Triaxial Wetting Test on Rockfill Materials under Stress Combination Conditions of Spherical Stress p and Deviatoric Stress q

A GCTSmedium-sized triaxial apparatus is used to conduct a single-linemethod wetting test on three kinds of rockfill materials of different mother rocks such as mixture of sandstone and slate, and dolomite and granite, and the test stress conditions is the combination of spherical stress p and deviatoric stress q. ,e test results show that (1) for wetting shear strain, the effects of spherical stress p and deviatoric stress q are equivalent, and wetting shear strain and deviatoric stress q show the power function relationship preferably. (2) For wetting volumetric strain, the effect of deviatoric stress q can be neglected because it is extremely insignificant, and spherical stress p is the main influencing factor and shows the power function relationship preferably. (3) ,e wetting strains decrease significantly with the increase in initial water content and sample density generally, but the excessively high dry density will increase the wetting deformation. Also, the wetting strains will decrease with the increase in the saturated uniaxial compressive strength and average softening coefficient of the mother rock. Based on the test results, a wetting strain model is proposed for rockfill materials. ,e verification results indicate that the model satisfactorily reflects the development law of wetting deformation.


Introduction
During the impounding process of core-wall rockfill dam, the rockfill materials of upstream dam shell usually experience the transition from "dry" to "wet." erefore, materials will be softened to a certain extent.e contact parts of the particles may be fragmented, thus the internal structure of rockfill body may be adjusted.It will eventually produce significant wetting deformation which may cause local collapsibility and threatens the dam safety.
In 1972, based on some monitoring data of dam bodies, Nobari and Duncan [1] investigated the development laws of stress and strain of earth-rockfill dams in impoundment and paid close attention to the effect of water on material properties.Since then, numerous wetting studies have been conducted on various kinds of rockfill materials [2][3][4][5][6], and multiple wetting models for rockfill materials have been developed [7][8][9][10][11][12][13][14][15].e wetting test usually is adopted with two methods of "double-line" and "single-line."e previous studies show that the single-line wetting test coincides with the process of impounding and wetting preferably [12,16].In single-line wetting tests, the stress conditions are usually adopted: the combination of confining pressure σ 3 and stress level S l , and the wetting model usually expressed as a function of confining pressure σ 3 and stress level S l .Actually, the impoundment process of the dam is usually accompanied by the simultaneous changes with confining pressure σ 3 and stress level S l .As Shen analysed [17] (Figure 1), during the rise of water level, the spherical stress of upstream dam shell rockfill materials clearly decreases, the deviatoric stress slightly changes, and the stress level increases.Generally, volumetric strain ε v and shear strain ε s have closer relationships with spherical stress p and deviatoric stress q, respectively, and as the basic variables, spherical stress p and deviatoric stress q are usually adopted in some models including Cambridge elastic-plastic model and its modi ed model [18,19].On that account, it is more favourable to adopt spherical stress p and deviatoric stress q as the basic variables of wetting tests and models.
In this study, a single-line wetting test conducted by a medium-sized triaxial apparatus is introduced using three kinds of rock ll materials whose mother rocks are the mixed of sandstone and slate and dolomite and granite .Spherical stress p and deviatoric stress q are used as the stress combination.e e ects of spherical stress p and deviatoric stress q on the wetting deformation of rock ll materials are investigated.

Test Materials and Equipment.
For the mixed rock ll materials, the mother rocks consist of sandstone (∼60%) and slate (∼40%).Sandstone has a saturated uniaxial compressive strength of >60 MPa and an average softening coe cient of 0.77, and slate has a saturated uniaxial compressive strength of 30-40 MPa and an average softening coe cient of 0.67.Dolomite has a saturated uniaxial compressive strength of 45-85 MPa and an average softening coe cient of 0.67-0.87,and granite has a saturated uniaxial compressive strength of 62-94 MPa and an average softening coe cient of 0.80-0.97.e rock ll materials of natural gradation have a maximum particle size of 600 mm.According to the test methods of soils [20], the method of mixing gradation scale is used to obtain the test gradation in which the maximum particle size is 40 mm.e gradation curves of rock ll materials are shown in Figure 2, and the gradation data are shown in Table 1.e triaxial test apparatus manufactured by GCTS (USA) is used.Both the con ning and axial pressures are provided using a servo pressure controller with a pressure control precision of 0.5 kPa.A con ning pressure-volume controller is used to measure the change of water quantity in the con ning pressure cell with the measurement accuracy of 0.01 ml.
e test sample diameter is 200 mm and the height is 400 mm.

