Fracture mechanics analysis in frost breakage of reservoir revetment on cold regions

XiaoZhou Liu , Peng Liu

1. Key Laboratory for Prediction & Control on Complicated Structure System of the Education Department of Liaoning Province,Dalian University, Dalian, Liaoning 116622, China

2. State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China

Fracture mechanics analysis in frost breakage of reservoir revetment on cold regions

XiaoZhou Liu1,2*, Peng Liu1

1. Key Laboratory for Prediction & Control on Complicated Structure System of the Education Department of Liaoning Province,Dalian University, Dalian, Liaoning 116622, China

2. State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China

Reservoir revetment in cold regions is often damaged by frost due to the joint action of low-temperatures and cryogenic environment in winter. This damage reduces or even eliminates the function of the reservoir revetment. In this paper, practical problems in engineering were analyzed for the drainage pumping station of Tuanjie Reservoir. Based on a traditional method of analysis and calculation, fracture mechanics was incorporated to provide quantitative analysis and calculation on the problem of anti-freeze damage from the viewpoint of fracture mechanics. Thus, a new idea is put forward to resolve anti-freezing of reservoir slope protection in cold regions.

slope protection; fracture mechanics; low temperature; ice stress

1. Introduction

In seasonal frozen soil habitats, reservoir slope protection and dam embankment revetment is often and easily damaged by winter freezing conditions of low-temperatures and environmental factors, such as ice thrust, frost heaving failure, thaw breakage, and wave destruction. However,present freezing damage calculation methods of reservoir slope protection does not allow for frost breakage (Electric Power Enterprise Standard of People’s Republic of China,1998). In terms of slope protection design, traditional methods and standards are still being used, often leading to direct frost damage of slope protection. In this paper, in regard to problems of frost breakage, we propose an effective form of slope protection for the Tuanjie Reservoir,Liaozhong County, Shenyang, China. This is based on anti-frost breakage analysis of the past hydraulic structures(Liuet al., 2005; Liet al., 2006), and frozen soil fracture mechanics, of which a quantitative analysis and calculation was performed on damage resulted from ice and freezing.Thus, a new approach is put forward to address the anti-frost breakage of reservoir slope protection in cold regions during winter.

2. Reservoir project overview

2.1. Project location and function

Tuanjie Reservoir is located in northern Liaozhong County, in the territory of Liuerbao town and Lengzibao town,on the main channel of Pu River. It is a medium-sized plain reservoir which is used mainly for flood protection, but also for irrigation and aquaculture. The main reservoir is 58 m long,dam length of 1,100 m, left dike of 12.29 km with six buildings, and right dike of 6.73 km with three buildings, for a total of nine ancillary buildings and dike length of 19.02 km.

2.2. Geological, hydrological and meteorological data of sites

2.2.1 Geological data

The reservoir basin belongs to the middle of the Liao River Basin, with no exposed bedrock on the surface, but is covered by loose stratum of Quaternary sand. Most of the soil filling the gate dam embankment is sub-clay, part of which is mixed with light sub-clay of different thickness.The soil layer under the embankment is divided into five layers from top to bottom, respectively, silt loam, sub-clay,light sub-clay, sand, and medium-fine sand. Soil layer:bearing strength of silt loam layer is 9 t/m2, bearing strength of sub-clay layer and light sub-clay layer is 16 t/m2, and bearing strength of fine sand layer is 15 t/m2.Other physical and mechanical properties are shown in Table 1.

Table 1 The physical and mechanical properties of soil and sand (Statistics of average temperature)

2.2.2 Hydrological and meteorological data

Tuanjie Reservoir is on Pu River, upstream from the entrance to Hu River. The upper reaches of Pu River before the sluice is 142 km north of Liaozhong, and the river basin area is 1,820 km2. According to the local weather station data,annual average temperature is 8.7 °C, accumulated temperature that is not less than 10 °C is 3,477.9 °C, and frost-free period is generally 165 days long. The average depth of frozen soil is 1.2 m. There is ice up to mid-November each year, and thawing in mid-March the following year. The average ice thickness of the reservoir is 0.7-0.8 m. The annual average temperature statistics are presented in Table 2.

Table 2 Average temperature statistics

2.3. Frost breakage situation

The reservoir is located in a typical seasonal frozen soil habitat in northern China, belonging to the plains-reservoir-type. The geographical location and cold environmental conditions contribute to damage of the reservoir slope protection.

(1) Although the form of buried stone slope protection was adopted for this reservoir, after many years of freezing and thawing cycle, up to 800 m of the slope protection collapsed, accounting for 2/5 of cross section of riverside slope (Figures 1 and 2). Meanwhile, the causeway slope height collapsed, and the average swell height of riverside slope is 1.1 m.

