Resilient Modulus Prediction Model for Fine-Grained Soils in Ohio: Preliminary Study

Transcription

1 Resilient Moulus Preiction Moel for Fine-Graine Soils in Ohio: Preliminary Stuy by Teruhisa Masaa: Associate Professor, Civil Engineering Department Ohio University, Athens, OH 4570 Tel: (740) Fax: (740) Sha M. Sargan: Yun Liao: Russ Professor, Civil Engineering Department Ohio University, Athens, OH 4570 Tel: (740) Fax: (740) Grauate Research Assistant, Civil Engineering Department Ohio University, Athens, OH 4570 Tel: (740) Fax: (740) Wor Count Total 5,067 (Abstract 65; Text,90; Tables,500; an Figures,500) Date of Submission: April 7, 006

2 ABSTRACT Resilient moulus of subgrae soil is one of the key material properties that are require for the mechanistic-empirical esign/analysis of multi-layere flexible pavement system. A stuy was initiate at Ohio University to examine the resilient moulus of fine-graine subgrae soils commonly foun in Ohio. The current stanar metho was first examine to unerstan the stress conitions the test proceure inuces on the soil specimen. Then, five stress moels were briefly escribe an evaluate in light of recent laboratory test results on A-4 soil samples recovere from a highway project site in the northeastern Ohio. The outcome of the initial stuy inicate the hyperbolic moel may be the most promising moel. Preliminary correlations were establishe between the hyperbolic moel constants an the test specimens basic properties. Aitional test results will be neee to evelop a resilient moulus preiction moel for the A-4 Ohio soils at higher statistical confience levels. Also, the moeling efforts shoul exten to aress the other subgrae soil types commonly foun in Ohio.

3 INTRODUCTION Resilient moulus of subgrae soil is one of the key material properties that are require for the mechanistic-empirical (M-E) esign/analysis of multi-layere flexible pavement system. At the highest level (Level ), the resilient moulus of the subgrae soil must be measure in the laboratory, using the representative soil samples recovere from the project site. The current stanar laboratory practice is to perform the resilient moulus test accoring to the proceures escribe in the AASHTO T-94 or SHRP P-46 test protocol. The test set-up use in the resilient moulus (RM) test is basically the same as that for the conventional triaxial compression (CTC) test. A cylinrical soil specimen, encase in a flexible membrane, is subjecte to an axial loaing applie by a piston, while the all-aroun chamber pressure acts on it. The only ifference between the CTC an RM tests is that the axial loa is applie as a series of -Hz pulse loa uring RM test while it is increase monotonically uring the CTC test. In the RM test, miniature LVDT s mounte near the test specimen measure the average recoverable axial strain. The resilient moulus (M R ) is calculate from the test measurements by: M R = σ /ε r () where σ = eviatoric stress; an ε r = recoverable axial strain. Most fine-graine soils exhibit a concave-upwar bilinear response curve, when their RM test ata are plotte in terms of M R versus σ. Breakpoint resilient moulus (M Ri ) is the resilient moulus locate at the point where two linear curves meet. Principal stresses involve in these test methos are: σ = σ + σ c ; an σ = σ = σ c ( & ) where σ = major principal stress; σ = eviatoric stress (= axial stress applie by the piston); σ c = chamber pressure (or confining stress); an σ or σ = minor principal stress. The stress path followe uring these tests can be represente by the parameters p an q: p = ( σ + σ ) ; an = ( σ σ ) q (4& 5) Octaheral shear stress (τ ) an normal stress (σ ) are efine as: τ = ( σ σ ) + ( σ σ ) + ( σ σ ) ; an σ = ( σ + σ + σ ) Applications of Equations an to Equations 4 through 7 result in: (6 & 7) σ = p + σ = q + σ ; an σ q = (4 & 5 )