Test
Procedure.Firstly, the con ning pressure σ 3 and axial stress σ 1 based on the designed stress conditions are calculated.Secondly, the con ning pressure is applied and the designed con ning pressure stable was kept until the specimen deformation is stable under the isotropic stress.
e sample is in contact with the atmosphere during this process.irdly, the axial strain rate (0.5%/min) is adopted until the designed axial stress is reached and also the deformation stability of the specimen under the stress state needs to be achieved.Finally, the sample will gradually be wetted and saturated from bottom to top (the water head of wetting test is about 60 cm).It indicates that the wetting deformation has been completed when no continuous bubbles are observed in the drain pipe; meanwhile, the sample has been stabilized as per the standard of deformation stability.Both under the isotropic stress and wetting process, the stabilization standard of sample deformation is 0.001%/min as the average axial strain rate within 10 min.
e parameters used in this study are provided in the following formulas: spherical stress p (σ 1 + 2σ 3 )/3 and deviatoric stress q σ 1 − σ 3 , where σ 1 and σ 3 represent the axial stress and con ning pressure, respectively.Sample volumetric strain ε v (v cell + v piston )/v 0 , where v cell is the volume change of water in the con ning pressure cell, v piston is the volume of the loading piston entering the pressure cell, and v 0 is the sample volume after the isotropic stress and deformation stabilization.In this study, volume expansion is taken as negative, and volume compression is taken as 2 Advances in Materials Science and Engineering positive.Shear strain ε s ε a − ε v × 1/3, where ε a is the axial strain.

Stress Conditions of Equal p and Unequal q.
In accordance with the combination of spherical stress p and deviatoric stress q designed in the test, the stress conditions included ve spherical stress p conditions, each corresponding to 3-5 deviatoric stress q conditions.e stress conditions of the test and corresponding wetting deformation results are shown in Table 2. e dry density of the test sample is 2.18 g/cm 3 , the test materials are air-dried, and the water content of test rock ll materials whose maximum size is equal to 5 mm is 0.4%.Based on the wetting test results, the curves of wetting volumetric strain and wetting shear strain with deviatoric stress under di erent spherical stress conditions are plotted, as shown in Figures 3 and 4. As indicated by the results, the deviatoric stress exerts varying e ect on both the wetting volumetric strain and shear strain.With the increase in deviatoric stress, the wetting shear strain shows signi cant increasing trend.e wetting volumetric strain also shows an increasing trend with the increase in deviatoric stress, but the magnitude of increase is not obvious.Corresponding to the ve spherical stress conditions, the wetting shear strain increases by about 2.33, 1.0, 1.67, 1.4, and 3.44 times respectively, when deviatoric stress increased from its minimum value to the maximum value.However, the wetting volumetric strain only increases by about 0.15, 0.09, 0.08, 0.07, and 0.08 times, respectively, indicating that the e ect of deviatoric stress on wetting volumetric strain is extremely insigni cant.

Stress Conditions of Equal q and
Unequal p. Based on the above test, the test under some stress conditions is supplemented.As per the combination of spherical stress p and deviatoric stress q, the test introduced three deviatoric stress q conditions, each corresponding to 3-4 spherical stress p conditions. e stress conditions and wetting deformation results are shown in Table 3.Based on the wetting test results, the curves of wetting volumetric strain and wetting shear strain with spherical stress under deviatoric stress conditions are plotted, as shown in Figures 5 and 6.
e spherical stress shows the relatively obvious e ect on both wetting volumetric strain and shear strain.Wetting shear strain decreased with the increase in spherical stress, and the wetting volumetric strain increased with the increase in spherical stress.Corresponding to three deviatoric stress conditions, when spherical stress increased from its minimum value to the maximum value, (i.e., increased by about 2, 2, and 0.36 times, resp.), the wetting shear strain decreases by about 0.35, 0.26, and 0.14 times, and the wetting volumetric strain increased by about 0.42, 0.39, and 0.17 times, respectively.e results indicate that spherical stress exerts the same degree of e ect on the wetting volumetric strain and shear strain.Advances in Materials Science and Engineering

