CC BY
9doi: 10.18720/MCE.76.12
Normal stresses of frost heaving as function of excess moisture
Нормальные напряжения морозного пучения как функция
избыточной влажности
O.V. Tretiakova,
Perm National Research Polytechnic University, Perm, Russia
Аспирант О.В. Третьякова,
Пермский национальный исследовательский политехнический университет, г. Пермь, Россия
Key words: frost heave; water sucking up; normal stress; soil interstices; soil interstitial volume; ice-cement; disjoining action of water films
Ключевые слова: морозное пучение; миграция воды из талой зоны; нормальное напряжение; поры грунта; свободное поровое пространство; замерзшая поровая вода; расклинивающее действие водных пленок
Abstract. Tangential and normal stresses are arises foundation area from the frost heave process. Currently known is the analysis of the tangential stresses based on adfreezing of the frozen soil to the lateral surface of foundation. However, the differences in values of normal stresses may be due to the fact that no single approach to normal stress evaluation has been developed yet. The purpose of our research is to work out the analysis method of the frost heave normal stresses. The stresses appear perpendicular to the surfaces of structures not allowing increase in the soil volume when cooled and frozen. Based on the author's research and other investigators' experience, analytical dependences for normal stresses of soil frost heaving were obtained. The stresses were calculated as a function of excess moisture, which volume exceeds the soil interstitial volume under freezing. The results obtained took into account such factors causing heaving process as ice formation during water freezing, accumulation of ice resulting from sucking up water and influence of unfrozen water. The proposed formulas allow for calculation of stresses in any kind soil.
Аннотация. При морозном пучении грунта, вблизи фундаментов развиваются касательные и нормальные напряжения. В настоящее время известен метод расчета касательных напряжений, основанный на определении сил смерзания грунта с боковыми поверхностями фундаментов. Однако значения нормальных напряжений морозного пучения в различных исследованиях имею большой разброс. Это говорит об отсутствии единого подхода к их расчету. Целью данной работы является разработка метода расчета нормальных напряжений морозного пучения. Последние возникают и действуют по нормали к поверхностям конструкций, которые ограничивают увеличение грунтов в объеме при охлаждении и промерзании. На основании исследований автора и опыта существующих работ получены аналитические зависимости для нормальных напряжений морозного пучения грунта в открытой системе. Значения напряжений вычислены как функция избыточной влажности, превышающей свободный объем пор грунта при промерзании. В полученных зависимостях учтены факторы, обуславливающие процесс пучения: льдовыделение при замерзании свободной поровой воды, влияние миграции влаги. Предложенные выражения позволяют выполнять расчет нормальных напряжений пучения для любого вида грунта.
Introduction
The seasonal decrease in temperature causes soil freezing leading to its volume increase. Uniform volume increase in a vast homogeneous bed does not usually result in occurrence of forces. However, any obstacle to volume increase can cause significant normal stress resulting in negative impact on embedded structures and foundations, which, in its turn, leads to heaving, deformation and cracks of structures. It has been studied by many authors [1-4]. Unbalanced loading of structures can cause horizontal shear and building tilt.
To prevent these negative effects, it is necessary to design structures capable of enduring the frost heaving stress based on the calculation [5-8] and modeling [9-12] or the frost heave stress must be partially or completely neutralized [13-15]. Proper evaluation of the frost heave stress can help solve the problem, which is possible after its detailed study. In Russia, N.A. Tsytovich gave basic theory of frost heave [16]. This research was carried out by many other authors. J.-M. Konrad [17, 18], R.L Harlan [19],
S.S.L. Peppin, R.W. Style [20] studied physics of frost heave. R.L. Michalowski [21] and Y. Zhang [22, 23] made some frost heave theoretical models.
The components of the frost heave process, being tangential and normal forces, are of different value and direction. V.S. Sazhin [24], V.I. Puskov [25], R.Sh. Abzhalimov [26] described mechanism of this process. This study is concerned with frost heave normal stresses.
The normal stresses of frost heaving are perpendicular to limiting surface, that is, lateral sides of foundations, which resist the increase in volume. Normal stresses acting on foundation bed occasion vertical uplift of foundation. Normal stresses acting on lateral surface causes the tangential forces.
Existing methods of studying the normal stresses of soil frost heaving comprise those used under laboratory conditions (in a closed and open system) [27-31] and under natural conditions (in open system) [32-36]. In a closed system normal stress values are determined by the pressure ice crystals under constrained water freezing and depend on the moisture properties of soil freezing. They may be significant and do not reflect the actual soil behaviour under natural freezing. When designing embedded structures, the stress-strain-state of the freezing soil in an open system is of great importance. The purpose of this study was to give a method of normal stresses under natural conditions in open system. The objectives were to study components of heaving stress in the open system, to determine mechanism the heaving normal stress and to develop a formula of the stress.
