Introduction
The drinking water reservoir created by the 62 m high Sance Rockfill Dam built in the late sixties of the last century is a key source of water supply of the Moravian-Silesian region in the Czech Republic (see Fig. 1). The monitoring results over more than 30 years showed unexpectedly large settlements and horizontal movements of the crest, which together with the steep downstream slope questioned the safety of the dam. Another problem to be solved was the unsatisfactory spillway capacity requiring reconstruction of the spillway, raising the maximum water level up to the crest and heightening the breakwater on the crest of the dam.
In order to simulate the monitoring results and understand the reasons for the unusual behavior of the dam, a two-dimensional (2D) finite element model (FEM) in the main cross section and a three-dimensional (3D) model of the left part of the dam and the valley were set up. Coupled mechanical-hydraulic-viscoplastic problems were solved using the CRISP-PATH FEM code with highly effective solver [
1]. The capabilities of the code were extended to capture saturated/unsaturated flow in porous medium and structural changes of rockfill like collapse settlement due to wetting, grain breakage and creep.
To get input data, extensive archival survey concerning geological conditions of the site, design of the dam, construction records and other archival documents was carried out and the long term monitoring records retrieved. Using these data the complete history of the dam starting from green field conditions, through embankment construction and reservoir operation, was simulated. Making use of crucial loading stages and the corresponding measurement results, the mechanical, hydraulic and rheological properties of materials forming the embankment and the bedrock were calibrated step-by-step.
The calibrated numerical models fitting the monitoring results were then applied for slope stability analysis and assessment of cracking and hydraulic fracturing hazard to the clay core of the dam. The stability analysis using the calibrated 2D model revealed that the safety of the downstream slope of the dam is on the margin, but no worsening of stability with time would occur.
The 3D model fitting the long-term measurement results and accounting for the shape of the valley, however, discovered the effect of the long term secondary creep of rockfill on the safety of the dam. Increasing settlement of the crest brings about development of tensile and distress zones along the clay core/bedrock contact, which escalates the cracking and hydraulic fracturing hazard to the impervious clay core.
This hazard was assessed for all post-construction stages of the dam, including an operational period up to 2050. No transversal cracks, but longitudinal cracks and hydraulic fracturing hazard were predicted for some critical loading stages. These results were accounted for by the rehabilitation concept and design of the dam.
Some results of the 2D analysis and description of the new double hardening creep model of rockfill are given in Ref. [
2]. The present paper, which is an extended version of the contribution [
3], focuses on the safety assessment of the dam making use of the calibrated 3D model.
Numerical codes, algorithms and constitutive models applied
The CRISP-PATH FEM code with highly effective solver [
1] and different constitutive models were used for solving the coupled mechanical-hydraulic-viscoplastic problems. The capabilities of the code were extended to capture phenomena like creep of rockfill, grain breakage, collapse settlement due to wetting, and also saturated/unsaturated flow in porous medium.
For the mechanical part of the solutions, a combined constitutive model using path dependent incrementaly-linear elasticity in the pre-peak regime and theory of plasticity in the peak regime was applied [
2,
4]. The concept of this path dependent model is based on in-situ strain path analysis of rockfill dams [
5]. Using proper switch functions and path dependent relations for calculating tangent values of the conventional deformational characteristics, the function of double hardening elastic-plastic models is approximated. In order to reduce the theoretical deficiencies of the hypoelastic variable stiffness approach used, the permissible range of deformation parameters is limited and small loading increments are applied (see Appendix A).
For the time dependent part of the solutions, the theory of multiface viscoplasticity with three viscoplastic surfaces (failure envelope and two continuously yielding surfaces with volumetric and deviatoric hardening) simulating long-term creep of rockfill was applied [
2]. The model combines Feda’s experimental relations of logarithmic creep [
6] with multiface viscoplasticity [
7]. The experimental relations determine the magnitude of the creep rate, while the direction of creep is given by the viscoplastic theory. Initiation and duration of creep depends on the position of moving deviatoric and volumetric yield surfaces (see Appendix B).
In order to simulate grain breakage, the path dependent model was extended. A stress limit for grain breakage and a new set of parameters for affected rockfill were introduced. The stress level at each integration point was continuously checked, and the new parameters were introduced as far as the stress limit was exceeded.
