorites or "a meteoric shower". However, these are all "missing meteorite" stories where the damage is much heavier than would be expected from a meteorite. I interpret these events as shockwave or airburst events. It is important to realize that the first four events happened before the science of meteor shock waves was developed so there was no chance for these events to be correctly understood when they happened. They also predate the sensor grid. The Chelyabinsk meteor event is the first event in history where a structure was destroyed and there is an official meteorite associated with the general event.  And it appears that the damage here was not caused by a meteorite object, but by a shock wave. The Jakarta Event just 3 years ago was not picked up by the worldwide grid of sensors. From personal communication with Peter Brown, University of Western Ontario; he would not rule out this as a shock wave event but added "I think it is unlikely that an airburst capable of producing significant overpressures at ground level would go unrecorded overland (or even the ocean). There are some 20 photos and several newscasts on Utube of this event and I interpret this event as a small, low altitude, airburst mainly because roof tiles were shattered and knocked down into the house. On average 23 buildings per year could be damaged by meteorites but none are destroyed. Meteorites maybe could destroy structures, but the occurrence rate must be considerably larger than 20 year study period used by Halliday et al. (1985) and larger than the 113 year study period I used.

I think all of the meteor related fatalities since 1900 except one, were caused by shock wave events and that most of these deaths are related to the collapse of a structure. It appears that only the fatalities at Tunguska and Zvezvan, Yugoslavia were not related to a structural collapse. It is possible that some of these shockwave events were large events that created limited damage because they occurred in sparsely populated areas. 

From this study, I have determined that on average 23 buildings per year are damaged by meteorites but none are probably destroyed. However, shockwave events that destroy at least one structure appear to occur once every 19 years. The average fatality rate from all meteor events since 1900 is one every 4 1/2 years with only one attributed to a meteorite. If these rates are anywhere near correct then we are living in denial of the potential damage to humanity from meteor shockwave events.

In the future structural damage events (like the ones discussed here) where no meteorite is connected with the damage, needs to be studied by engineers that understand blast damage. A damage map should be made that shows blast displacements. This helps us to understand the forces at work and ultimately the energy of the blast. The specific science that addresses this kind of damage is called structural dynamics. The key evidence is that a meteor shock wave will create a higher overpressure outside the structure and thus weaker parts of the structure (like doors and windows) will be knocked inward. It is also essential to collect witness reports that include descriptions of the sounds, the track of the object, vibrations, damage, and location of the observer. There are online forms to report witness information at the International Meteor Organization, the Canadian Space Agency's Meteorite and Impacts Advisory Committee, and the American Meteor Society. I  also see the benefit of mapping glass breakage events because it is a direct result of the energy released. Also, did the glass just break or was it knocked out of the frame like we saw at Chelyabinsk?

These reports since 1900 indicate that a shock wave event will destroy one or more structures once every 19 years or so. If these events are real, the greatest danger to human life and to the structures we build, come from shock wave events and not meteorites. Also, these events must result from objects smaller than the one that hit Chelyabinsk because objects that size hit Earth about once every 90 years. Depending on the structure, the event must produce an overpressure at the ground level of 3-4 psi for a structure to be destroyed.

REFERENCES

1. BROWN, P., SPALDING, R.E., REVELLE, D.O., TAGLIAFERRI, E., &WORDEN, S.P. (2000). The flux of small near-Earth objects colliding with the Earth. Nature. 403:165-166. doi:10.1038/35003128

2. COLLINS, G.S., MELOSH, H.J., AND MARCUS, R.A.,(2005). Earth Impact Effects Program: A Web-based computer program for calculating the regional environmental consequences of a meteoroid impact on Earth. Meteoritics & Planetary Science 40, Nr 6, 817–840.

3. HALLIDAY, A. T. BLACKWELL, and A. A. GRIFFIN. (1985). Meteorite impacts on humans and on buildings. Nature. 318: 317. doi:10.1038/318317a0

4. HILLS, J.G. & GODA, P. (1998). Damage from the impacts of small asteroids. Planet Space Sci. 46, 21-19-229.

5. LEWIS, JOHN (1996). Rain of Iron and Ice. Helix Books. 236. ISBN 0-201-48950-3

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