Initial Water Content.
To research the e ect of di erent initial water contents on wetting deformation, the water content of the test materials (maximum size <5 mm) is prepared according to particle weights, and the sample water contents are 5% and 10%.e sample dry density is 2.18 g/cm 3 .In this test, the spherical stress p is set at 2,000 kPa, and the deviatoric stress q is set at 900 kPa, 1,500 kPa, and 2,400 kPa.
e gradation and test procedure of the test materials are the same as described above.e stress conditions and wetting deformation results of the test are shown in Table 4.
Clearly, with the increase in the sample's initial water content, the wetting strains decrease signi cantly, indicating that the initial water content is an important factor in uencing the wetting deformation of materials.Under the three deviatoric stress conditions (from low to high), when the initial water content increases from 0.4% to 5%, the wetting volumetric strain decreases by about 0.51%, 0.48%, and 0.59%, and the wetting volumetric strain decreases by about 0.80%, 0.80%, and 0.77%.Under the three deviatoric stress conditions (from low to high), when the initial water content increased from 5 to 10%, the wetting shear strain decreases by about 0.12%, 0.24%, and 0.33%, and the wetting volumetric strain decreases by about 0.41%, 0.42%, and 0.50%, respectively.
e results indicate that the wetting deformation will decrease signi cantly as the water content of ne particles increases.Adopting suitable watering on materials during dam construction will not only improves the compaction of dam body, but also reduces the wetting deformation.

Sample Density.
To investigate the e ect of di erent sample densities on wetting deformation, two sample dry densities (ρ d ) are designed, that is, 2.12 g/cm 3 and 2.05 g/cm 3 .In the test, the spherical stress p is 2,000 kPa, and the deviatoric stress q is set at 900 kPa, 1,500 kPa, and 2,400 kPa.e test procedure is the same as described above,  q = 900 kPa q = 1500 kPa q = 3000 kPa and the test materials are air-dried.e stress conditions and wetting deformation results are shown in Table 5.
Clearly, with the increase in sample density, the wetting deformation decreases firstly and then slightly increased, but the wetting deformation shows decreasing trend on the whole when the sample density increases from 2.05 g/cm 3 to 2.18 g/cm 3 , in which when ρ d increases from 2.05 g/cm 3 to 2.12 g/cm 3 , the wetting volumetric strain decreases by about 24%, and the wetting shear strain decreases by 20-35%.When ρ d increases from 2.12 g/cm 3 to 2.18 g/cm 3 , the wetting volumetric strain increases by 17-22%, and the wetting shear strain increases by 3-10%.
e results indicate that, with the increase in sample density, the porosity of rockfill materials decreased, causing closer contacts among rockfill particles and reducing the wetting deformation.But when the sample density is further increased, more fragmentation of rockfill materials during the sample preparation occurred due to excessively high density resulting in the content of fine particles in the test materials, and the wetting deformation increased consequently.During the filling and compacting process of rockfill materials, it is necessary to adopt appropriate compaction parameters and compaction density so as to reduce the wetting deformation.Especially it should avoid using excessively high compaction density which will make the wetting deformation increased.

Mother Rock.
To study the effect of different the mother rock on wetting deformation, the other two kinds of materials with different mother rocks are adopted, such as dolomite and granite.For all the three materials, the gradation of rockfill materials is the same as shown in Figure 2 and also adopted with the same relative density.e sample density of dolomite and granite materials are 2.22 g/cm 3 and 2.05 g/cm 3 , respectively, and the test materials are also airdried.
In the test, the spherical stress p is 2,000 kPa, and the deviatoric stress q is set at 900 kPa, 1,500 kPa, and 2,400 kPa.
e stress conditions and wetting deformation results are shown in Table 6.
e test results show that the mother rock has significant effect on wetting deformation.For the three kinds of test materials, the saturated uniaxial compressive strength and average softening coefficient of the mother rock decrease generally from granite, and dolomite to mixed materials.And both the wetting volumetric strain and wetting shear strain increase significantly 3-5 times, respectively, than granite materials.For granite materials, the wetting volumetric strain is just about 0.4%, and the wetting shear strain is just 0.1-0.4%; it shows that there is just slight wetting deformation for the rock with high strength due to less particle breakage during wetting process.

