Water level variations have caused numerous dam slope collapse disasters around the world, illustrating the large influence of water level fluctuations on dam slopes. The required indoor tests were conducted and a numerical model of an actual earth-filled dam was constructed to investigate the influences of the water level fluctuation rate and the hysteresis of the soil–water characteristic curve (SWCC) on the stability of the upstream dam slope. The results revealed that the free surface in the dam body for the desorption SWCC during water level fluctuations was higher than that for the adsorption SWCC, which would be more evident at higher water levels. The safety factor of the upstream dam slope initially decreased and then increased for the most dangerous water level as the water level rose and fell. The water level fluctuation rate mainly influenced the initial section of the safety factor variation curve, while the SWCC hysteresis mainly affected the minimum safety factor of the water level fluctuations. The desorption SWCC is suggested for engineering design. Furthermore, a quick prediction method is proposed to estimate the safety factor of upstream dam slopes with identical structures.
Practice has revealed that water level fluctuations have significant effects on the dam slope safety factor (FS) and can result in huge casualties to the people in the vicinity. A considerable proportion of dam slope failures around the world are triggered by water storage in reservoirs. Based on previous studies, 49% of the slope sliding events near Roosevel Lake between 1941 and 1942 were triggered by water storage and 30% were triggered by water release [
Generally, the FS of a dam slope is influenced by both the hydrostatic pressure and the pore water pressure (matrix suction if it is negative) [
Furthermore, fluctuations in the water level can induce a change in the angle of the matrix suction friction and the unit weight, subsequently inducing a change in the slope safety factor. Current slope stability analysis under seepage adopts the Fredlund and Morgenstern’s dual variables model [
In recent years, more studies have concentrated on dam slope stability during water level variations and some have considered the SWCC. Wang et al. [
Although many studies have been conducted on dam stability under water level fluctuations, the results are not sufficient to direct engineering projects because previous studies did not take into account the hysteresis of the SWCC in addition to the FS. As would be expected, the change in the free surface with water level fluctuations has a duration, which in turn causes a lag in the FS of the dam slope. Thus, the variation curve of the slope safety factor with water level fluctuations should contain a hysteresis loop. The study of the FS hysteresis loop under SWCC hysteresis is of great importance to engineering projects.
Based on an actual earth dam in China, in this study, the finite element software Geo-studio was used to analyze the FS of the dam slope during water level fluctuations. First, the soil parameters were obtained through geotechnical experiments, including direct shear tests and permeability tests. Second, a numerical model was constructed using the Geo-studio software, within which the seep/w module was used to calculate the seepage field and the slope/w module was used to calculate the FS of the dam slope. Additionally, the SWCC hysteresis and the water level fluctuation rate were taken into account in the calculation to investigate their influences on the FS of the dam slope. Finally, the FS data for the dam slope under water level drawup were used to construct prediction equations for the FS under water level drawdown, which facilitate the earth dam construction and operation for dam structures identical to that analyzed in this study.
Hanyu reservoir is located on the Hanyu River in Hu County, Shaanxi province (
The catchment area of the dam is about 11.7 km2, with an annual precipitation of approximately 591.1 mm. The precipitation is mainly concentrated in summer, so the reservoir water level is usually at a normal elevation of 568.90 m during the summer; while during the dry season it can fall to the sedimentation elevation of 559.40 m. It can be reasonably concluded that the reservoir’s water level fluctuates between 568.90 m and 559.40 m with the seasons.