(2) Many supporting structures such as through-dam culverts have varying levels of frost heave fracture and water leakage, which diminish their function.

(3) Although several structures have been recently rebuilt, and the capacity of reservoir slope protection has been strengthened, this still does not fundamentally resolve the problem of frost heave and ice-push.

Figure 1 Dyke frost damage

Figure 2 Slope protection frost damage

3. Analysis of frost breakage

With slope protection as the object of this study, and from the viewpoint of mechanical and physical damage to the slope, there are three basic aspects to consider: (a) External causes: The external load directly on slope protection is mainly caused by environmental conditions, such as ice load and wind blown water forming a "wave wash". (b) Interior causes: Slope protection structure should include the surface layer, filtration layer, and an anti-freeze layer. Under this is the base soil layer which freezes in the winter. It is well known that frozen soil mass produces a frost heave deformation, and this confined distortion produces a frost heave force. The frost heave of the base soil layer is bound by the slope protection, so a frost heave force is applied to the slope protection. The frost heave of the base soil layer also produces a frost-heave force on the undersoil, but this is not the focus of this study. The base soil layer generates an upward frost heave deformation during the winter, Thus,when the weather warms and temperatures rise, the soil begins to melt, and the thawed soil drops from the frost heave deformation position, causing the slope protection braces to fall through. This thawing procedure can also be produced by the weight of the soil. (c) Structural causes: The strength and stiffness of the slope protection structure do not meet design requirements, such as surface discontinuity and roughness.

From the aforementioned analysis we can see that there are three main factors for frost breakage of this reservoir slope protection: ice thrust, frost heave and wave wash.Among them, ice thrust and frost heave play major roles,while wave wash plays a supporting role.

3.1. Ice thrust breakage

After the reservoir has become icebound, any sudden warming or temperature increase (such as after a cold wave)will cause volumetric expansion, producing static ice pressure (ice stress for short). This ice stress acts upon the slope causing upward displacement, such as sliding and rolling.This is commonly known as an ice-push effect (ice-push for short) (Yang, 1994). There are three basic conditions for the generation of ice-push: (a) There is a large ice stress which occurs in an ice sheet. (b) There is a greater adfreezing force between an ice sheet and slope protection. (c) The resistance force of the cushion or base layer below the slope protection is small. In addition, ice-push generally occurs in shallow plain reservoirs with a long dam, and little change in water level during winter.

In early winter, seasonal cold waves often occur and temperatures fluctuate. When temperatures rise sharply after a cold wave, greater ice stress is produced. If the overall strength of the slope is small, and the adfreezing force is large, then the surface of the cushion or base soil layer below the slope will slide upward, being squeezed out or misplaced,resulting in extensive damage of the slope.

In early winter the ice is thin (20-30 cm) and the strength is small, but the adfreezing force is large with the slope. When the ice stress produced in the ice sheet is less than the adfreezing force, ice push does not occur, but fractures easily occur in the weak part of the ice sheet.

At the same time, ice swells up from the ice breakage,causing an upward arch and producing a loud sound. From a distance it looks like a long ice arris (fictional horn of a horse) which is commonly known as a "unicorn", as shown in Figure 3.

During the "unicorn" phenomenon, the energy of the ice sheet has been released. If this occurs within the vicinity of the slope, slope damage may occur, but if distant from the slope, it will have little effect on the slope.

Similarly, in late winter with a sharp rise in temperature,there is greater ice stress in the ice sheet, with a total value of ice stress which is much greater than that in early winter.This period is considered as the risk period for slope protection damage. Because the frequency of ice-push is higher in early winter, but the extent of damage is smaller,the damage degree is lower. Conversely, in late winter, the frequency of ice-push is lower, but the influence range is large, resulting in heavy damage. Usually 100-1,000 meters of slope protection could collapse because of an ice push.Therefore, anti-ice-push damage control should be timed at the end of winter.

Figure 3 Unicorn pictorial

3.2. Frost heave and thawing

The issue of frost heave in relation to slope protection refers to the destructive effect produced by frost heaving(expansion of frozen water) on the base soil below the slope protection, there are suitable conditions for frost heave in the soil under the base of plain reservoir revetment. The base soil below the slope of a plain reservoir contains suitable conditions for frost heaving. The first is soil quality,fine-grained soil is very sensitive to frost-heave; the second,water freeze and expand causing destruction; then the slope is light weight, so it is prone to frost heaving.

For seasonal frozen soils, when the weather turns warm after winter, ground temperatures rise, and frozen soils begin to melt, then the soils begin to fall from the original position of frost heave, which produces thawing. Frost heave and thawing are interdependent. There is bound to frost heave with thawing, frost heave inevitably causes local uplift, dislocation, tilt, cracking, arching and other failure modes;when thawing can not reset, and wave wash effects exist, the melted soils under the frozen soils layer is undermined, and large areas will collapse while thawing. Frost heave and thawing occur every year, which then accumulates and intensifies year after year.