To model the collapse settlement of the upstream rockfill during the first reservoir filling, an improved version of the initial strain approach applied [
8]. The approach is based on the results of large-scale experiments accounting for crucial factors influencing collapse settlement of rockfill, like stress state and porosity of rockfill and water content of rock.
2D analysis in the characteristic cross section
Monitoring results, 2D FEM model and its calibration
The Sance Rockfill Dam was built on Ostravice River in the Moravian-Silesian region of former Czechoslovakia (1965-1969). The dam was founded on bedrock formed by sandstone, and the rockfill shells were constructed from quarry run sandstone (uniaxial strength 90-128 MPa, porosity 20%-23%) compacted in layers. Local silty clay was used for sloping impervious core protected by well-designed filters and transition zones from debris (see Fig. 2).
The deformation of the dam and its foundation was monitored in three cross sections by precise levelling, telescopic cross-arms and trigonometrically. The cross arms revealed sensitivity of rockfill to grain breakage under overburden load during construction. The bench marks along the crest registered collapse settlement of the upstream rockfill due to saturation at the first filling of the reservoir. Unexpectedly large settlements and horizontal movements of the crest (0.9% respectively 0.6% of the dam height) proceeding at constant rate have been observed during the last 31 years of reservoir operation.
2D FEM model aiming at fitting the field behavior was set up in the characteristic cross section (DOFβ = 35196) and the process of construction (1965-1969), first filling of the reservoir (1969-1972) and operation (1972-2003) was simulated in 46 construction layers and 11 operational phases. The total number of loading increments repeatedly solved during the calibration process was 429.
The calibration process focusing on deformation parameters consisted of the following phases: 1) setting up initial values of parameters using archival documents, 2) calibration of parameters according to the cross-arm settlement records during construction, 3) tuning for fitting the horizontal displacements due to first reservoir filling, 4) tuning all parameters after introducing creep and 5) tuning considering reservoir level fluctuation.
Grain breakage of rockfill at overburden weight exceeding 0.3-0.45 MPa was discovered as the decisive factor controlling both the time-independent and time-dependent displacements of the dam. Thus, the calibration focused on the deformational parameters of compacted rockfill and on the stress limit and deformation modulus for simulating grain breakage. The resulting set of basic parameters for the materials of the Sance Rockfill Dam is given in Table 1.
The symbols in Table 1 stand for unit weight, Poisson’s ratio, initial deformation modulus, unloading modulus, effective cohesion and friction angle and coefficients of permeability along the layer of the material and perpendicularly to it, respectively.
Using these parameters together with the rheological parameters, acceptable agreement on the calculation and measurement results was obtained (see Figs. 2 and 3). The cumulated post-construction settlement of the crest from 1972 to 2003 amounts to -282 mm according to the measurements and -286.2 mm according to the 2D model.
It should be added that the rheological parameters originally derived for rockfill of the Goldisthal Dam [
6] proved to be equally valid for rockfill of the Sance Dam, i.e. for rockfill constructed from shale and sandstone, respectively. The reason is that in both cases the upstream and downstream slopes of the dams are made of rockfill sensitive to structural changes due to grain breakage.
Stability analysis using strength reduction method
The calibrated 2D model and the computational phase corresponding to the present time (2003), which was influenced by structural changes of rockfill during dam construction, reservoir filling and operation, applied for the stability analysis. Cohesion reduced to 1 kPa was introduced to the non-cohesive materials, which made it possible to compare the safety factors calculated by the model with those according to the Czech Standard.
Three standard loading cases with maximum operational water level and different fluctuation and three extreme loading cases with extremely high water level (up to the crest of the dam) and rapid drawdown were considered.
The analysis discovered four possible slope failure mechanisms shown in Fig. 4. Slip surfaces smp1 and smp2 corresponding to the standard loading cases cross only non-cohesive materials and thus meet the requirements of the Czech Standard CSN 736850: FS= 1.25>[1.2]. The maximum rapid drawdown corresponding to the extreme cases resulted in a longitudinal crack along the crest and an imperfect slip surface labeled smp3, which does not cross the surface. This is due to flatness of the bottom part of the upstream slope preventing slip. At higher strength reduction, however, a slip surface labeled smp4 develops which crosses the clay core, and the safety factor does not satisfy the Standard: FS= 1.4<[1.5].