As
In the case of reservoir water level fluctuations, calculating the seepage of the dam is a transient seepage problem, in which the output variables are related to time [
Genuchten et al. [
And the SWCC which depicts the relation between the volumetric water content and the pressure head is expressed as:
Then, by incorporating the SWCC and considering Darcy’s law, the following governing
From the SWCC we can derive
Here, H0(x, y) is the initial water head;
From the above, the following functional (
The solving of the seepage problem under water fluctuations is equivalent to finding the minimum value of this functional. For a given element, this functional can be decomposed as
The water heads in an element can be obtained by interpolating the water heads of all the element nodes, which is expressed as the follows:
For each nodal head h1, h2, h3, …, hn, the partial derivative of
Substituting
Letting
Similarly, for each nodal head h1, h2, h3, …, hn, deriving the partial derivative of
Letting
For each nodal head h1, h2, h3, …, hn, deriving the partial derivative of
Letting
For each nodal head h1, h2, h3, …, hn, deriving the partial derivative of
Letting
Thus, for each element, it has
Assembling the partial derivatives of the functional of all the elements with respect to
Here,
For saturated-unsaturated seepage problems,
It should be noted that, [
The traditional approach to analyzing slope stability is the limit equilibrium method (LEM), which considers the saturated soil strength. While many other methods have been developed, the LEM is still the most reliable and acceptable method in geotechnical studies. More importantly, the unsaturated soil strength has been adopted in the LEM, which has extended this method to unsaturated soils [
When calculating the safety factors,
The Morgenstern–Price method [
Another safety factor can be derived from the force equilibrium as follows:
The profile of the dam analyzed in this study is shown in
For convenience, the origin of the coordinates was set as the toe of the upstream slope. The highest water level was 28.9 m (the normal water level) and the lowest water level was 19.4 m (the sedimentation elevation). The water level rose from 19.4 m to 28.9 m, stayed at this level for 6 days, and then dropped to 19.4 m at a constant rate. The variations in the water level of the reservoir used in this study are intuitively shown in
The FEM model and the discrete grid of the dam are shown in
There were six materials involved: the dam body material, the silt in front of the dam, the drainage arris body, the loam layer, the sandy gravel layer, and the red clay layer. In contrast to saturated seepage problems, in this study, unsaturated permeating problems, which refers to a varying permeability delineated by a permeability function, were incorporated. In this study, the permeability function estimated using the Van Genuchten theory [
Materials | Kh (m/s) | Kr | Desorption SWCC | ||||
---|---|---|---|---|---|---|---|
a (kPa) | m | n | θs | θr | |||
Dam body material | 5.40E-06 | 0.20 | 869.57 | 0.51 | 2.03 | 0.520 | 0.218 |
Sludge in front of the dam | 1.52E-08 | 0.92 | 6578.95 | 0.15 | 1.17 | 0.446 | 0.000 |
Drainage arris body | 6.00E-04 | 1.00 | 1265.82 | 0.90 | 10.40 | 0.250 | 0.153 |
Loam layer | 3.30E-07 | 0.33 | 2364.07 | 0.52 | 2.06 | 0.396 | 0.131 |
Sandy gravel layer | 6.00E-04 | 1.00 | 1265.82 | 0.90 | 10.40 | 0.250 | 0.153 |
Red clay | 1.00E-08 | 1.00 | 6578.95 | 0.64 | 2.76 | 0.434 | 0.218 |
Note: Kh is the saturated permeability coefficient; Kr is the ratio of the unsaturated permeability coefficient to the saturated permeability coefficient; a is the air entry value; m is the parameter related to the residual water content; n is the parameter controlling the slope of the soil-water characteristic curve at the inflection point; and θs and θr are the saturated and residual volumetric water contents, respectively. All of the parameters in
Material | Kh (m/s) | Kr | Adsorption SWCC | ||||
---|---|---|---|---|---|---|---|
a′ (kPa) | m′ | n′ | θs | θr | |||
Dam body material | 5.40E-06 | 0.20 | 500.00 | 0.64 | 2.76 | 0.434 | 0.218 |
Note: Kh is the saturated permeability coefficient; Kr is the ratio of the unsaturated permeability coefficient to the saturated permeability coefficient; a′ is the air entry value; m′ is the parameter related to the residual water content; n′ is the parameter controlling the slope of the soil-water characteristic curve at the inflection point; and θs and θr are the saturated and residual volumetric water contents, respectively. All of the parameters in
The saturated permeability coefficients of all of the materials were determined through variable head permeability experiments, that is, the water head applied on the the specimen in the test was varied. First, the sample specimens were collected in the field using ring knives. Then, the samples were weighed using a balance to calculate the density of the specimens. Finally, the specimens were placed in the permeameter to determine the permeability coefficients (Kh) of the soils. The permeability experiment steps are shown in
The Mohr-Coulomb criterion, which has been extended to consider the influence of the matrix suction, was used to describe the shear strengths of the model materials due to its conciseness and wide acceptance. The shear strength parameter values essential in the slope stability analysis were determined through indoor direct shear experiments, and the density of each material was tested using the aforementioned ring knife experiment. The strength parameter values and the densities are presented in
Materials | γ (kN/m3) | γs (kN/m3) | C’ (kPa) | Φ’ (°) | Φb (°) |
---|---|---|---|---|---|
Dam body | 19.00 | 19.60 | 14.00 | 21.00 | 10.50 |
Sludge in front of the dam | 16.90 | 18.00 | 17.00 | 18.00 | 9.00 |
Drainage arris body | 21.60 | 22.42 | 0.00 | 35.00 | 17.50 |
Loam layer | 16.70 | 20.40 | 15.00 | 12.00 | 6.00 |
Sandy gravel layer | 21.60 | 22.00 | 0.00 | 34.00 | 17.00 |
Red clay layer | 21.60 | 21.38 | 60.00 | 16.00 | 8.00 |
To detail the free surface variation subject to the water level fluctuations, the FEM model in
Comparing
As can be seen in
Broadly utilized in the geotechnical field, the safety factor is commonly accepted as the only recognized indicator for evaluating slope stability under various conditions, including under water level fluctuations. Earth filled dams under water level fluctuation exactly describes this problem, and their FS values also fluctuate wildly.