Generally speaking, soil frost heave must meet the following conditions:

(1) The soil is sensitive to frost heaving;

(2) The initial moisture and external moisture (groundwater, atmospheric precipitation, water from anthropogenic activity) supply exist;

(3) Conditions and timing are suitable for freezing.

These three conditions are indispensable, which are also anti-frost heaving and thawing conditions.

3.3. Wave wash

For the revetment structure, thickness and filtration layer are designed according to anti-wave requirements. Thus, it should withstand a wave wash condition. However, because of ice push and frost heave, the integrity and continuity of the slope protection surface is severely compromised, resulting in damage such as arching, dislocation, distortion,and cracking. When the cushion and base soil becomes loose,the filtration layer structure is damaged, thus undermining the original anti-wave design capacity, and causing severe damage from wave wash. Therefore, both frost heave and thawing cause wave-wash. The direct threat to the safety of reservoirs is serious wave wash of ice-push and frost heave.Therefore, anti-ice-push and anti-frost heave must be considered in the initial design of slope protection.

4. Schematic design and calculation of frost breakage

4.1. Schematic design

According to the aforementioned analysis, this slope project intends to use flat reinforced concrete slabs as shown in Figure 4. Slope protection should have two components, a surface layer, and a cushion, where the surface layer thickness ist1, cushion thickness ist2, and a total thickness ist=t1+t2. The surface layer is reinforced concrete slabs, with a thickness of 10-25 cm, plane size should be in a range of 2m×2m to 4m×4m, but not too large in order to prevent subsidence cracking. Cushions are three layers of gravel,pebbles and sand, respectively. The base soil layer is under the cushion.

Figure 4 The slope protection structure composed of flat reinforced concrete slabs, and cushion layer

In the design of slope protection, the following should be noted: surface layer thickness should meet anti-ice-push stability and strength requirements in order to check anti-wave computations or design; cushion thickness should meet anti-frost heaving requirements, which ist2=Hd-t1,whereHdis frozen depth of project location.

4.2. Anti-ice-push calculations

4.2.1 Calculations of anti-ice-push stability of slope protection

The conditions of anti-ice-push stability of slope protec-tion include non-slippage of the entire structure, and no local pull-off. From the view of fracture mechanics, push-slope force isPH, resistance include: concrete slab and ice sheet weightW=Gsinα; frictional resistanceF=(PV+Gcosα)f+cL,then safety factor of anti-ice-push stabilityKis as follows(Yang, 1994; Li and Zhu, 2002):

In Equation(1):

G—the sum weight of reinforced concrete slab and ice sheet above slab,

wheret1is reinforced concrete slab thickness (determined as 0.15 m according to actual situation);γkis gravity density of reinforced concrete (determined as 25 kN/m2); height of slope protection above and below ice are, respectively,H1=4 m,H2=1.57 m; slope ratiom=2.5; The reduction factor of adfreezing forceK'=0.55; standard adfreezing forceτ=100 kPa; ice thicknessδ=1.0 m; slope angleα=22°; friction factorf=0.25; cohesionc=20 kPa.

Substituting known conditions into the formula, results are as follows:

ThenK=1.78＞1; which meet anti-ice-push stability requirements.

4.2.2 Structural strength calculation of slope protection

When calculating anti-ice-push strength, the slope can be simplified as a 1-m wide board on an elastic foundation. The stress formula of a plate on an elastic foundation (Guet al.,1985; Yang, 1994) is as follows:

wherePVandPHare vertical and horizontal components of ice stress (kN), respectively;Eandvare elastic modulus and Poisson’s ratio of the plate, respectively;tis thickness of plating (m);kis coefficient of soil reaction (kN/m2); andbis loaded area related parameters (m).

For reinforced concrete revetment plate, the corresponding parameters should be chosen as:PV=59.24 kN,PH=148.09 kN,E=2.6×107kPa,v=0.18,t=0.15 m,k=105kN/m2, loaded area:u×u=1m×1m,b=0.57,u=0.57 m.

The internal stress of reinforced concrete revetment plate is:

To meet anti-ice-push strength safety requirements, reinforcement of the concrete slope protection plane should be 5Φ and 16 rebars per meter, cross-sectional area of which are:5×2.0=10 cm2=10-3m2, tensile strength of rebar [RP]=240 MPa=240×103kPa, and assurance factorK=F/[RP]=1.71＞1.