Wetting Shear Strain Model.
As indicated by the deformation trend of wetting shear strain in Section 3, the wetting shear strain and deviatoric stress p show relatively good power function relationship; the test results and power function fitting curves are plotted, as shown in Figure 7.
To be specific, the wetting test results are shown by icons of different shapes, and the power function relationships are expressed by curves.
e relationship expression can be expressed as follows: where a and b are the fitting parameters related to the spherical stress p, q is the wetting deviatoric stress, and p a is the standard atmospheric pressure, mainly introduced for the purpose of coordinating the magnitudes of deviatoric stress and wetting strain.Parameter a mainly represents the development of the magnitude of wetting shear strain with normalized deviatoric stress q, and parameter b mainly represents the development speed of the magnitude of wetting deformation with normalized deviatoric stress q. e following values can be seen: p � 1000 kPa, ε s � 0.108 × (q/p a ) 0.857 , R 2 � 0.98 p � 1500 kPa, ε s � 0.105 × (q/p a ) 0.929 , R 2 � 0.99 p � 2000 kPa, ε s � 0.071 × (q/p a ) 1.027 , R 2 � 0.99 p � 2500 kPa, ε s � 0.050 × (q/p a ) 1.120 , R 2 � 0.99 p � 3000 kPa, ε s � 0.039 × (q/p a ) 1.177 , R 2 � 0.99 Clearly, during deviatoric stress q approached 0, the stress conditions of the sample are close to isotropic state, and the wetting shear strain approaches 0 as well.e trend indicates that under isotropic conditions, the wetting shear strain of rock ll materials is not obvious.When the deviatoric stress q increased, the corresponding con ning pressure decreased, the axial stress increased, and the sample is at relatively high stress level.At this state, the wetting shear strain increases obviously and indicates that the e ect of deviatoric stress on wetting shear strain is relatively signi cant.Both the parameters a and b are related to spherical stress p and the relationship curves of the two parameters with normalized spherical stress p are plotted, as shown in Figure 8.
e wetting parameters a and b show relatively good linear relationship with normalized spherical stress.e curves indicate that e calculation formula for wetting shear strain can be deduced from ( 1) and (2): e following values can be seen: a 0.1515 − 0.0039 × (p/p a ), R 2 0.95 b 0.6893 + 0.0166 × (p/p a ), R 2 0.99 e results indicate that the wetting shear strain is related to h, f, k, and g. e wetting shear strain parameters of the test materials are as follows: h 0.1515, f 0.0039, k 0.6893, and g 0.0166.After substituting the wetting parameters into the calculation (3), the wetting shear strain of model calculation can be obtained.Comparison with the wetting shear strain measured experimentally and the model calculated are shown in Figure 9. e model calculation and experimental results show consistent trends (the test and model data are shown in Table 7), and the shear strain model relatively satisfactorily re ect the wetting test results.

Wetting Volumetric Strain Model.
As indicated by the above results, spherical stress p is the main factor in uencing the wetting volumetric strain, and deviatoric stress q exerts an extremely insigni cant e ect on wetting volumetric strain.erefore, the e ect of deviatoric stress on wetting volumetric strain in the wetting volumetric strain model is    Advances in Materials Science and Engineering neglected.
e relationship curves between normalized spherical stress p of di erent magnitudes and wetting volumetric strain ε v are plotted, as shown in Figure 10.
Clearly, under the same spherical stress p conditions, with the increase in spherical stress p, the wetting volumetric strain ε v increases with a change law of power function as where ε v is the wetting volumetric strain, s and t are the test parameters of wetting volumetric strain, which are the same for the same material under the same test conditions and p is the wetting spherical stress.e following values can be seen: .94 e wetting volumetric strain parameters of the test materials are as follows: s 0.3249, and t 0.6287.Clearly, the model calculation and experimental results are consistent, and the experimental and model data are shown in Table 8.