To investigate the dam slope stability under water level drawup–drawdown cycles, The calculated seepage field was input into the slope/w tool to calculate the slope stability under the water level variations, in which the Morgernstern method was utilized. It was found that similar to the variations in the water level, the FS of the upstream dam slope fluctuated with the water level.
To clarify the reasons for the deviation in the critical drawdown ratio, we reconstructed the FEM model by removing the sludge in the reservoir and set the water level variation from the dam crest to the slope foot, while the other boundary conditions and material properties remained unchanged. The variation in the FS with the water level obtained through simulation is shown in
It should be emphasized that the FS at the beginning of the water level drawup was higher than that of at the end of water level drawdown. The pore water pressure was much lower at the beginning of the water level increase than that at the end of drawdown process due to the dissipation of the excess pore water pressure formed during drawdown continues after the drawdown stopped. This difference in the pore water pressure, which is critical to the slope stability, must cause the different FS values.
Notably, the variation in the FS during the water level drawup did not follow the path of that during the water level drawdown. In addition, it had an approximately identical minimum FS value with a negligible change, while the water level fluctuation rate varied. As a result, in engineering practice, if the minimum FS of the upstream dam slope during a water level drawdown is determined the minimum FS of the water level drawup is also determined, and vice versa. An exciting finding from
It can be seen from
As saturated soil mechanics developed, it has been broadly recognized that the matrix suction and the angel of suction friction play important roles in the soil strength [
Similarly, the minimum FS of the adsorption SWCC is about 41.4% higher than that of the desorption SWCC under water level drawdown. This could be due to the higher permeability derived from the adsorption SWCC letting the water stored in the upstream dam slope swiftly discharge, which is favorable to the dam slope’s stability. As the FS decrease in the initial stage of water level drawdown was mainly caused by the excess pore water pressure in the upstream slope, which depends on the water discharge, the difference between the FS was inevitably maximized at the critical water level, resulting in an evident difference in the minimum FS at this point. In the later stage, the excess pore water pressure dissipated gradually, thus gradually leading to a smaller difference in the FS. In summary, the desorption SWCC should be adopted in the evaluation of upstream dam slope stability under water level fluctuations because it provides a lower critical FS, which is more reliable for assessment. This is consistent with the conclusion of Al-Labban [
Generally, the dam slope stability can be determined through numerical simulation such as the LEM and FEM; however, these methods require a large amount of time. To simplify the calculation process, Gao et al. [
Taking
As
As can be seen from
Then, by substituting x = 24.9 into
Since point E is the intersection point of the FS variation curves for water level drawup and drawdown, the y coordinate of point E on the FS variation curve for water level drawdown can be obtained by substituting
In the current case study, v was equal to 1 m/d, producing an xE value of 20.56 through
Through regression analysis of the coordinates of points D, E, and F, the FS variation curve for water level drawdown for water levels of lower than 24.9 m can be derived using
By combining
To validate the accuracy of the prediction equation (
Dam slope collapse events have occurred worldwide under water level fluctuations and have caused numerous casualties to the people living nearby and thus studying dam slope stability under water level drawup and drawdown is of great importance. Based on an actual dam, the effects of the water level fluctuation rate and the hysteresis of the SWCC on the FS of the dam slope were studied via numerical simulations. Based on the calculation results, the following conclusions were drawn:
The free surface in the dam body for the desorption SWCC during water level fluctuations was higher than that for the adsorption SWCC, which would be more evident at higher water levels. The FS of the upstream dam slope under water level drawup initially decreased and then increased, with the minimum value occurring at a reservoir water level of about 36.9% of the slope height, which is referred to as the critical water level. Similarly, the FS of the upstream dam slope initially decreased and then increased, with a critical reservoir water level of around 55.4% of the slope height during water level drawdown. The FS variation curve did not follow that of the water level drawup; however, it had a minimum FS value identical to that for water level drawup. The critical water levels during both water level drawup and drawdown were not affected by the water level fluctuation rate and the SWCC hysteresis. The minimum FS of both the water level drawup and drawdown were apparently affected by the SWCC hysteresis. The minimum FS of the adsorption SWCC was higher than that of the desorption SWCC under both water level drawup and drawdown. Consequently, it is advised that the desorption SWCC be used in engineering practice for the sake of reliability. Under the circumstance of a determined FS variation curve for water level drawup, a method using a prediction equation was derived to quickly estimate the FS variation curve for water level drawdown. It has application value regarding controlling dam slope stability during water level drawdown for dam structures identical to that analyzed in this study.
This study was directed by professor Zhou Zhijun of Changan University, China, and was attributed to the cooperation of Ye Wanjun’s researching team in Xi’an University of Science and Technology, China.