Methods
The open system is a soil body freezing under natural conditions. These conditions are formed on the experimental area, a construction site or in the soil body next to embedded structures built before. The open system is characterized by water sucking up from adjacent soil layers. In addition, this system is exposed to the influence of the stress-strain state of the adjacent layers subject to the shrinkage or increase in volume. In most cases, water sucking up in the unfrozen zone causes soil shrinkage in adjacent unfrozen layers.
Therefore, in the open system the normal heaving forces are caused by the pressure of ice-cement, influence of ice created by sucked up water, disjoining action of unfrozen water films and shrinkage of adjacent soil layers. In addition to soil properties, the values of normal heaving forces in the open system depend on the hydraulic conductivity of soil, compressibility of the underlying layers, structural rigidity and sensing forces of frost heaving.
Schematically heaving normal stress for the open system is shown in Figure 1. As can be seen in the figure, heaving stress in the open system consists of the following components,
- volumetric heaving stresses caused by accumulation of ice-cement resulting from
crystallization of interstitial water;
- heaving stresses caused by influence of water sucking up due to
a) crystallization of free capillary water,
b) crystallization of bound water,
c) disjoining action of unfrozen water films;
- shrinkage stress.
Figure 1. Components of heaving stress in the open system
The ice and unfrozen water whose overall amount is less than the soil interstices volume does not usually affect the walls of interstices and cause internal stresses in the soil. Accordingly there is no increase in the soil volume. Frost heave occurs if the amount of the frozen and unfrozen water exceeds the volume of the soil interstices. Unfrozen film water fed by sucking up, has a disjoining action on the freezing soil and is similar to swelling. In addition, "excess ice" acts as a "wedge" between the ice in the interstice volume and the walls of interstices. This results in stress in the soil causing displacement of the soil interstices, which in its turn, leads to increase in the soil volume. The normal stresses of frost heaving are developed due to foundations constraining action on the soil volume increase. Thus frost heaving stresses are, on one hand, the function of the soil porosity, on the other hand, the function of "excess moisture" resulting in the formation of "excess ice", which the normal stresses reflect. "Excess ice" is the amount of ice exceeding the free interstice volume not filled by frozen and unfrozen film water. The normal stress value is also characterized by the rigidity of the foundation structure.
Condition under which soil heaving pressure occurs can be presented as follows
vice ^ vunfrouz. water ^ v pore , (1)
where Vice, Vunfroz.water and Vpore are the ice-cement volume, volume of unfrozen film water and soil interstices, respectively.
Based on this, the expression for normal heaving stresses in the open system can be written as
^heave ~ ( ^excess ice ^ ^unfrouz. water ^shrincage.) " kan. , (2)
where "o~excess ice <JuVjfroz water" are the ice pressure and unfrozen water pressure due to water sucking up;
"ashrincage" is an unloading effect resulting from the soil shrinkage in the adjacent layers due to water sucking up;
" kan " is the anisotropy factor taking into account the direction of heaving forces.
To define the pressure of "excess ice", we considered the distribution of water phase states in frozen soil (Figure 2). The total actual ice pressure results from two values, i.e.
a) ice-cement pressure together with 9 percent volumetric gain;
b) ice pressure caused by capillary and bound film water freezing due to water sucking up.
The (b) parameter (ice pressure) is a variable.
The <Jexcess ice (site 4b in Figure 2) reflects the difference between ice pressure due to total water
sucked up (site 4a and 4b in Figure 2) and that of water sucked up in the interstitial volume (site 4a in Figure 2). The interstitial volume is the space free of ice-cement (site1 and 2 in Figure 2) and unfrozen film water (site 3 in Figure 2).
Figure 2. Water phase states in frozen soil 1 - ice-cement; 2 - 9 percent volumetric gain of interstitial water; 3 - unfrozen film water 4a and 4b - frozen sucked up water together with 9 percent volumetric gain (4a - in a soil interstices volume, 4b - in excess of soil interstices volume - "excess ice")
We deduced the expression of "excess ice pressure"
a ■ =amigr--amigr- ■ e■ (1 -w -109• w),
^excess ice ^ ice ice. V* "w "V '
(3)
where "w" is the natural moisture of soil and "ww" is the water content due to unfrozen water, e - porosity ratio.