Similar analysis performed for the computational phase in 2050, when additional settlement of the crest due to creep of rockfill occurs, producing the same safety factors. Thus, according to the 2D model, no worsening of the safety of the dam due to long term creep of rockfill is predicted.
3D model for assessing cracking and hydraulic fracturing hazard to clay core
3D model and its calibration
While no stress changes with time occur in the main cross section of the dam, this is not true for the left side and right side abutments, where the clay core is connected with the bedrock. Since no displacements take place along this contact, increasing settlement of the central part of the dam induces differential settlement along the crest. This results in development of compressive zones in the central part of the clay core and tensile zones at the abutments. Distress zones develop along the crest, which raises the cracking and hydraulic fracturing hazard to the clay core [
9].
In order to assess this hazard and secure the long-term safety of the dam, a 3D model encompassing the left side part of the dam and the valley was set up. While the shape of the dam and the valley was generally simplified, the spatial configuration and shape of the clay core and the dam/bedrock contact was carefully modeled to fit the reality (see Fig. 7). The size of the model is 600 m×200 m×158.30 m, the number of degrees of freedom: DOFβ=β368149.
The mechanical and rheological parameters calibrated by the 2D model were used in the 3D model, practically without further calibration. Also, new boreholes deepened from the crest and laboratory tests of the extracted soil samples allowed verifying the properties of the upper part of the clay core. The higher stiffness of the clay core in comparison with the figures of archival documents discovered by the calibration process was approved. The calibrated oedometer modulus is Ep/β =β6/0.534β=β11.24 MPa (ββ=βν-ν2/(1-ν), ν is Poisson’s ratio), while the average oedometer modulus according to the new tests is 10.6 MPa.
Once again, the whole process of the dam construction, reservoir filling and operation was performed using the 3D model and the results were compared with the monitoring results in 18 measuring points.
The horizontal and vertical displacements measured and calculated in a measuring point on the downstream side of the crest are shown in Fig. 5.
Assessment of cracking and hydraulic fracturing hazard
The cracking and hydraulic fracturing hazard was estimated for critical loading stages produced by long-term creep up to 2050, extremely high water level reaching the crest of the dam and flooding of the bottom part of the downstream rockfill. The maximum displacement components at the crest cumulated for the whole period from 1969 to 2050 amount to -250 mm in the horizontal direction along the crest, -828 mm in the vertical direction and 554 mm in the horizontal direction perpendicular to the crest. The clay core is required to accommodate these deformations without loss of integrity due to cracking or hydraulic fracturing.
Cracking of the crest in the transversal direction occurs if the longitudinal component of the current tensile strain or tensile stress on the crest exceeds the limit values of the compacted clay not at local points, but in a continuous narrow zone crossing the surface (dry cracks). Experimental values of tensile strength of the clay and the corresponding limit strains have not been measured in the laboratory yet. In the present work an estimated value of tensile strength 30 kPa was considered.
In Fig. 6 the development of the horizontal strain and stress components in the longitudinal section of the clay core is presented from 2003 to 2050. The maximum tensile strain on the crest is 0.3% in 2003 and 0.45% in 2050. Neither the absolute value nor the strain rate indicates cracking [
9]. This corresponds with the development of tensile stresses on the crest, which do not exceed the tensile strength of 30 kPa.
Concerning the cracking hazard in the longitudinal direction, a critical loading stage with rapid water level raised from the operational level 502 m up to crest level 508 m El. was considered, which causes collapse settlement of the upper part of the upstream rockfill. This induces a longitudinal crack along the crest as shown in Fig. 7. The long term monitoring results showed sensitivity of the crest to longitudinal cracking as well. In 1976, a longitudinal crack (length 9 m) occurred on the crest near to the left abutment. On other hand, long-term water level fluctuation during reservoir operation causes step-by-step saturation of rockfill, which reduces the longitudinal cracking hazard to the crest.