4 τ = ( σ ) + ( σ ) = σ ; an σ ( σ + σ ) = c (6 & 7 ) Table lists the four stress parameter (p, q, τ, σ ) values calculate for the loa sequences the soil specimen goes through uring the stanar RM test for fine-graine soil specimens. The chamber pressure is zero uring Loa Sequence Nos. through 5. So, uring these loa sequences, test results reflect the effect of the eviatoric stress only. TABLE σ c (psi) Loa Sequence Applie During RM Test σ No. of p (psi) Cycles (psi) Seq. No. q (psi) τ σ (psi) (psi) 6.0 * Up to [Note] * Initial conitioning loa cycles. Figure shows the p-q iagram for the RM test. During the five loa sequences uner each chamber pressure level, both p an q values are increase by 4 psi. The stress path makes a 45 angle with the p-axis to make sure that the stress state oes not approach the yiel surface. Figure shows the changes in the aheral stresses uring the RM test. The aheral shear stress (τ ) goes through the same cycle three times, with its value changing between 0.94 an 4.7 psi. The Octaheral normal stress (σ ) goes through a graual stepwise ecline. The ratio between the Octaheral stresses (σ /τ ) remains a constant (at about 0.7) uring Loa Sequence Nos. through 5, because the chamber pressure is zero. LABORATORY TEST PROGRAM In the current stuy, a laboratory test program was initiate to try to measure accoring to the SHRP P-46 test protocol the resilient moulus (M R ) of six subgrae soil samples taken from a project site on Rt. 0 in Wayne County (near Akron), Ohio. Table summarizes the basic properties of these soil samples. Tables an 4 present the test ata. Each soil sample was rie, pulverize, an then recompacte insie a split mol, using the static compaction metho, to prouce the test specimen. 4

5 q (psi) p (psi) FIGURE p-q Diagram (Stress Path) of RM Test Octaheral Stress (psi) 8 4 Normal Shear Loa Sequence No. FIGURE Octaheral Stress Changes During RM Test TABLE Basic Properties of Subgrae Soil Samples Property Sample Sample Sample Sample 4 Sample 5 Sample 6 Location West Boun Sta East Boun Sta West Boun Sta East Boun Sta East Boun Sta East Boun Sta S00 (%) LL (%) PI (%) OMC (%) γ -max (pcf) Type A-4 A-4 A-4 A-4 A-4 A-4 5

6 TABLE RM Test Results for Sample Nos. an Sample Sample (Test A) Sample (Test B) w =.%; γ = 5.0 pcf w =.%; γ = 5.4 pcf w =.%; γ = 6.7 pcf σ c (psi) σ (psi) ε r (%) M R (ksi) σ (psi) ε r (%) M R (ksi) σ (psi) ε r (%) M R (ksi) TABLE 4 RM Test Results for Sample Nos. an 5 Sample (Test A) Sample (Test B) Sample 5 σ c w = 5.%; γ = 9.8 pcf w =.%; γ =.9 pcf w =.5%; γ =.7 pcf (psi) σ (psi) ε r (%) M R (ksi) σ (psi) ε r (%) M R (ksi) σ (psi) ε r (%) M R (ksi) Figures through 5 were prouce base on the ata from Sample (Test A). Figure shows fluctuations of the resilient moulus uring the entire loa sequences. The bilinear nature of the relationship between the resilient moulus an eviatoric stress is appearing three times. Figure 4 plots the resilient moulus against the eviatoric stress. The bilinear tren is shown clearly in the plot. Figure 5 examines the relationship between the resilient moulus an the Octaheral stresses. Here, the plot correlates the resilient moulus an the Octaheral stress ratio (σ /τ ) in the logarithmic scale. Despite some scattering, the emerging relationship appears to be nearly linear. 6

7 Resilient Moulus (ksi) Loa Sequence No. FIGURE Fluctuations of M R During RM Test Resilient Moulus (ksi) Deviatoric Stress (psi) FIGURE 4 Plot of Resilient Moulus vs. Deviatoric Stress 00 Resilient Moulus (ksi) 0 0 Octaheral Stress Ratio (σ/τ) FIGURE 5 Plot of Log (M R ) vs. Log (σ /τ ) 7