Upon rearrangement, expression (3) is as follows
G
excess ice
= omr \1 - e ■ (1 - ww -1.09 • w)],
(4)
Stresses due to the "excess ice pressure" in soil were expressed in terms of the Hook's law
G
migr. _ ice ~
h
E
heave
M
(5)
where "h heave" is the displacement of soil under frost heave (cm), "Em" is the deformation modulus of frozen soil (KN/cm2) [37, 38], "z" is the depth of soil freezing vertically, soil thickness horizontally (cm).
Substituting the expression (5) in the expression (4), we obtained the formula for excess ice pressure
Gexcess ice h
E
heave '
M
[1 - e ■ (1 - ww -1.09 ■ w)],
(6)
z
z
Using the A.L. Nevzorov's formula [39], we expressed the displacement of soil under frost heave resulting from water sucking up as follows
hheave = 109 ■ SP ■ T ■ grad t, (7)
where "SP" is the segregation soil potential (cm2/hour- Celsius degree), "t" is the frost heaving time (hour) and "grad t" is the temperature gradient (Celsius degree/cm).
The expression (7) was substituted into the (6). By combining (6) and (7), we obtained the equation (8). The formula for excess ice pressure taking into account soil properties and frost soil thickness without regard to shrinkage and unfrozen water was transformed into
E
^excess ice = 109 • SP -t-grad t • ^ • [l - e • (l -Ww-1.09 • w)] (8)
z
The value of frost heave normal stresses equals the 'excess ice' pressure that results from «excess moisture» exceeding soil interstitial volume under freezing. We neglected the small pressure of unfrozen film water sucked up in frozen soil. The heave stress expression (2) was rewritten without regard to shrinkage and unfrozen film water as follows:
^heave ~ ^excess ice - kan. (9)
Then, the expression (8) was substituted into the expression (9). Gravity water content was conversed to the volumetric water content. As a result the formula of normal stress as the function of moisture that resulted in formation of "excess ice" was obtained.
(heave = 109 • SP -T- grad t
E,
M
1 - e
1 -w.
,P<L -1.09 • w • — Pw
Л
d_
Pw j
• h„
(10)
where " pd /pW is the gravity water content to volumetric water content conversion factor.
The "excess ice" reflects the difference between ice pressure due to total water sucked up and that of water sucked up in the interstitial volume.
The formula of normal stress as the function of excess ice under total moisture capacity was written as
(heave = 1.09• SP-T-gradt• Em• Wsat WW • k„
z n •i1 - ww)
(11)
where "wsat" - total moisture capacity, n - soil porosity.
Results
Table 1. The normal stresses calculated by formula
z
№ formula Evaluation Sheave KN/m2
10 (Theave = 109 • SP • T • gradt • EM • z ' f y 1 - e • 1 -ww •fpL -1.09 • w •fpL V fw pw • k 134
11 (heave = 1.09 • SP • T • gradt • Em • \ • kan z n Ч1 - ww) 165
Table 1 displays calculation of frost heaving stress in clay by formula (10) and (11). The normal stresses of frost heaving in the open system were calculated as a function of "excess moisture" exceeding the free soil interstitial volume under freezing.
Table 2. The comparison of stresses calculated by formula to Guidance on design of substructures and foundations on heaving soil (1979)
Methods Thickness of frozen layer under the foundation base or on the lateral surface of foundation, m Direction of frost heave normal stress The frost heave normal stress, kH/m2
The research Formula evaluation 1.0 Horizontal lateral 134 - 165
Guidance on designing of substructures and foundations on heaving soil (1979) Tabular date 1.0 Vertical 100 - 600
Table 3. The comparison of stresses calculated by formula to other authors' result
Methods Foundation depth, m Thickness of frozen layer under the foundation base or on the lateral surface of foundation, m Temperature of soil Rate of heave mm/day Direction of frost heave normal stress The frost heave normal stress, kH/m2
This research (2016) Formula evaluation 1.0 1.0 -4.0 1.7 Horizontal 134-165
A.E. Fedosov (1935) Laboratory test Vertical and horizontal 150-180
N.N. Morareskul, N.A. Tsytovich (1950) Laboratory test Vertical and horizontal 500-800
B.I. Dalmatov Field test 0.9 - 1 Horizontal 30 - 35
(1954) 1.45 -1.72 64 - 66
V O. Orlov (1958) (frost zone out of contact with 0.18 -0.9 0.95 160
0.33 -1.4 1.36 510
Field test 1.09 0.41 -2.4 1.35 Vertical 950
0.51 -4.4 1.22 3100
permafrost 0.6 -4.7 1.12 3800
embedding on 4,5m) 0.67 -4.9 0.96 4700
N.A. Tolkachev (1964) Field test Vertical 310-430
B.E. Slavin (1969) Field test 1 - 6 Vertical and horizontal 182 -322
E.A. Marov (1970-1971) Field test 0.3 2.4 Vertical 760
V.S. Sazhin, V.Ia. Shishkin Field test 1.2 0 - 1.2 Horizontal 1400 -1600
(1982)
E.D. Ershov (1985) Laboratory test 0.5 Vertical and horizontal 220 -620
Guidelines for -2 63.9
accounting and preventing strains and forcers of frost heaving soils (Production and Research Institute for Survey and Construction) (1986) Formula evaluation 0.9 -4 Vertical 183
A.G. Alekseev (2006) Field test 2.0 1 - 2 Horizontal 20-190
The comparison of stresses calculated by formula with tabular data of RF Code is displayed in Table 2. As can be seen in Table 2, the normal stresses, calculated by formula (10, 11), agree with the tabular data of RF Code provided the anisotropy factor is taken into consideration.
