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The difference in modulus makes the dif-ference in stiffness of the compound beams. In prac-tice, Young’s modulus E of soil-cement should be taken as 4 to 5 times as large as the E50 measured from the soil-cement sample. This datum still com-plies with a safety factor within 1.5 to 2.5. 3.3 Stiffness contribution coefficient after crack-ing After cracking, the compound beam becomes an elasto-plastic structure and the stiffness coefficient decreases gradually. The cracking develops with an increase of the load and with a relative slippage be-tween soil-cement and the H-beam. These changes redistribute the shear stress in the beam and reduce the stiffness of the soil-cement. Therefore, the stiff-ness contribution coefficient changes greatly after cracking whether the compound beam is a single or a different joint double H-beam. However, the stiffness of the compound beam compared to a pure H-steel beam (11.14 kN/m2) is still much larger, indicating that the adhesive stress between the soil-cement and the H-beam is not zero after cracking, or even after a failure. The compound beam can still resist the bend-ing moment in excavation. Therefore, the relative stiffness coefficient in the soil-cement should be cal-culated according to its cracking state. The interaction between soil-cement and H-steel becomes rather complicated.
So far, there are no rules available to indicate how to change a soil-cement relative stiffness contribution coefficient after crack-ing. However, according to our experimental results, the stiffness of compound beams decreases quickly after cracking. Compared with the H-steel at the same load, the stiffness of a compound beam is still 28.8% larger than for a single H-steel clay-cement com-pound beam and 46.5% larger for a single H-steel sand-cement compound beam. Therefore, the soil-cement still contributes to the stiffness of the compound beam. In Tables 3–4 the soil-cement stiff-ness contribution coefficients, after cracking, are presented. The coefficient changes from beam to beam. Particularly, the joint forms of a double H-steel compound beam have a great effect on the stiffness contribution coefficients. The rigid joint compound beam has the largest coefficient of soil-cement, indi-cating that the rigid joint can take full advantage of the soil-cement. The rigid joint at the end of the dou-ble H-beam provides the strongest constraint on the relative rotations of the double H-beams at that end. This reduces the relative slippage between the H-beam and soil-cement. Therefore, a rigid joint is the best combination and is recommended for practi-cal projects. Table 4 Bending stiffness and relative stiffness contribution coefficients after cracking Beam No. Measured stiffness (kN/m2) Coefficient αfor H-steel Coefficient βfor soil-cement 1H00 11.16 – – 1HCB 282 1.0 0.288 1HCM 35.8 – – 1HSB 765 1.0 0.465 2HCN 487 1.0 0.321 2HCH 428 1.0 0.157 2HCR 618 1.0 0.691 Note: This table does not list calculated stiffness
. 4 Conclusions The strength of soil-cement contributes a great deal to the critical loads of small H-steel compound beams. In our experiments, cracking and failure loads of sand-cement beams were 3 times as large as those of clay-cement beams. This result is caused not only by greater strength of sand-cement but also by the greater adhesive force between the H-beam and sand-cement. All compound beams show shear-com-pression failures induced by crossing inclined cracks. Failure loads are much larger than cracking loads. However, pure soil-cement beams fail due to vertical cracks, its failure load is almost the same as the cracking load. The position of a single H-steel compound beam has a great effect on the cracking load, but little effect on failure load. The effect of joint forms at one end of a double compound H-beam is of vital importance in both cracking and failure loads. The cracking load for joint form is, in decreasing order, hinge joint > rigid joint > non-joint beam and the ranking of the failure load is rigid joint > hinge joint > non-joint beam. Three joint forms have almost the same decreasing load, indicating that joint forms have little effect on the shear stress in compound beams. Cracking has a great effect on the deflection of all beams. Before cracking, beam deflections increase linearly with loads. After cracking, the deflection is nonlinear and affected by the number and position of H-beams as well as soil types in soil-cement com-pound beams. Joint forms of H-beams have little ef-fect. The stiffness contribution coefficient is a good in-dex to describe the interaction of H-beam and soil-cement. For a single H-steel compound H-beam, the stiffness contribution coefficient varies with soil type. For example, the coefficient for sand-cement is probably twice that of clay-cement.