Model Verification
e relationship curves of wetting shear strain ε s and normalized wetting deviatoric stress q under sample density, initial water content, and mother rock conditions are plotted, as shown in Figures 11-13, respectively.Under the three kinds of test conditions, the correspondence between wetting shear strain ε s and normalized wetting deviatoric stress q can be relatively satisfactorily simulated with a power function in each case, and the tting curves show very high correlation with the test results.
e following results can be seen: 3 , ε v 2.252 + 0.012 × (q/p a ), R 2 0.99 ρ d 2.12 g/cm 3 , ε v 1.707 + 0.009 × (q/p a ), R 2 0.92 ρ d 2.18 g/cm 3 , ε v 2.027 + 0.012 × (q/p a ), R 2 0.82 ω 0.4%, ε v 2.027 + 0.012 × (q/p a ), R 2 0.82 ω 5%, ε v 1.595 + 0.007 × (q/p a ), R 2 0.97 ω 10%, ε v 0.771 + 0.009 × (q/p a ), R 2 0.99 Mixture of sandstone and slate: ε v 1.707 + 0.009 × (q/p a ), R 2 0.92 Dolomite: ε v 1.116 + 0.009 × (q/p a ), R 2 0.99 Granite: ε v 0.375 + 0.003 × (q/p a ), R 2 0.90      Advances in Materials Science and Engineering sandstone and slate, and dolomite and granite under the stress combination conditions of spherical stress p and deviatoric stress q, and the e ects of initial water content, sample density, and mother rocks on the wetting deformation also are performed.e relationships between wetting strain characteristics and stress conditions are obtained.Based on the wetting test on rock ll materials under di erent stress conditions, a wetting strain model for rock ll materials and the related wetting parameters are proposed, and the model is veri ed with several test conditions.e veri cation results indicate that the model relatively satisfactorily re ects the development trend of wetting deformation.It should be noted that the process of the wetting deformation of rock ll materials is complex, and it is affected by numerous factors.In order to improve the accuracy of the wetting model, further studies are still needed.

Figure 3 :
Figure 3: q versus ε v curve (stress conditions of equal p and unequal q).

Figure 5 :
Figure 5: p versus ε v curve (stress conditions of equal q and unequal p).

Figure 6 :Figure 4 :
Figure 6: p versus ε s curve (stress conditions of equal q and unequal p).

Figure 8 :
Figure 8: a, b versus p/p a curve ( tting of parameters a and b).

qFigure 9 :
Figure 9: ε s versus q curve (comparison of experimental and model results).

Figure 10 :
Figure 10: p/p a versus ε v curve (comparison of experimental and model results).

Aρ d = 2 .
single-line wetting test is conducted on three kinds of rock ll materials of di erent mother rocks such as mixed of 18 g/cm 3 ρ d = 2.12 g/cm 3 ρ d = 2.05 g/cm3

Figure 11 :
Figure 11: q/p a versus ε s curve (di erent sample dry density conditions).

Figure 12 :
Figure12: q/p a versus ε s curve (di erent initial water content conditions).

Figure 14 :
Figure 14: q/p a versus ε v curve (di erent sample dry density conditions).

Figure 15 :
Figure15: q/p a versus ε v curve (di erent initial water content conditions).

Table 1 :
Grain-size distribution data of test material.

Table 2 :
Test stress conditions and test results (stress conditions of equal p and unequal q).

Table 3 :
Test stress conditions and test results (stress conditions of equal q and unequal p).

Table 5 :
Test stress conditions and test results (different dry densities).

Table 4 :
Test stress conditions and test results (different initial water contents).

Table 6 :
Test stress conditions and test results (di erent mother rocks).

Table 7 :
Test stress conditions and results (compared with test results and model results for ε s ).

Table 8 :
Test stress conditions and results (compared with test results and model results for ε v ).