:This study focuses on the phenomenon of ground instability causing mobile cranes to overturn. A mobile crane is a truck comprising machinery for hoisting equipment. It is usually supported by four outriggers, each of which is located at a different corner in order to restrict crane pitching during hoisting operations. Nevertheless, the crane may become quite unstable if the outriggers should happen to sink into the bearing ground. Many accidents have occurred due to overturning of such mobile cranes, and number of casualties reaches approximately 100 in Japan, furthermore, it is also considered that the same problem would exist in countries throughout the world.
    Main causes of the accidents were both overconfidence and mistake in the evaluation to the bearing capacity of the ground, i.e. the prevention of penetration measures was not used. Accordingly, clarification of the risk of overturning due to the ground penetration by the outriggers is needed to ensure safety. In this paper, firstly, investigations of characteristics of the mobile cranes, an analysis of the accidents and a survey of researches in the past are conducted to make sure the purpose of this study.
    Secondary, a series of bearing capacity tests were carried out on the model ground. Unsaturated soil is considered to be the normal ground condition for the setting up of mobile crane. Therefore, the tests were performed using two types of the model ground to induce different ground penetration characteristics, and these types were 1) uniform, soft loam, and 2) layered ground with a hard surface covering soft soil. The bearing capacity of layered ground with a hard surface overlaying soft ground is higher than that of uniform soft ground. However, the velocity of penetration into layered ground is higher than that of uniform soft ground. Consequently, it is important to evaluate the risk of overturning not only in terms of the bearing capacity of the ground, but also with regard to the penetration velocity caused by brittle failure of the bearing ground. The index of brittle failure for the bearing ground ( R _E ) was defined with reference to the results for the relationship between the acting pressure ( q ) and normalized ground penetration by outrigger (s / D).
    Thirdly, theoretical analysis of both the static equilibrium and the dynamic equilibrium were introduced to calculate the critical depth of outrigger ground penetration at which the crane overturns. The results showed that the critical depth due to the dynamic equilibrium was much smaller than that due to the static equilibrium, and therefore, it is necessary to consider the dynamic reaction of mobile cranes in order to prevent overturning. A series of experimental simulations using a mobile-Crane model was performed in a centrifuge in order to examine realistic overturning behavior due to ground penetration. It was found that brittle failure of the ground resulted in rapid outrigger penetration and tended to make the mobile crane overturn more easily when compared with ductile failure of the ground. It was also confirmed through back-analysis of experimental records that the mobile crane had already satisfied the kinetic conditions for overturning prior to reaching to the critical settlement of static equilibrium in cases where rapid penetration occurred. In addition, numerical simulation was carried out to examine the experimental results, and in this, the updated Lagrangian method was used to solve the equation of motion. Through study of the results of experimentation and simulation, it was found that an index of relative instability ( I _r ) -- specifically, the ratio of critical depth for kinetic equilibrium (I _k ) to that for static equilibrium (s _s ) -- had a linear relationship to the common logarithm of an index for brittle failure of bearing ground ( R _E ) as derived from the load-settlement curve for ground penetration.
    Fourthly, relationship between bearing characteristics of the ground and risk of the overturning was investigated. The supporting surface's failure risk ( r _p ) is defined as the ratio of the acting pressure ( q _a ) to the ground's yield pressure ( q _y ). The kinetic risk of overturning due to ground penetration ( r _k ) is defined as the ratio of the static risk of overturning due to ground penetration ( r _s ) to I _r . r _s is defined as the ratio of s _a to s _y , where s _a is the ground penetration induced by q _a , and s _y is the ground penetration at the static equilibrium for the mobile crane. It was made sure from the experiments that the crane overturns at r _p > r _k = 1. In particular, r _p nearly equal r _k = 1, when the outriggers penetrated quickly due to brittle failure of the ground (I _r = 0.4). It was clarified that the crane reached kinetic equilibrium soon after q _a reached q _y .
    This study concludes that mobile cranes become highly unstable as a result of rapid penetration of the outriggers, and therefore occurrence of rapid penetration must be considered in evaluation of risk. Calculation of probability for safety of overturning ( P _SS ) was performed in consideration of uncertainty existing in both r _p and r _k . By using general mean value of the coefficient of variation from N-value, P _SS > 0.977 at safety factor on bearing capacity ( F _s ) = 3 resulted whereas P _SS > 0.837 at F _s = 1.5. Accordingly, this study proposes to set the crane by F _s = 3 to prevent the overturning.