8 MODELING OF RM BEHAVIORS OF FINE-GRAINED SOILS At Level or of the M-E esign proceure, a preiction moel may be use to estimate the resilient moulus of subgrae soil below Level. Thus, it is important that a reliable moel is ientifie. There have been a number of moels propose by other researchers for estimating the resilient moulus of fine-graine soils. The most basic moel use in conjunction with the RM testing of fine-graine soils is a power moel: M R = K(σ ) n where K, n = moel constants (8) However, the power moel cannot represent the bilinear relationship between the resilient moulus an eviatoric stress. The n value of 0 leas to the 0-th orer relationship (M R = K). A small negative value for n leas to a slightly nonlinear concave upwar curve with no apparent break point. A bilinear moel has been evelope by Dingqing an Selig (994) to embrace the concept of the breakpoint resilient moulus: M R = K + K σ for σ < σ i (9.a) = K + K 4 σ for σ > σ i (9.b) where K, K, K, an K 4 = moel constants (K an K always positive; K always negative; K 4 occasionally negative); an σ i = breakpoint eviator stress. A hyperbolic moel was propose by Drumm et al. (99) for estimating the resilient moulus of fine-graine soils foun in Tennessee: M R K + nσ = where K, n = moel constants (0) σ A semi-log moel was propose by Frelun et al. (977), who examine the resilient responses of a glacial till material: Log (M R ) = K n σ where K, n = moel constants () A log-log moel is presente in the SHRP P-46 test protocol as a means to plot the test ata. This moel, given by Eq., is mathematically almost equivalent to the power moel. Log (M R ) = K + n Log (σ ) where K, n = moel constants () With the fining mae in the previous section, an aitional moel (i.e., Octaheral moel) may be worthy of evaluation: Log σ ( M ) = + R K n Log τ where K, n = moel constants () 8

9 Unlike all of the above moels, the Octaheral moel incorporates the effects of both eviatoric stress an confining stress. When the confining stress is set equal to zero, Eq. cannot express M R as a function of σ. In orer to overcome this problem, Eq. is moifie to: Log ( M ) R σ K + n Log = ( τ ) where K, n = moel constants ( ) EVALUATION OF MODELS Table 5 summarizes the results of the ata analysis performe for each caniate moel, which inclue moel constant values an the coefficient of etermination (r ) value. Comparing the overall average r values, the hyperbolic moel was consiere to be the best moel, followe by the Octaheral stress moel an the bilinear moel. The semi-log moel was the least successful in fitting to the experimental RM test ata. For the bilinear moel, the breakpoint resilient moulus (M Ri ) was etermine to be.78 ksi (Sample ), 8. ksi (Sample A), 4.80 ksi (Sample B),.7 ksi (Sample A), 6.5 ksi (Sample B), an 4.87 ksi (Sample 5). The breakpoint eviatoric stress (σ i ) was.9 psi (Sample ), 6.8 psi (Sample A), 5.00 psi (Sample B), 4.45 psi (Sample A), 8.4 psi (Sample B), an 5.05 psi (Sample 5). The axial strain corresponing to the breakpoint (ε i ) was 0.06% (Sample ), 0.07% (Sample A), 0.0% (Sample B), 0.% (Samples A, B), an 0.0% (Sample 5). TABLE 5 Evaluation of Stress Moels Power Moel Eq. 8 Bilinear Moel Eq. 9 K n r K K (r ) K K 4 (r ) Sample Sample (A) Sample (B) Sample (A) Sample (B) Sample Average Hyperbolic Moel Eq. 0 Semi-Log Moel - Eq. Octaheral Moel - Eq. K n r K n r K n r Sample Sample (A) Sample (B) Sample (A) Sample (B) Sample Average

