Entrapped air - reason for the unexpected pore pressure behaviour in levees and earth dams.

 

HENRYK ZARADNY

 

Hydroengineering Institute of the Polish Academy of Sciences

ul. Koscierska 7, 80-953 Gdansk, Poland

Phone: +48 58 552-20-11, Fax: +48 58 552-42-11, e-mail: henzar@ibwpan.gda.pl

 

 

ABSTRACT

The soil air can be entrapped by water seeping through the dike and the dam. Air entrapment occurs in the upper segment of the dike below its crest and most commonly in the lower part of the dam core. The pressure of entrapped air is in general much higher than the pore water pressure. It can be a hazard for the earth structure stability.

 

INTRODUCTION

During intensive rainfall, overflow or wave overtopping, water infiltrated into the dike may close up air pores, which leads to generation of the high air pressure greater than the pressure in the surrounding ground water. As a result of the above phenomenon, unfavourable high saturation at the top part of the dike (caused by the zone of "entrapped" air reducing the ability of soil to transport water downwards) or also a change in the topsoil structures may occur. This takes place when air pressure cannot be balanced by the weight of the overlying soil. As it was reported in works of Zaradny [7] and Abo Elela [1], the location of the "entrapped" air depends on the geometry of an earth structure as well as on the movement direction of seeping water. For the dike it is positioned in the upper segment below its crest but for an earth dam in lower part of its core, e.g. Høeg [4].

 

ANALYSIS OF PRESSURES AND FORCES ACTING ON THE ENTRAPPED AIR IN SOIL

In order to define the pressure generated in the unsaturated section of the dike/dam, it is important to consider the method of determining fluid potential at any arbitrary point of the earth structure. As it is well known fluid potential is expressed by the amount of work done to transport a unit mass of the fluid from a given reference datum z = z₀, at standard state p = p₀, to the point (z) and a state at which the potential F is determined. Assuming that the standard state can be taken arbitrarily then one can use the atmospheric pressure p_atm for the sake of convenience. For such assumptions the expression for potential is as follows:

(1)

where: z₀ = 0, p₀ = p_atm, p - p_atm - the manometric pressure and g - acceleration due to gravity.

It is important to explain here that the kinetic energy for the process under consideration is negligibly small (compared to the other values) and e neglected. If one assumes that soil water potential is known then the potentials of other fluids as e.g. air can be determined. After simplification that is by neglecting the energy in the fluid due to effects at the fluid-water-soil interface, the following expressions can be written:

- for an arbitrary fluid having density r

(2)

- so for water having density r_w

(3)

By finding the value of p - p_atm from Equation 3 and upon substitution into Eq. 2 the following form is obtained:

(4)

The transition from potential to the force field is given as follows:

(5)

where: E - force acting on a unit mass of fluid with density r,

g - force of gravity attraction,

Þ force acting on a unit mass of water (if p_atm

is constant).

 

In case where the energy connected with the interface effects (fluid in contact with water and soil) cannot be neglected without affecting the accuracy of F estimates, the relationship for F can be written as follows:

(6)

where: p - the capillary pressure, r - the fluid density, usually depending on pressure

(r = f(p)).

After assumption that r = f(p) » constant, Eq. 6 takes a form:

(7)

It follows from the above that the pressure in the fluid will be p^*= p - p_atm + p_c. The capillary pressure p_c results from the fluid interaction at the water and soil interfaces. From the theory of molecular pressure for a curvilinear surface (convex or concave) with R₁ and R₂ as the major radii of curvature follows for a flat surface R₁, R₂ = ¥ that p_c = 0. However for a concave surface (such as water in unsaturated soil) the major radii of curvature are for water negative and so p_c < 0. For the fluid on the other side of the interface the major radii are positive because the surface is convex and then p_c > 0.

If it is assumed that the air of density r_air is being considered then:

(8)

and

(9)

where: F_air - the air potential without considering the capillary pressure (p_c = 0).

The above inequality (Eq. 9) results from the fact that both the first term (1/r_air - 1/r_w) and the second term (p_c/r_air) are positive. Thus the air will tend to move towards smaller potentials. Under conditions of hydrostatic equilibrium the above direction will be vertical. In the case of water motion, to find the direction of air movement one must take into account the hydrodynamic conditions in the zone of air entrapment.