4.3. Anti-frost-heaving calculation of reinforced concrete slope protection plate

Frost heave damage of reinforced concrete slope protection is mainly produced from the cushion and base soil layers. If the cushion layer is thick enough, then only the cushion layer will frost, while the base soil layer melts, thus preventing frost heave. In this case, one only needs to calculate frost heave of the cushion layer. The cushion layer is paved respectively with gravel, pebbles and sand, because frost heave produced by gravel and pebbles is extremely small,therefore, one only needs to calculate frost heave generated by sand of the cushion layer. Otherwise, one would have to calculate frost heave generated by the cushion and base soil layers. However, if the cushion material is not sensitive to frost heave, then it basically does not produce frost heave and one would only have to calculate frost heave produced by the base soil layer.

In addition, anti-frost heave designs are mainly for the slope above the water surface, while the non-frozen zone below the water surface don’t need to be considered for anti-frost heave.

According to the local measured data, frost depth isHd=1.2 m, then the cushion thickness of structural slope protection of reinforced concrete slab should meet the following requirements:t2=Hd-t1=1.2-0.15=1.05 m, average depth of groundwater is calculated byd=0.95 m.

According to Electric Power Enterprise Standard of People’s Republic of China (1998), the local sand surface frost-heaving capacity is Δh=35 mm, then the calculation formula for frost-heaving capacity of the sand layer under reinforced concrete slab is:

whereαPis the load correction factor,αP=e-0.034×90=0.047;design frost depthzd=1.2 m; frost depth under basezb=zf-ds,if the ice layer is not considered,zbcan be calculated withzf=zd+φads-1.67δi, in which correction factorφa=0.35, base thicknessds=0.15 m, ice depth above baseδi=0, thenzf=1.2+0.35×0.15-1.67×0=1.25 m, sozb=1.25-0.15=1.1 m.Substituting the calculated parameters into Formula(3),frost-heaving capacity of sand layer under reinforced concrete slab can be obtained as:

Then frost heave deformation of reinforced concrete slab slope protection can be calculated with Formula(4)(Timoshenko and Woinowsky, 1977; Guet al., 1985) as follows:

where according to Electric Power Enterprise Standard of People’s Republic of China (1998), normal frost heaving pressureq=σn=75 kPa, values for the remaining parameters are: slab lengtha=4 m;Eandvare respectively taken asE=2.6×107kPa andv=0.18;t1=0.15 m; then the known conditions are incorporated into the formula to calculate forD=Et13/[12(1-v2)]. Finally, when the calculated thickness of sand is 0.9 m, then the frost heave deformation of reinforced concrete slab is

An reinforced concrete slab is very resistant to deformation, while the computed frost heave deformation of reinforced concrete slab is only 10 mm. If one also considers the impact of gravel and pebble layers, then frost heave on a reinforced concrete slab is even smaller. Thus, very little damage occurs to the structure of slope protection.

5. Conclusion

(1) Through analysis of frost breakage of Tuanjie Reservoir, it can be seen that there are three main factors leading to damage of reservoir slope protection: ice thrust, frost heave and wave wash. These three factors do not act independently but together, thus increasing the destructive action on structures of slope protection. Among the three, ice thrust and frost heave are the primary factors because wave wash stems from ice thrust and frost heave. Thus, to prevent wave wash, one must first prevent ice thrust and frost heave.

(2) The basic requirements for anti-ice thrust of slope protection structure are: (a) Integrity of slope protection is fine,stiffness and strength meets design requirements; (b) Slope protection surface is smooth, and the freezing power between ice sheet and slope is less than the intensity of ice; (c) Friction of cushion layer and base soil layer under slope protection is stronger than ice thrust, these three are indispensable. At the same time, the basic conditions that cause frost heave are: (a)Cushion and base soil layers are sensitive to frost heave; (b)These layers are provided with initial moisture and an outside water supply; (c) Low-temperature environment and conditions, these three are also indispensable.

(3) This study introduces a fracture mechanics approach for frost breakage of a water conservancy project, based on a traditional analysis method. The stability and strength of the fracture mechanics theory, taking into account the structures’own flaws and other factors, is in line with the actual ice breakage of hydraulic structures. Through the anti-freeze damage calculation of reinforced concrete slab slope, the results meet the requirements for anti-ice thrust and anti-frost heave. Meanwhile, the research method also provides a new idea for analysis and problem solving of frost breakage of plain reservoir revetment.

The financial supports are provided by the National Natural Science Foundation of China (Grant No.50809007);the Scientific Research Item of Liaoning Institution of Higher Education (No.2008023); and the Open Fund of the State Key Laboratory of Frozen Soil Engineering(SKLFSE200907).

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10.3724/SP.J.1226.2011.00319

*Correspondence to: Dr. XiaoZhou Liu, Key Laboratory for Prediction & Control on Complicated Structure System of the Education Department of Liaoning Province, Dalian University, Dalian, Liaoning 116622, China. Email: lxzxmy0125@163.com

18 February 2011 Accepted: 11 May 2011