The comparison of stresses calculated by formula with the results obtained by other researchers is displayed in Table 3.
So, the formula values of frost heave normal stress for layers of seasonal freezing proved true when compared with those, obtained by numerous researchers. The differences in values may be due to the fact that no single approach to normal stress evaluation has been developed yet.
Discussion
Division of frost heave stress into tangential and normal seems to be reasonable. Currently widely known is the analysis of the tangential stresses based on adfreezing of the frozen soil to the lateral surface of foundation. Research of academic specialists into frost heave direction led us to infer that it is possible to work out an analysis method of the heave normal stresses.
Research into frost heave normal stresses in open and closed systems seems to be representative. The normal stresses in the open system prove to be more reasonable as they take into account such factors causing heaving process as accumulation of ice due to sucking up water and influence of unfrozen water and stress-strain behaviour of soil below. Based on the research we can conclude that the normal stresses of frost heaving in the open system are a function of porosity and "excess moisture" whose volume exceeds the soil interstitial volume under freezing.
Soil and sucking up water that exceeds the soil interstitial volume after freezing causes increase in soil volume, which together with expansion constraint of foundations results in the heave normal stresses.
The comparison of stresses in Table 3 is worth mentioning that the normal stress values obtained in our research are comparable to those of other researchers. They correlate most with the results of B.I. Dalmatov (1954) [32] it taking into account the deformation modulus of the frozen soil. According to Table 3 our results can be associated with stress values obtained by A.E. Fedosov (1935) [40], B.E. Slavin (1969) [41], E.D. Ershov (1985) [28], A.G. Alekseev (2006) [35] and researchers from Production and Research Institute for Survey and Construction (1986). Our results agree with N.N. Morareskul' [27] and V.S. Sazhin' stresses [24] allowing for the anisotropy factor. Field tests carried out by E.A. Marov indicated significant increase of stresses depending on the thickness of the soil layer frozen [33]. Marov's results are comparable with our data under reduced layer soil thickness. Stress testing under the close system, i.e. in laboratory conditions, shows the high value stresses, which do not reflect the actual soil behaviour under natural freezing. In addition, research into the normal stresses in the permafrost region suggests these conditions be different from the seasonal freezing conditions (V.O. Orlov 1958) [42].
To make the analysis method work, several objectives need to be achieved:
• Statistical data on temperature and moisture of the soil at various depths within autumn-winter seasons should be provided, information on the freezing soil velocity is needed, which requires cartographic reference material.
• The method supposes revision of deformation modulus of frozen soil.
• To confirm the results obtained, a certain number of experiments should be carried out in different kinds of soil.
• The analysis method needs further interpretation in design programs.
Conclusion
As, a result of the research carried out it was found that
1. Frost heave occurs if the amount of the frozen and unfrozen water exceeds the volume of the soil interstices. Thus frost heaving normal stress is, on one hand, the function of the soil porosity on the other hand, it is the function of "excess moisture" resulting in the formation of "excess ice". "Excess ice" is the amount of ice exceeding the free interstice volume not filled with frozen and unfrozen film water after freezing.
2. The normal stresses in the open system prove to be more reasonable.
3. The formulas (10, 11) for the normal stresses of frost heaving in the open system as a function of excess moisture exceeding the free soil interstitial volume under freezing, and their results appear to
be relevant to the tabular data of RF Code available and other authors' results. The expression obtained make it possible to define normal stress in any hydrogeological and climatic conditions.
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