The unity force can be described as follows:

(10)

where: E_air - force acting on air without considering the capillary pressure (p_c = 0),

1/r_air grad p_c - the component resulting from capillary force.

The forces acting on water and on air are illustrated in Fig. 1.

 

In soil physics, in place of the capillary pressure p_c, the suction pressure p_s or soil pressure potential y (for an unsaturated soil y = - p_s) are more readily used. Both values depend on the water content q in the soil and have a wide fluctuation ranges (0 £ p_s £ 10⁷ hPa and -10⁷ £ y £ 0 hPa) as it is illustrated in Fig. 2.

 

OCCURRENCE OF ENTRAPPED AIR IN DIKES AND DAMS

For a given soil the force decreases with the increase in water content of the soil at t = t₀, i.e. when the air entrapment phenomenon begins. Air pressure in the region of entrapped air gradually increases with a simultaneous reduction in volume of this region.

At the same time the value of pressure gradient will be growing accompanied by increase of the forces acting on the air due to the component resulting from capillary forces. In the case of there will be no equilibrium between the entrapped air and its surroundings that might bring about failure of the earth structure.

It is seen from our studies that the failure is most likely to occur in the upper part of the dike slightly below the crest. A crevice (light line running across the upper right side of the entrapped air area) can be observed in Photo. No. 1 taken at 250 minutes.

This zone was earlier a small part of main area shown in Photo. No. 2 taken at t = 18 minutes. One can observe it on the upper left-hand side of the main area. The modelling device and description of experiments are presented in [7] and [1].

 

Photo. No. 1. Left-hand side of he dike fragment tested with clear area of entrapped air and a diagonal crack running from the top part of that area - the situation at t = 250 minutes.		Photo. No. 2. The modelling device with the tested dike fragment. The zone of entrapped air (light coloured part) at t = 18 minutes is visible on the left-hand side of the dike.

 

From these studies the following conclusions are drawn:

air entrapment occurs in the upper segment of the dike below crest. Specific location and size of air entrapped zones depend mainly on the intensity and scope of infiltration acting on the crest and slopes as well as on the rate of groundwater table rising,

the zones of entrapped air are practically impermeable to water so they restrict its movement downwards. This can cause a formation of unfavourable high saturation of soils in the upper part of the dikes,

if the force is not in equilibrium with the dike soil environment then the dike structure will be endangered and damage will occur (for example as a crack), which will bring about the loss of dike stability. In the dike wave overtopping the latter phenomenon can cause dike breaching, as was the case in the Netherlands in February 1953.

In the dams the entrapped air can occur in the lower part of core. It happens particularly often in the case of unsatisfactory compaction of the material in an earth core that accompanies low degree of saturation. This phenomenon is usually much pronounced if reservoir impoundment runs with very high speed.

Manifestation of these phenomena had place in the core of W.A.C Bennett dam in Canada. As reported Høeg [4] it is very large (45×10⁶ m³ earthfill structure with a crest length of 2042 m, completed in 1967), 183 m - high dam with a thick broadly graded glacial till core (Fig. 3). As reported Høeg [4], the measured piezometric head in location EPO4 increased between 1970 and 1976 to values much higher than those predicted (about 55 m). However, since that time (1976) the measured pore pressure has continuously decreased but always (till 1992) was higher than that predicted based on saturated steady flow theory. Similarly several other dams described in the literature have shown pore pressures in the downstream part of the core which were higher than expected. Many hypotheses have been proposed over the years, some of the explanations are also proposed by Høeg [4].

Basing on our experience we think that the reported by Høeg [4] pressures result from the phenomena of air entrapment in the material in the dam core, which for W.A.C Bennett dam was low saturated (50 - 90 per cent) after compaction.

 

 

Fig. 3. Cross-section of the W.A.C Bennett dam in Canada (according to [4]): 1 - glacial till core.