10 FURTHER DISCUSSIONS Table 6 lists the basic physical properties an the hyperbolic moel constants for the test specimens. Statistical analysis inicate that the hyperbolic moel constants (K, n) are both correlate strongly to the moisture content with relative to the OMC (= w OMC), as seen in Figure 6, an moerately correlate to the percent fines (S00) an relative compaction (R). A multi-variable linear regression analysis prouce the following outcome for the A-4 soils: K = (PI) (S00).9(w OMC) +.(R) with r.00 n = (PI) 0.00(S00).8(w OMC) + 0.9(R) with r.00 M Ri = (PI) (S00).65(w OMC) (R) with r.00 TABLE 6 List of Test Specimen Properties an Hyperbolic Moel Constants Test Specimen Property Data Hyperbolic Moel PI (%) S00 (%) w OMC (%) R (%) K n Sample Sample (A) Sample (B) Sample (A) Sample Values of K an n K n w - OMC (%) FIGURE 6 Plot of K an n Values vs. (w OMC) CLOSING REMARKS Resilient moulus of subgrae soil is one of the key material properties that are require for the mechanistic-empirical esign/analysis of multi-layere flexible pavement system. A stuy was initiate at Ohio University to examine the resilient moulus of fine-graine subgrae soils commonly foun in Ohio. The current stanar metho was first examine to unerstan the stress conitions the test metho inuces on the soil specimen. The examination showe the cyclic nature of the stress path an the Octaheral stresses create by the stanar test metho. 0

11 Analysis of the typical RM test results on a A-4 soil specimen confirme the bilinear relationship between the resilient moulus an the eviatoric stress. This bilinear relationship emerges because the soil specimen is somewhat overconsoliate uring the specimen preparation stage (by the static compaction metho). The maximum compressive loa applie to the soil layers uring the specimen compaction closely matche the breakpoint eviatoric stress (σ i ) for each test specimen. This shows that the breakpoint eviatoric stress (σ i ) is basically the preconsoliation pressure. The analysis also reveale a possible linear relationship between the resilient moulus an the Octaheral stress ratio (σ /τ ) in the logarithmic scale. Five stress moels were briefly iscusse an evaluate in light of recent laboratory test results. The outcome of the initial stuy inicate that the hyperbolic moel may be the most promising moel. This implies that the eviatoric stress alone can aequately express the resilient moulus of the fine-graine soils. It is further note here that the Octaheral stress moel, Eq., is similar to the universal moel recently recommene by AASHTO (Yan an Quintus, 00): M R k θ τ = k pa p a p a + k (4) The constants in the hyperbolic moel appear to be strongly influence by the basic soil properties. Preliminary correlations were establishe between the hyperbolic moel constants an the test specimens basic properties (ex. S00, PI, w, OMC, γ, γ -max, ). Also, the initial relation between the breakpoint resilient moulus an the specimen properties was also obtaine. Aitional test results will be neee to evelop a resilient moulus preiction moel for the A-4 Ohio soils at higher statistical confience levels. Also, the moeling efforts shoul exten to aress the other subgrae soil types (A-6, A-7) commonly foun in Ohio. REFERENCES. Dingqing, L., an Selig, E. T. Resilient Moulus for Fine-Graine Subgrae Soils. Journal of Geotechnical Engineering, Vol. 0, No. 6, ASCE, 994, pp Drumm, E. C., Boateng-Poku, Y., an Pierce, T. J. Estimation of Subgrae Resilient Moulus from Stanar Tests. Journal of Geotechnical Engineering, Vol. 6, No. 5, ASCE, 99, pp Frelun, D. G., Bergan, A. T., an Sauer, E. K. Relation Between Resilient Moulus an Stress Conitions for Cohesive Subgrae Soils. Transportation Research Recor, No. 64, 977, pp Yan, A., an Quintus, H. L. V. Stuy of LTPP Laboratory Resilient Moulus Test Data an Response Characteristics: Final Report. Publication No. FHWA-RD-0-05, U.S. Dept. of Transportation, Feeral Highway Aministration, McLean, VA, 00, 7 pp.