The Origin of Hogwallows and Gilgai Landforms - PART II

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The Origin of Hogwallows and Gilgai - PART II10/31/2013. 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 and 12/24/2024.

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 a vertical 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 up to failure. 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 are load-reactive ie, 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. I call this depth the "rebound depth."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 vertical 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 occurs 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. However, there is a lifting influence before 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 do not cause gilgai 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, and 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,  2/11/2024, and again on 3/11/2025.

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. 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 164 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 can be seen in Mayne and Kulhawy (1982). 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, ichalowski (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. (Note that Figure 1 was removed because it was an early version that is now outdated. The latest version will be published in a paper in 2025. This paper will be titled: Influence of Stress History on the Weathering of Expansive Clays.) 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.