According to the criterion formulated in total stresses, hydraulic fracturing of compacted clay occurs if the reservoir water pressure along the upstream side of the clay core exceeds the minimum total stress component in the clay core enlarged by the tensile strength of the clay. This condition is expressed by the safety factor against hydraulic fracturing s4β= (σ3 + |σt|)/pv£ 1. Here, the symbols stand for minimum total principal stress, tensile strength and potential water pressure in a given point. The latter is determined by the difference between the elevation of the reservoir water level and the position of the point. Hydraulic fracturing of the clay core occurs if this condition is fulfilled for a zone forming a continuous path from the upstream side to the downstream side of the core.
The maximum water level reaching the crest combined with long-term creep up to 2050 was shown to be the critical loading stage for hydraulic fracturing. The zones with s4£ 1 in the cross section of the clay core are shown in Fig. 8. This cross section is at a distance of 135 m from the central cross section of the dam. In 2003, the zones do not connect the upstream and downstream sides of the core yet, but in 2050 such a continuous flow path comes into being, thus, according to the model hydraulic fracturing occurs. The length of the affected zone at the left abutment is 25 m.
The hydraulic fractures controlled by the minimum total stress component used to have a direction parallel with the crest, which is less dangerous with regards to the piping hazard. Furthermore, a well-designed downstream filter with specific grain size distribution protects the core against piping.
Up to now the measurement of longitudinal displacements has not been so frequent and as reliable as the remaining quantities measured on the dam. As a part of the reconstruction, extensometers will be installed in the upper part of the clay core in order to monitor the longitudinal displacements close to the left side and right side abutments of the dam.
Using the 3D model and strength reduction method, and assuming the standard loading case with operational water level, a similar stability analysis was carried out as described above using a 2D model. A similar slip surface and the same safety factor FSβ=β1.4, which do not satisfy the Czech Standard, were obtained (see Fig. 9). As part of the rehabilitation a bench will be placed on the downstream side of the dam. The bench influences the position and shape of the slip surface in such a way that the new safety factor accommodates the Standard.
Conclusions
1) Unfavourable deformational trends with constant creep rate, stability of steep downstream slope and unsatisfactory spillway capacity required rehabilitation of the 62 m high Sance Rockfill Dam built in the late sixties of the last century.
2) To understand the behavior and predict future performance, 2D and 3D numerical models, well fitting the observed construction and post-construction deformations of the dam, were set up and the calibrated models were used for slope stability analysis and assessment of cracking and hydraulic fracturing hazard to the clay core.
3) The lifetime of the dam starting from green field condition up to present time (2003) was simulated and further performance up to 2050 predicted. Coupled mechanical-hydraulic-viscoplastic problems were solved with an account for unsaturated flow in the clay core and structural changes of rockfill due to grain breakage, collapse settlement due to wetting and creep.
4) Making use of crucial loading stages and the corresponding measurement results, the mechanical, hydraulic and rheological properties of materials forming the embankment and the bedrock were calibrated step-by-step.
5) The analysis showed that the observed performance of the dam is due to structural changes of rockfill caused by the quality of sandstone and degree of compaction of the fill, which do not match exactly with a dam of this height.
6) According to the 2D stability analysis the safety of the downstream slope is on the margin, but no worsening with time due to creep of rockfill is expected.
7) An account of the 3D model for the valley’s shape discovered, however, unfavourable influence of the long-term creep of rockfill escalating differential settlements of the crest and inducing tensile and distress zones in the clay core.
8) No transversal cracking hazard to the clay core was predicted and the longitudinal cracking hazard is limited to a hypothetic loading case, when rapid water level rises and collapse settlement of the unsaturated rockfill occurs due to wetting.
9) No hydraulic fracturing hazard to the clay core was detected at the present time (2003), but according to the model, hydraulic fracturing in the upper part of the clay core could occur in the future (2050). In such a case the downstream filter with specific grain size distribution is designed to protect the clay core against piping.
10) As a part of the rehabilitation of the dam, extensometers in the clay core along the crest will be installed and the longitudinal displacements of the dam carefully monitored. In order to improve the stability conditions of the downstream slope, a supporting bench will be placed on the downstream side of the dam.
Higher Education Press and Springer-Verlag Berlin Heidelberg
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