 

In Fig. 4, one can read for 1976 the piezometric head h_EPO4 = 611.5 m, which is about 55 m above the predicted value. If for material in the core one takes by analogy the values of suction given by Rijtema [5] for the clay loam:

suction in cm 0 2.5 10 31 100 200 500 2500 16000

saturation S_w % 100 98.2 96.4 94.6 92.3 88.3 82.2 76.8 57.3

then suction h_s = p_s /r_w g = 55 m corresponds the value of saturation S_w = 72.5%. Comparing this value (S_w = 72.5%) with that reported in [4] - S_w = 50 - 90% we can state that the value (h = 55 m) exceeds the predicted value corresponds well to the suction of compacted soil so it seems evident that measured values of pore pressure concern gas phase (no liquid phase - water).

Fig. 4. Measured piezometric head versus time from 1969 - 1992 for the W.A.C Bennett dam (according to [4]), where: (a)        shows piezometric head versus reservoir level and time in piezometer EPO4, (b)        shows the variation of piezometric head with time.

 

Looking on the results in Fig. 4 we can distinguish the following stages:

·        till 1976 - air pressure gradually increases with a simultaneous reduction in volume of entrapped area caused by seeping water. This process in the core material is usually sluggish if one considers that for suction h_s = 55 m, hydraulic conductivity of clay loam is equal to 9.8 10^-6 cm/day and only k_sat = 0.98 cm/day for full saturation [5],

·        1976 - 1980 - air pressure gradually decreases which is caused by diffusion and solubility of air in water (Aksielrud, Altszuler [2]),

·        1980 -1984 - air pressure decreased about 15 m in spite that the reservoir elevation rise about 10 m. Probably just then in the core material occurred the structural changes!

·        since 1984 - air pressure decreases with different rates. In 1992 (end of recording of pore pressure) the values of the pore pressures in EPO4 were still higher than those predicted from a seepage analysis. The difference was about 2.5 m, which seems reasonable from point of view of prediction accuracy obtained for steady state solution for a homogeneous core.

Presented explanation has been positively verified in nature in 14 June 1996. Then a sinkhole was discovered at the crest of W.A.C Bennett dam [4]. As reported Høeg [4]: "subsequent inspections below the paved roadway revealed a depression about 1 m deep and 1.5 m in diameter. A 50 mm - diameter steel pipe within a 150 mm steel casing, used as a survey benchmark founded on bedrock some 110 m below, was found at the bottom of sinkhole".

In my opinion it was resulted by the core material structural changes caused by high air pore pressure. That changes have begun much earlier than 1996 (probably about 12 -15 years earlier). Delay in the manifestation of these changes at the crest was probably caused by the paved surface.

 

CONCLUSIONS

The phenomena presented above seem to be important source of danger for river embankments and dams stability. The investigation conducted in Hydroengineering Institute PAS can give not only theoretical but also practical instructions for overcoming such phenomena, which endangered stability of the earth structures.

In these studies the modern two-dimensional modelling device [7] and mathematical modelling of water and air movement in soil were used [6].

 

REFERENCES

[1]. Abo Elela M., Filtration Phenomena in Earth Dike during Intensive Precipitation, Ph.D. thesis under H. Zaradny supervision, Hydroengineering Institute PAS, Gdansk, 1996/1997, 153 pp.,

[2]. Aksielrud G. A., M.A. Altszuler, Mass movement in porous media, WNT - Warsaw, 1987, 296 pp., (in Polish),

[3]. Feddes R., P. Kowalik & H. Zaradny, Field Water Use and Crop Yield, PUDOC - the Netherlands, 1978, 189 pp.,

[4]. Høeg K., Performance evaluation, safety assessment and risk analysis for dams, The International Journal on Hydropower & Dams, U.K., Vol. three, issue six, 1996, 51-58 p.,

[5]. Rijtema P. E., Soil Moisture Forecasting, Nota 513, Institut voor Cultuurtechniek en Waterhuishouding - Wageningen, 1969, 28 pp.,

[6]. Zaradny H., Groundwater Flow in Saturated and Unsaturated Soil, Balkema/ Rotterdam/Brookfield, 1993, 279 pp.,

[7]. Zaradny H., Physical modelling of infiltration into dikes for stability purposes, Contract No. DWW-510, the final term 1994, Hydroengineering Institute PAS, Gdansk, 1995, 70 pp.